S3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from dotenv import load_dotenv\n",
    "load_dotenv(dotenv_path='.env')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The elements of statistical learning - https://hastie.su.domains/ElemStatLearn/\n",
    "- Weather Dataset - https://www.kaggle.com/datasets/guillemservera/global-daily-climate-data\n",
    "- DEEP LEARNING: HTML from here - https://atcold.github.io/NYU-DLSP21/\n",
    "- Speech Recognition and Graph Transformer Network I - https://github.com/Atcold/NYU-DLSP21/blob/master/docs/en/week11/11-1.md"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from langchain.document_loaders import (\n",
    "    UnstructuredCSVLoader,\n",
    "    UnstructuredHTMLLoader,\n",
    "    UnstructuredImageLoader,\n",
    "    PythonLoader,\n",
    "    PyPDFLoader,\n",
    "    JSONLoader,\n",
    ")\n",
    "\n",
    "from langchain.document_loaders.csv_loader import CSVLoader\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CSV Loader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "csv_weather_cities_location = \"./csv_data/cities.csv\"\n",
    "csv_weather_countries_location = \"./csv_data/countries.csv\"\n",
    "\n",
    "csv_weather_loader = CSVLoader(csv_weather_cities_location)\n",
    "weather_data = csv_weather_loader.load()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "station_id: 41515\n",
      "city_name: Asadabad\n",
      "country: Afghanistan\n",
      "state: Kunar\n",
      "iso2: AF\n",
      "iso3: AFG\n",
      "latitude: 34.8660000397\n",
      "longitude: 71.1500045859\n"
     ]
    }
   ],
   "source": [
    "print(weather_data[0].page_content)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>station_id</th>\n",
       "      <th>city_name</th>\n",
       "      <th>country</th>\n",
       "      <th>state</th>\n",
       "      <th>iso2</th>\n",
       "      <th>iso3</th>\n",
       "      <th>latitude</th>\n",
       "      <th>longitude</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>41515</td>\n",
       "      <td>Asadabad</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Kunar</td>\n",
       "      <td>AF</td>\n",
       "      <td>AFG</td>\n",
       "      <td>34.866000</td>\n",
       "      <td>71.150005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>38954</td>\n",
       "      <td>Fayzabad</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Badakhshan</td>\n",
       "      <td>AF</td>\n",
       "      <td>AFG</td>\n",
       "      <td>37.129761</td>\n",
       "      <td>70.579247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>41560</td>\n",
       "      <td>Jalalabad</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Nangarhar</td>\n",
       "      <td>AF</td>\n",
       "      <td>AFG</td>\n",
       "      <td>34.441527</td>\n",
       "      <td>70.436103</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>38947</td>\n",
       "      <td>Kunduz</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Kunduz</td>\n",
       "      <td>AF</td>\n",
       "      <td>AFG</td>\n",
       "      <td>36.727951</td>\n",
       "      <td>68.872530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>38987</td>\n",
       "      <td>Qala i Naw</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>Badghis</td>\n",
       "      <td>AF</td>\n",
       "      <td>AFG</td>\n",
       "      <td>34.983000</td>\n",
       "      <td>63.133300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1240</th>\n",
       "      <td>67475</td>\n",
       "      <td>Kasama</td>\n",
       "      <td>Zambia</td>\n",
       "      <td>Northern</td>\n",
       "      <td>ZM</td>\n",
       "      <td>ZMB</td>\n",
       "      <td>-10.199598</td>\n",
       "      <td>31.179947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1241</th>\n",
       "      <td>68030</td>\n",
       "      <td>Livingstone</td>\n",
       "      <td>Zambia</td>\n",
       "      <td>Southern</td>\n",
       "      <td>ZM</td>\n",
       "      <td>ZMB</td>\n",
       "      <td>-17.860009</td>\n",
       "      <td>25.860013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1242</th>\n",
       "      <td>67633</td>\n",
       "      <td>Mongu</td>\n",
       "      <td>Zambia</td>\n",
       "      <td>Western</td>\n",
       "      <td>ZM</td>\n",
       "      <td>ZMB</td>\n",
       "      <td>-15.279598</td>\n",
       "      <td>23.120025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1243</th>\n",
       "      <td>67775</td>\n",
       "      <td>Harare</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>Harare</td>\n",
       "      <td>ZW</td>\n",
       "      <td>ZWE</td>\n",
       "      <td>-17.817790</td>\n",
       "      <td>31.044709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1244</th>\n",
       "      <td>67975</td>\n",
       "      <td>Masvingo</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>Masvingo</td>\n",
       "      <td>ZW</td>\n",
       "      <td>ZWE</td>\n",
       "      <td>-20.059617</td>\n",
       "      <td>30.820020</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1245 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     station_id    city_name      country       state iso2 iso3   latitude  \\\n",
       "0         41515     Asadabad  Afghanistan       Kunar   AF  AFG  34.866000   \n",
       "1         38954     Fayzabad  Afghanistan  Badakhshan   AF  AFG  37.129761   \n",
       "2         41560    Jalalabad  Afghanistan   Nangarhar   AF  AFG  34.441527   \n",
       "3         38947       Kunduz  Afghanistan      Kunduz   AF  AFG  36.727951   \n",
       "4         38987   Qala i Naw  Afghanistan     Badghis   AF  AFG  34.983000   \n",
       "...         ...          ...          ...         ...  ...  ...        ...   \n",
       "1240      67475       Kasama       Zambia    Northern   ZM  ZMB -10.199598   \n",
       "1241      68030  Livingstone       Zambia    Southern   ZM  ZMB -17.860009   \n",
       "1242      67633        Mongu       Zambia     Western   ZM  ZMB -15.279598   \n",
       "1243      67775       Harare     Zimbabwe      Harare   ZW  ZWE -17.817790   \n",
       "1244      67975     Masvingo     Zimbabwe    Masvingo   ZW  ZWE -20.059617   \n",
       "\n",
       "      longitude  \n",
       "0     71.150005  \n",
       "1     70.579247  \n",
       "2     70.436103  \n",
       "3     68.872530  \n",
       "4     63.133300  \n",
       "...         ...  \n",
       "1240  31.179947  \n",
       "1241  25.860013  \n",
       "1242  23.120025  \n",
       "1243  31.044709  \n",
       "1244  30.820020  \n",
       "\n",
       "[1245 rows x 8 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(csv_weather_cities_location)\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "file_path = \"./mixed_data/ESLII_print12_toc (1).pdf\"\n",
    "\n",
    "sl_loader = PyPDFLoader(file_path)\n",
    "sl_data = sl_loader.load_and_split()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "page_content='Springer Series in Statistics\\nTrevor Hastie\\nRobert TibshiraniJerome FriedmanSpringer Series in Statistics\\nThe Elements of\\nStatistical Learning\\nData Mining, Inference, and Prediction\\nThe Elements of Statistical LearningDuring the past decade there has been an explosion in computation and information tech-\\nnology. With it have come vast amounts of data in a variety of fields such as medicine, biolo-gy, finance, and marketing. The challenge of understanding these data has led to the devel-opment of new tools in the field of statistics, and spawned new areas such as data mining,machine learning, and bioinformatics. Many of these tools have common underpinnings butare often expressed with different terminology. This book describes the important ideas inthese areas in a common conceptual framework. While the approach is statistical, theemphasis is on concepts rather than mathematics. Many examples are given, with a liberaluse of color graphics. It should be a valuable resource for statisticians and anyone interestedin data mining in science or industry. The book’s coverage is broad, from supervised learning(prediction) to unsupervised learning. The many topics include neural networks, supportvector machines, classification trees and boosting—the first comprehensive treatment of thistopic in any book.\\nThis major new edition features many topics not covered in the original, including graphical\\nmodels, random forests, ensemble methods, least angle regression & path algorithms for thelasso, non-negative matrix factorization, and spectral clustering. There is also a chapter onmethods for “wide” data (p bigger than n), including multiple testing and false discovery rates.\\nTrevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at\\nStanford University. They are prominent researchers in this area: Hastie and Tibshiranideveloped generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS andinvented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of thevery successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.\\n›springer.comSTATISTICS\\nisbn 978-0-387-84857-0Trevor Hastie • Robert Tibshirani • Jerome Friedman\\nThe Elements of Statictical Learning\\nHastie • Tibshirani • Friedman\\nSecond Edition' metadata={'source': './mixed_data/ESLII_print12_toc (1).pdf', 'page': 0}\n",
      "885\n"
     ]
    }
   ],
   "source": [
    "print(sl_data[0])\n",
    "print(len(sl_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from langchain.text_splitter import (\n",
    "    CharacterTextSplitter,\n",
    "    RecursiveCharacterTextSplitter,\n",
    ")\n",
    "\n",
    "splitter1 = CharacterTextSplitter(\n",
    "    chunk_size=1000,\n",
    "    chunk_overlap=100,\n",
    ")\n",
    "\n",
    "splitter2 = RecursiveCharacterTextSplitter(\n",
    "    chunk_size=1000,\n",
    "    chunk_overlap=0\n",
    ")\n",
    "\n",
    "sl_data1 = sl_loader.load_and_split(splitter1)\n",
    "sl_data2 = sl_loader.load_and_split(splitter2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "764 2474\n",
      "2252 305\n"
     ]
    }
   ],
   "source": [
    "print(len(sl_data1), len(sl_data1[0].page_content))\n",
    "\n",
    "print(len(sl_data2), len(sl_data2[0].page_content))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 3/3 [00:03<00:00,  1.19s/it]\n"
     ]
    }
   ],
   "source": [
    "from langchain.document_loaders import DirectoryLoader\n",
    "\n",
    "mixed_loader = DirectoryLoader(\n",
    "    path=\"./mixed_data\",\n",
    "    use_multithreading=True,\n",
    "    show_progress=True,\n",
    ")\n",
    "\n",
    "mixed_data = mixed_loader.load_and_split()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(len(mixed_data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summarization\n",
    "\n",
    "Issue: LLM context window is limited, and so feeding an entire document into the model is not possible.\n",
    "\n",
    "Solution: Summarize the document into a smaller text.\n",
    "\n",
    "Two main strategies:\n",
    "\n",
    "## Map-reduce strategy\n",
    "\n",
    "Split document into chunks, summarize each chunk, then combine the summaries into a single summary.\n",
    "\n",
    "## Refinement strategy\n",
    "\n",
    "Split document into chunks, and iterativery refine the summary by summarizing the chunks against the output summary.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'The book \"The Elements of Statistical Learning\" provides an overview of the important ideas in data mining, machine learning, and bioinformatics. The authors cover a range of topics, including neural networks, support vector machines, and classification trees. This second edition includes additional topics such as graphical models and ensemble methods. The authors are well-respected statisticians and researchers in the field.'"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from langchain.chains.summarize import load_summarize_chain\n",
    "from langchain.chat_models import ChatOpenAI\n",
    "\n",
    "llm = ChatOpenAI()\n",
    "\n",
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    chain_type=\"stuff\"\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'This summary provides information about two weather stations in Afghanistan. The first station is located in Asadabad, Kunar, with a latitude of 34.8660000397 and a longitude of 71.1500045859. The second station is in Fayzabad, Badakhshan, with a latitude of 37.1297607616 and a longitude of 70.5792471913.'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chain.run(weather_data[:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Custom prompt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Write a concise summary of the following:\n",
      "\n",
      "\n",
      "\"{text}\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\n"
     ]
    }
   ],
   "source": [
    "print(chain.llm_chain.prompt.template)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Este texto describe el libro \"The Elements of Statistical Learning\", escrito por Trevor Hastie, Robert Tibshirani y Jerome Friedman. El libro aborda las áreas de estadística, minería de datos, aprendizaje automático y bioinformática, y presenta herramientas y conceptos importantes en estos campos. La nueva edición incluye temas adicionales como modelos gráficos, métodos de ensamble y clustering espectral. Los autores son destacados investigadores en el campo de la estadística y han desarrollado diversas técnicas y herramientas utilizadas en la modelización estadística y minería de datos.'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from langchain.prompts import PromptTemplate\n",
    "\n",
    "spanish_template_example = \"\"\"\n",
    "Write concise summary of the following text in Spanish:\n",
    "\"{text}\"\n",
    "\n",
    "CONCISE SUMMARY IN SPANISH:\n",
    "\"\"\"\n",
    "\n",
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    prompt=PromptTemplate.from_template(spanish_template_example)\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Map-reduce chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\u001b[1m> Entering new MapReduceDocumentsChain chain...\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"Springer Series in Statistics\n",
      "Trevor Hastie\n",
      "Robert TibshiraniJerome FriedmanSpringer Series in Statistics\n",
      "The Elements of\n",
      "Statistical Learning\n",
      "Data Mining, Inference, and Prediction\n",
      "The Elements of Statistical LearningDuring the past decade there has been an explosion in computation and information tech-\n",
      "nology. With it have come vast amounts of data in a variety of fields such as medicine, biolo-gy, finance, and marketing. The challenge of understanding these data has led to the devel-opment of new tools in the field of statistics, and spawned new areas such as data mining,machine learning, and bioinformatics. Many of these tools have common underpinnings butare often expressed with different terminology. This book describes the important ideas inthese areas in a common conceptual framework. While the approach is statistical, theemphasis is on concepts rather than mathematics. Many examples are given, with a liberaluse of color graphics. It should be a valuable resource for statisticians and anyone interestedin data mining in science or industry. The book’s coverage is broad, from supervised learning(prediction) to unsupervised learning. The many topics include neural networks, supportvector machines, classification trees and boosting—the first comprehensive treatment of thistopic in any book.\n",
      "This major new edition features many topics not covered in the original, including graphical\n",
      "models, random forests, ensemble methods, least angle regression & path algorithms for thelasso, non-negative matrix factorization, and spectral clustering. There is also a chapter onmethods for “wide” data (p bigger than n), including multiple testing and false discovery rates.\n",
      "Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at\n",
      "Stanford University. They are prominent researchers in this area: Hastie and Tibshiranideveloped generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS andinvented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of thevery successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.\n",
      "›springer.comSTATISTICS\n",
      "isbn 978-0-387-84857-0Trevor Hastie • Robert Tibshirani • Jerome Friedman\n",
      "The Elements of Statictical Learning\n",
      "Hastie • Tibshirani • Friedman\n",
      "Second Edition\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"This is page v\n",
      "Printer: Opaque this\n",
      "To our parents:\n",
      "Valerie and Patrick Hastie\n",
      "Vera and Sami Tibshirani\n",
      "Florence and Harry Friedman\n",
      "and to our families:\n",
      "Samantha, Timothy, and Lynda\n",
      "Charlie, Ryan, Julie, and Cheryl\n",
      "Melanie, Dora, Monika, and Ildiko\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
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      "\n",
      "\n",
      "\"vi\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
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      "\n",
      "\n",
      "\"This is page vii\n",
      "Printer: Opaque this\n",
      "Preface to the Second Edition\n",
      "In God we trust, all others bring data.\n",
      "–William Edwards Deming (1900-1993)1\n",
      "We have been gratiﬁed by the popularity of the ﬁrst edition of The\n",
      "Elements of Statistical Learning. This, along with the fast pace of research\n",
      "in the statistical learning ﬁeld, motivated us to update our book with a\n",
      "second edition.\n",
      "We have added four new chapters and updated some of the existi ng\n",
      "chapters. Because many readers are familiar with the layout of the ﬁrst\n",
      "edition, we have tried to change it as little as possible. Her e is a summary\n",
      "of the main changes:\n",
      "1On the Web, this quote has been widely attributed to both Deming and R obert W.\n",
      "Hayden; however Professor Hayden told us that he can claim no credit for th is quote,\n",
      "and ironically we could ﬁnd no “data” conﬁrming that Deming actual ly said this.\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"viii Preface to the Second Edition\n",
      "Chapter What’s new\n",
      "1.Introduction\n",
      "2.Overview of Supervised Learning\n",
      "3.Linear Methods for Regression LAR algorithm and generaliza tions\n",
      "of the lasso\n",
      "4.Linear Methods for Classiﬁcation Lasso path for logistic re gression\n",
      "5.Basis Expansions and Regulariza-\n",
      "tionAdditional illustrations of RKHS\n",
      "6.Kernel Smoothing Methods\n",
      "7.Model Assessment and Selection Strengths and pitfalls of cr oss-\n",
      "validation\n",
      "8.Model Inference and Averaging\n",
      "9.Additive Models, Trees, and\n",
      "Related Methods\n",
      "10.Boosting and Additive Trees New example from ecology; some\n",
      "material split oﬀ to Chapter 16.\n",
      "11.Neural Networks Bayesian neural nets and the NIPS\n",
      "2003 challenge\n",
      "12.Support Vector Machines and\n",
      "Flexible DiscriminantsPath algorithm for SVM classiﬁer\n",
      "13.Prototype Methods and\n",
      "Nearest-Neighbors\n",
      "14.Unsupervised Learning Spectral clustering, kernel PCA,\n",
      "sparse PCA, non-negative matrix\n",
      "factorization archetypal analysis,\n",
      "nonlinear dimension reduction,\n",
      "Google page rank algorithm, a\n",
      "direct approach to ICA\n",
      "15.Random Forests New\n",
      "16.Ensemble Learning New\n",
      "17.Undirected Graphical Models New\n",
      "18.High-Dimensional Problems New\n",
      "Some further notes:\n",
      "•Our ﬁrst edition was unfriendly to colorblind readers; in pa rticular,\n",
      "we tended to favor red/greencontrasts which are particularly trou-\n",
      "blesome. We have changed the color palette in this edition to a large\n",
      "extent, replacing the above with an orange/bluecontrast.\n",
      "•We have changed the name of Chapter 6 from “Kernel Methods” to\n",
      "“Kernel Smoothing Methods”, to avoid confusion with the mac hine-\n",
      "learningkernelmethodthatisdiscussedinthecontextofsu pportvec-\n",
      "tor machines (Chapter 12) and more generally in Chapters 5 an d 14.\n",
      "•In the ﬁrst edition, the discussion of error-rate estimatio n in Chap-\n",
      "ter 7 was sloppy, as we did not clearly diﬀerentiate the notio ns of\n",
      "conditional error rates (conditional on the training set) a nd uncondi-\n",
      "tional rates. We have ﬁxed this in the new edition.\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"Preface to the Second Edition ix\n",
      "•Chapters 15 and 16 follow naturally from Chapter 10, and the c hap-\n",
      "ters are probably best read in that order.\n",
      "•In Chapter 17, we have not attempted a comprehensive treatme nt\n",
      "of graphical models, and discuss only undirected models and some\n",
      "new methods for their estimation. Due to a lack of space, we ha ve\n",
      "speciﬁcally omitted coverage of directed graphical models .\n",
      "•Chapter 18 explores the “ p≫N” problem, which is learning in high-\n",
      "dimensional feature spaces. These problems arise in many ar eas, in-\n",
      "cluding genomic and proteomic studies, and document classi ﬁcation.\n",
      "We thank the many readers who have found the (too numerous) er rors in\n",
      "the ﬁrst edition. We apologize for those and have done our bes t to avoid er-\n",
      "rorsinthisnewedition.WethankMarkSegal,BalaRajaratna m,andLarry\n",
      "Wasserman for comments on some of the new chapters, and many S tanford\n",
      "graduate and post-doctoral students who oﬀered comments, i n particular\n",
      "Mohammed AlQuraishi, John Boik, Holger Hoeﬂing, Arian Male ki, Donal\n",
      "McMahon, Saharon Rosset, Babak Shababa, Daniela Witten, Ji Zhu and\n",
      "Hui Zou. We thank John Kimmel for his patience in guiding us th rough this\n",
      "new edition. RT dedicates this edition to the memory of Anna M cPhee.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "August 2008\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"x Preface to the Second Edition\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"This is page xi\n",
      "Printer: Opaque this\n",
      "Preface to the First Edition\n",
      "We are drowning in information and starving for knowledge.\n",
      "–Rutherford D. Roger\n",
      "The ﬁeld of Statistics is constantly challenged by the probl ems that science\n",
      "andindustrybringstoitsdoor.Intheearlydays,theseprob lemsoftencame\n",
      "from agricultural and industrial experiments and were rela tively small in\n",
      "scope. With the advent of computers and the information age, statistical\n",
      "problems have exploded both in size and complexity. Challen ges in the\n",
      "areas of data storage, organization and searching have led t o the new ﬁeld\n",
      "of “data mining”; statistical and computational problems i n biology and\n",
      "medicine have created “bioinformatics.” Vast amounts of da ta are being\n",
      "generated in many ﬁelds, and the statistician’s job is to mak e sense of it\n",
      "all: to extract important patterns and trends, and understa nd “what the\n",
      "data says.” We call this learning from data .\n",
      "The challenges in learning from data have led to a revolution in the sta-\n",
      "tisticalsciences.Sincecomputationplayssuchakeyrole, itisnotsurprising\n",
      "that much of this new development has been done by researcher s in other\n",
      "ﬁelds such as computer science and engineering.\n",
      "The learning problems that we consider can be roughly catego rized as\n",
      "eithersupervised orunsupervised . In supervised learning, the goal is to pre-\n",
      "dict the value of an outcome measure based on a number of input measures;\n",
      "in unsupervised learning, there is no outcome measure, and t he goal is to\n",
      "describe the associations and patterns among a set of input m easures.\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"xii Preface to the First Edition\n",
      "This book is our attempt to bring together many of the importa nt new\n",
      "ideas in learning, and explain them in a statistical framewo rk. While some\n",
      "mathematical details are needed, we emphasize the methods a nd their con-\n",
      "ceptual underpinnings rather than their theoretical prope rties. As a result,\n",
      "we hope that this book will appeal not just to statisticians b ut also to\n",
      "researchers and practitioners in a wide variety of ﬁelds.\n",
      "Just as we have learned a great deal from researchers outside of the ﬁeld\n",
      "of statistics, our statistical viewpoint may help others to better understand\n",
      "diﬀerent aspects of learning:\n",
      "There is no true interpretation of anything; interpretatio n is a\n",
      "vehicle in the service of human comprehension. The value of\n",
      "interpretation is in enabling others to fruitfully think ab out an\n",
      "idea.\n",
      "–Andreas Buja\n",
      "We would like to acknowledge the contribution of many people to the\n",
      "conception and completion of this book. David Andrews, Leo B reiman,\n",
      "Andreas Buja, John Chambers, Bradley Efron, Geoﬀrey Hinton , Werner\n",
      "Stuetzle, and John Tukey have greatly inﬂuenced our careers . Balasub-\n",
      "ramanian Narasimhan gave us advice and help on many computat ional\n",
      "problems, and maintained an excellent computing environme nt. Shin-Ho\n",
      "Bang helped in the production of a number of the ﬁgures. Lee Wi lkinson\n",
      "gavevaluabletipsoncolorproduction.IlanaBelitskaya,E vaCantoni,Maya\n",
      "Gupta,MichaelJordan,ShantiGopatam,RadfordNeal,Jorge Picazo,Bog-\n",
      "dan Popescu, Olivier Renaud, Saharon Rosset, John Storey, J i Zhu, Mu\n",
      "Zhu, two reviewers and many students read parts of the manusc ript and\n",
      "oﬀered helpful suggestions. John Kimmel was supportive, pa tient and help-\n",
      "ful at every phase; MaryAnn Brickner and Frank Ganz headed a s uperb\n",
      "production team at Springer. Trevor Hastie would like to tha nk the statis-\n",
      "tics department at the University of Cape Town for their hosp itality during\n",
      "the ﬁnal stages of this book. We gratefully acknowledge NSF a nd NIH for\n",
      "their support of this work. Finally, we would like to thank ou r families and\n",
      "our parents for their love and support.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "May 2001\n",
      "The quiet statisticians have changed our world; not by disco v-\n",
      "ering new facts or technical developments, but by changing t he\n",
      "ways that we reason, experiment and form our opinions ....\n",
      "–Ian Hacking\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"This is page xiii\n",
      "Printer: Opaque this\n",
      "Contents\n",
      "Preface to the Second Edition vii\n",
      "Preface to the First Edition xi\n",
      "1 Introduction 1\n",
      "2 Overview of Supervised Learning 9\n",
      "2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9\n",
      "2.2 Variable Types and Terminology . . . . . . . . . . . . . . 9\n",
      "2.3 Two Simple Approaches to Prediction:\n",
      "Least Squares and Nearest Neighbors . . . . . . . . . . . 11\n",
      "2.3.1 Linear Models and Least Squares . . . . . . . . 11\n",
      "2.3.2 Nearest-Neighbor Methods . . . . . . . . . . . . 14\n",
      "2.3.3 From Least Squares to Nearest Neighbors . . . . 16\n",
      "2.4 Statistical Decision Theory . . . . . . . . . . . . . . . . . 18\n",
      "2.5 Local Methods in High Dimensions . . . . . . . . . . . . . 22\n",
      "2.6 Statistical Models, Supervised Learning\n",
      "and Function Approximation . . . . . . . . . . . . . . . . 28\n",
      "2.6.1 A Statistical Model\n",
      "for the Joint Distribution Pr( X,Y) . . . . . . . 28\n",
      "2.6.2 Supervised Learning . . . . . . . . . . . . . . . . 29\n",
      "2.6.3 Function Approximation . . . . . . . . . . . . . 29\n",
      "2.7 Structured Regression Models . . . . . . . . . . . . . . . 32\n",
      "2.7.1 Diﬃculty of the Problem . . . . . . . . . . . . . 32\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"xiv Contents\n",
      "2.8 Classes of Restricted Estimators . . . . . . . . . . . . . . 33\n",
      "2.8.1 Roughness Penalty and Bayesian Methods . . . 34\n",
      "2.8.2 Kernel Methods and Local Regression . . . . . . 34\n",
      "2.8.3 Basis Functions and Dictionary Methods . . . . 35\n",
      "2.9 Model Selection and the Bias–Variance Tradeoﬀ . . . . . 37\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "3 Linear Methods for Regression 43\n",
      "3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43\n",
      "3.2 Linear Regression Models and Least Squares . . . . . . . 44\n",
      "3.2.1 Example: Prostate Cancer . . . . . . . . . . . . 49\n",
      "3.2.2 The Gauss–Markov Theorem . . . . . . . . . . . 51\n",
      "3.2.3 Multiple Regression\n",
      "from Simple Univariate Regression . . . . . . . . 52\n",
      "3.2.4 Multiple Outputs . . . . . . . . . . . . . . . . . 56\n",
      "3.3 Subset Selection . . . . . . . . . . . . . . . . . . . . . . . 57\n",
      "3.3.1 Best-Subset Selection . . . . . . . . . . . . . . . 57\n",
      "3.3.2 Forward- and Backward-Stepwise Selection . . . 58\n",
      "3.3.3 Forward-Stagewise Regression . . . . . . . . . . 60\n",
      "3.3.4 Prostate Cancer Data Example (Continued) . . 61\n",
      "3.4 Shrinkage Methods . . . . . . . . . . . . . . . . . . . . . . 61\n",
      "3.4.1 Ridge Regression . . . . . . . . . . . . . . . . . 61\n",
      "3.4.2 The Lasso . . . . . . . . . . . . . . . . . . . . . 68\n",
      "3.4.3 Discussion: Subset Selection, Ridge Regression\n",
      "and the Lasso . . . . . . . . . . . . . . . . . . . 69\n",
      "3.4.4 Least Angle Regression . . . . . . . . . . . . . . 73\n",
      "3.5 Methods Using Derived Input Directions . . . . . . . . . 79\n",
      "3.5.1 Principal Components Regression . . . . . . . . 79\n",
      "3.5.2 Partial Least Squares . . . . . . . . . . . . . . . 80\n",
      "3.6 Discussion: A Comparison of the Selection\n",
      "and Shrinkage Methods . . . . . . . . . . . . . . . . . . . 82\n",
      "3.7 Multiple Outcome Shrinkage and Selection . . . . . . . . 84\n",
      "3.8 More on the Lasso and Related Path Algorithms . . . . . 86\n",
      "3.8.1 Incremental Forward Stagewise Regression . . . 86\n",
      "3.8.2 Piecewise-Linear Path Algorithms . . . . . . . . 89\n",
      "3.8.3 The Dantzig Selector . . . . . . . . . . . . . . . 89\n",
      "3.8.4 The Grouped Lasso . . . . . . . . . . . . . . . . 90\n",
      "3.8.5 Further Properties of the Lasso . . . . . . . . . . 91\n",
      "3.8.6 Pathwise Coordinate Optimization . . . . . . . . 92\n",
      "3.9 Computational Considerations . . . . . . . . . . . . . . . 93\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"Contents xv\n",
      "4 Linear Methods for Classiﬁcation 101\n",
      "4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101\n",
      "4.2 Linear Regression of an Indicator Matrix . . . . . . . . . 103\n",
      "4.3 Linear Discriminant Analysis . . . . . . . . . . . . . . . . 106\n",
      "4.3.1 Regularized Discriminant Analysis . . . . . . . . 112\n",
      "4.3.2 Computations for LDA . . . . . . . . . . . . . . 113\n",
      "4.3.3 Reduced-Rank Linear Discriminant Analysis . . 113\n",
      "4.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 119\n",
      "4.4.1 Fitting Logistic Regression Models . . . . . . . . 120\n",
      "4.4.2 Example: South African Heart Disease . . . . . 122\n",
      "4.4.3 Quadratic Approximations and Inference . . . . 124\n",
      "4.4.4L1Regularized Logistic Regression . . . . . . . . 125\n",
      "4.4.5 Logistic Regression or LDA? . . . . . . . . . . . 127\n",
      "4.5 Separating Hyperplanes . . . . . . . . . . . . . . . . . . . 129\n",
      "4.5.1 Rosenblatt’s Perceptron Learning Algorithm . . 130\n",
      "4.5.2 Optimal Separating Hyperplanes . . . . . . . . . 132\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "5 Basis Expansions and Regularization 139\n",
      "5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 139\n",
      "5.2 Piecewise Polynomials and Splines . . . . . . . . . . . . . 141\n",
      "5.2.1 Natural Cubic Splines . . . . . . . . . . . . . . . 144\n",
      "5.2.2 Example:SouthAfricanHeartDisease(Continued)146\n",
      "5.2.3 Example: Phoneme Recognition . . . . . . . . . 148\n",
      "5.3 Filtering and Feature Extraction . . . . . . . . . . . . . . 150\n",
      "5.4 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . 151\n",
      "5.4.1 Degrees of Freedom and Smoother Matrices . . . 153\n",
      "5.5 Automatic Selection of the Smoothing Parameters . . . . 15 6\n",
      "5.5.1 Fixing the Degrees of Freedom . . . . . . . . . . 158\n",
      "5.5.2 The Bias–Variance Tradeoﬀ . . . . . . . . . . . . 158\n",
      "5.6 Nonparametric Logistic Regression . . . . . . . . . . . . . 161\n",
      "5.7 Multidimensional Splines . . . . . . . . . . . . . . . . . . 162\n",
      "5.8 Regularization and Reproducing Kernel Hilbert Spaces . 167\n",
      "5.8.1 Spaces of Functions Generated by Kernels . . . 168\n",
      "5.8.2 Examples of RKHS . . . . . . . . . . . . . . . . 170\n",
      "5.9 Wavelet Smoothing . . . . . . . . . . . . . . . . . . . . . 174\n",
      "5.9.1 Wavelet Bases and the Wavelet Transform . . . 176\n",
      "5.9.2 Adaptive Wavelet Filtering . . . . . . . . . . . . 179\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Appendix: Computational Considerations for Splines . . . . . . 186\n",
      "Appendix:B-splines . . . . . . . . . . . . . . . . . . . . . 186\n",
      "Appendix: Computations for Smoothing Splines . . . . . 189\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"xvi Contents\n",
      "6 Kernel Smoothing Methods 191\n",
      "6.1 One-Dimensional Kernel Smoothers . . . . . . . . . . . . 192\n",
      "6.1.1 Local Linear Regression . . . . . . . . . . . . . . 194\n",
      "6.1.2 Local Polynomial Regression . . . . . . . . . . . 197\n",
      "6.2 Selecting the Width of the Kernel . . . . . . . . . . . . . 198\n",
      "6.3 Local Regression in IRp. . . . . . . . . . . . . . . . . . . 200\n",
      "6.4 Structured Local Regression Models in IRp. . . . . . . . 201\n",
      "6.4.1 Structured Kernels . . . . . . . . . . . . . . . . . 203\n",
      "6.4.2 Structured Regression Functions . . . . . . . . . 203\n",
      "6.5 Local Likelihood and Other Models . . . . . . . . . . . . 205\n",
      "6.6 Kernel Density Estimation and Classiﬁcation . . . . . . . 20 8\n",
      "6.6.1 Kernel Density Estimation . . . . . . . . . . . . 208\n",
      "6.6.2 Kernel Density Classiﬁcation . . . . . . . . . . . 210\n",
      "6.6.3 The Naive Bayes Classiﬁer . . . . . . . . . . . . 210\n",
      "6.7 Radial Basis Functions and Kernels . . . . . . . . . . . . 212\n",
      "6.8 Mixture Models for Density Estimation and Classiﬁcatio n 214\n",
      "6.9 Computational Considerations . . . . . . . . . . . . . . . 216\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "7 Model Assessment and Selection 219\n",
      "7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 219\n",
      "7.2 Bias, Variance and Model Complexity . . . . . . . . . . . 219\n",
      "7.3 The Bias–Variance Decomposition . . . . . . . . . . . . . 223\n",
      "7.3.1 Example: Bias–Variance Tradeoﬀ . . . . . . . . 226\n",
      "7.4 Optimism of the Training Error Rate . . . . . . . . . . . 228\n",
      "7.5 Estimates of In-Sample Prediction Error . . . . . . . . . . 230\n",
      "7.6 The Eﬀective Number of Parameters . . . . . . . . . . . . 232\n",
      "7.7 The Bayesian Approach and BIC . . . . . . . . . . . . . . 233\n",
      "7.8 Minimum Description Length . . . . . . . . . . . . . . . . 235\n",
      "7.9 Vapnik–Chervonenkis Dimension . . . . . . . . . . . . . . 237\n",
      "7.9.1 Example (Continued) . . . . . . . . . . . . . . . 239\n",
      "7.10 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . 241\n",
      "7.10.1K-Fold Cross-Validation . . . . . . . . . . . . . 241\n",
      "7.10.2 The Wrong and Right Way\n",
      "to Do Cross-validation . . . . . . . . . . . . . . . 245\n",
      "7.10.3 Does Cross-Validation Really Work? . . . . . . . 247\n",
      "7.11 Bootstrap Methods . . . . . . . . . . . . . . . . . . . . . 249\n",
      "7.11.1 Example (Continued) . . . . . . . . . . . . . . . 252\n",
      "7.12 Conditional or Expected Test Error? . . . . . . . . . . . . 254\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "8 Model Inference and Averaging 261\n",
      "8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 261\"\n",
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      "8.2 The Bootstrap and Maximum Likelihood Methods . . . . 261\n",
      "8.2.1 A Smoothing Example . . . . . . . . . . . . . . 261\n",
      "8.2.2 Maximum Likelihood Inference . . . . . . . . . . 265\n",
      "8.2.3 Bootstrap versus Maximum Likelihood . . . . . 267\n",
      "8.3 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . 267\n",
      "8.4 Relationship Between the Bootstrap\n",
      "and Bayesian Inference . . . . . . . . . . . . . . . . . . . 271\n",
      "8.5 The EM Algorithm . . . . . . . . . . . . . . . . . . . . . 272\n",
      "8.5.1 Two-Component Mixture Model . . . . . . . . . 272\n",
      "8.5.2 The EM Algorithm in General . . . . . . . . . . 276\n",
      "8.5.3 EM as a Maximization–Maximization Procedure 277\n",
      "8.6 MCMC for Sampling from the Posterior . . . . . . . . . . 279\n",
      "8.7 Bagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282\n",
      "8.7.1 Example: Trees with Simulated Data . . . . . . 283\n",
      "8.8 Model Averaging and Stacking . . . . . . . . . . . . . . . 288\n",
      "8.9 Stochastic Search: Bumping . . . . . . . . . . . . . . . . . 290\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 292\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293\n",
      "9 Additive Models, Trees, and Related Methods 295\n",
      "9.1 Generalized Additive Models . . . . . . . . . . . . . . . . 295\n",
      "9.1.1 Fitting Additive Models . . . . . . . . . . . . . . 297\n",
      "9.1.2 Example: Additive Logistic Regression . . . . . 299\n",
      "9.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . 304\n",
      "9.2 Tree-Based Methods . . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.1 Background . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.2 Regression Trees . . . . . . . . . . . . . . . . . . 307\n",
      "9.2.3 Classiﬁcation Trees . . . . . . . . . . . . . . . . 308\n",
      "9.2.4 Other Issues . . . . . . . . . . . . . . . . . . . . 310\n",
      "9.2.5 Spam Example (Continued) . . . . . . . . . . . 313\n",
      "9.3 PRIM: Bump Hunting . . . . . . . . . . . . . . . . . . . . 317\n",
      "9.3.1 Spam Example (Continued) . . . . . . . . . . . 320\n",
      "9.4 MARS: Multivariate Adaptive Regression Splines . . . . . 3 21\n",
      "9.4.1 Spam Example (Continued) . . . . . . . . . . . 326\n",
      "9.4.2 Example (Simulated Data) . . . . . . . . . . . . 327\n",
      "9.4.3 Other Issues . . . . . . . . . . . . . . . . . . . . 328\n",
      "9.5 Hierarchical Mixtures of Experts . . . . . . . . . . . . . . 329\n",
      "9.6 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . 332\n",
      "9.7 Computational Considerations . . . . . . . . . . . . . . . 334\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 334\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335\n",
      "10 Boosting and Additive Trees 337\n",
      "10.1 Boosting Methods . . . . . . . . . . . . . . . . . . . . . . 337\n",
      "10.1.1 Outline of This Chapter . . . . . . . . . . . . . . 340\"\n",
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      "10.2 Boosting Fits an Additive Model . . . . . . . . . . . . . . 341\n",
      "10.3 Forward Stagewise Additive Modeling . . . . . . . . . . . 342\n",
      "10.4 Exponential Loss and AdaBoost . . . . . . . . . . . . . . 343\n",
      "10.5 Why Exponential Loss? . . . . . . . . . . . . . . . . . . . 345\n",
      "10.6 Loss Functions and Robustness . . . . . . . . . . . . . . . 346\n",
      "10.7 “Oﬀ-the-Shelf” Procedures for Data Mining . . . . . . . . 35 0\n",
      "10.8 Example: Spam Data . . . . . . . . . . . . . . . . . . . . 352\n",
      "10.9 Boosting Trees . . . . . . . . . . . . . . . . . . . . . . . . 353\n",
      "10.10 Numerical Optimization via Gradient Boosting . . . . . . 358\n",
      "10.10.1 Steepest Descent . . . . . . . . . . . . . . . . . . 358\n",
      "10.10.2 Gradient Boosting . . . . . . . . . . . . . . . . . 359\n",
      "10.10.3 Implementations of Gradient Boosting . . . . . . 360\n",
      "10.11 Right-Sized Trees for Boosting . . . . . . . . . . . . . . . 361\n",
      "10.12 Regularization . . . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.1 Shrinkage . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.2 Subsampling . . . . . . . . . . . . . . . . . . . . 365\n",
      "10.13 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 367\n",
      "10.13.1 Relative Importance of Predictor Variables . . . 367\n",
      "10.13.2 Partial Dependence Plots . . . . . . . . . . . . . 369\n",
      "10.14 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . 371\n",
      "10.14.1 California Housing . . . . . . . . . . . . . . . . . 371\n",
      "10.14.2 New Zealand Fish . . . . . . . . . . . . . . . . . 375\n",
      "10.14.3 Demographics Data . . . . . . . . . . . . . . . . 379\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 380\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384\n",
      "11 Neural Networks 389\n",
      "11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 389\n",
      "11.2 Projection Pursuit Regression . . . . . . . . . . . . . . . 389\n",
      "11.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 392\n",
      "11.4 Fitting Neural Networks . . . . . . . . . . . . . . . . . . . 395\n",
      "11.5 Some Issues in Training Neural Networks . . . . . . . . . 397\n",
      "11.5.1 Starting Values . . . . . . . . . . . . . . . . . . . 397\n",
      "11.5.2 Overﬁtting . . . . . . . . . . . . . . . . . . . . . 398\n",
      "11.5.3 Scaling of the Inputs . . . . . . . . . . . . . . . 398\n",
      "11.5.4 Number of Hidden Units and Layers . . . . . . . 400\n",
      "11.5.5 Multiple Minima . . . . . . . . . . . . . . . . . . 400\n",
      "11.6 Example: Simulated Data . . . . . . . . . . . . . . . . . . 401\n",
      "11.7 Example: ZIP Code Data . . . . . . . . . . . . . . . . . . 404\n",
      "11.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 408\n",
      "11.9 Bayesian Neural Nets and the NIPS 2003 Challenge . . . 409\n",
      "11.9.1 Bayes, Boosting and Bagging . . . . . . . . . . . 410\n",
      "11.9.2 Performance Comparisons . . . . . . . . . . . . 412\n",
      "11.10 Computational Considerations . . . . . . . . . . . . . . . 414\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 415\"\n",
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      "\"Contents xix\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "12 Support Vector Machines and\n",
      "Flexible Discriminants 417\n",
      "12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 417\n",
      "12.2 The Support Vector Classiﬁer . . . . . . . . . . . . . . . . 417\n",
      "12.2.1 Computing the Support Vector Classiﬁer . . . . 420\n",
      "12.2.2 Mixture Example (Continued) . . . . . . . . . . 421\n",
      "12.3 Support Vector Machines and Kernels . . . . . . . . . . . 423\n",
      "12.3.1 Computing the SVM for Classiﬁcation . . . . . . 423\n",
      "12.3.2 The SVM as a Penalization Method . . . . . . . 426\n",
      "12.3.3 Function Estimation and Reproducing Kernels . 428\n",
      "12.3.4 SVMs and the Curse of Dimensionality . . . . . 431\n",
      "12.3.5 A Path Algorithm for the SVM Classiﬁer . . . . 432\n",
      "12.3.6 Support Vector Machines for Regression . . . . . 434\n",
      "12.3.7 Regression and Kernels . . . . . . . . . . . . . . 436\n",
      "12.3.8 Discussion . . . . . . . . . . . . . . . . . . . . . 438\n",
      "12.4 Generalizing Linear Discriminant Analysis . . . . . . . . 4 38\n",
      "12.5 Flexible Discriminant Analysis . . . . . . . . . . . . . . . 440\n",
      "12.5.1 Computing the FDA Estimates . . . . . . . . . . 444\n",
      "12.6 Penalized Discriminant Analysis . . . . . . . . . . . . . . 446\n",
      "12.7 Mixture Discriminant Analysis . . . . . . . . . . . . . . . 449\n",
      "12.7.1 Example: Waveform Data . . . . . . . . . . . . . 451\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "13 Prototype Methods and Nearest-Neighbors 459\n",
      "13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2 Prototype Methods . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2.1K-means Clustering . . . . . . . . . . . . . . . . 460\n",
      "13.2.2 Learning Vector Quantization . . . . . . . . . . 462\n",
      "13.2.3 Gaussian Mixtures . . . . . . . . . . . . . . . . . 463\n",
      "13.3k-Nearest-Neighbor Classiﬁers . . . . . . . . . . . . . . . 463\n",
      "13.3.1 Example: A Comparative Study . . . . . . . . . 468\n",
      "13.3.2 Example: k-Nearest-Neighbors\n",
      "and Image Scene Classiﬁcation . . . . . . . . . . 470\n",
      "13.3.3 Invariant Metrics and Tangent Distance . . . . . 471\n",
      "13.4 Adaptive Nearest-Neighbor Methods . . . . . . . . . . . . 475\n",
      "13.4.1 Example . . . . . . . . . . . . . . . . . . . . . . 478\n",
      "13.4.2 Global Dimension Reduction\n",
      "for Nearest-Neighbors . . . . . . . . . . . . . . . 479\n",
      "13.5 Computational Considerations . . . . . . . . . . . . . . . 480\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481\"\n",
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      "14 Unsupervised Learning 485\n",
      "14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 485\n",
      "14.2 Association Rules . . . . . . . . . . . . . . . . . . . . . . 487\n",
      "14.2.1 Market Basket Analysis . . . . . . . . . . . . . . 488\n",
      "14.2.2 The Apriori Algorithm . . . . . . . . . . . . . . 489\n",
      "14.2.3 Example: Market Basket Analysis . . . . . . . . 492\n",
      "14.2.4 Unsupervised as Supervised Learning . . . . . . 495\n",
      "14.2.5 Generalized Association Rules . . . . . . . . . . 497\n",
      "14.2.6 Choice of Supervised Learning Method . . . . . 499\n",
      "14.2.7 Example: Market Basket Analysis (Continued) . 499\n",
      "14.3 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . 501\n",
      "14.3.1 Proximity Matrices . . . . . . . . . . . . . . . . 503\n",
      "14.3.2 Dissimilarities Based on Attributes . . . . . . . 503\n",
      "14.3.3 Object Dissimilarity . . . . . . . . . . . . . . . . 505\n",
      "14.3.4 Clustering Algorithms . . . . . . . . . . . . . . . 507\n",
      "14.3.5 Combinatorial Algorithms . . . . . . . . . . . . 507\n",
      "14.3.6K-means . . . . . . . . . . . . . . . . . . . . . . 509\n",
      "14.3.7 Gaussian Mixtures as Soft K-means Clustering . 510\n",
      "14.3.8 Example: Human Tumor Microarray Data . . . 512\n",
      "14.3.9 Vector Quantization . . . . . . . . . . . . . . . . 514\n",
      "14.3.10K-medoids . . . . . . . . . . . . . . . . . . . . . 515\n",
      "14.3.11 Practical Issues . . . . . . . . . . . . . . . . . . 518\n",
      "14.3.12 Hierarchical Clustering . . . . . . . . . . . . . . 520\n",
      "14.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . 528\n",
      "14.5 Principal Components, Curves and Surfaces . . . . . . . . 53 4\n",
      "14.5.1 Principal Components . . . . . . . . . . . . . . . 534\n",
      "14.5.2 Principal Curves and Surfaces . . . . . . . . . . 541\n",
      "14.5.3 Spectral Clustering . . . . . . . . . . . . . . . . 544\n",
      "14.5.4 Kernel Principal Components . . . . . . . . . . . 547\n",
      "14.5.5 Sparse Principal Components . . . . . . . . . . . 550\n",
      "14.6 Non-negative Matrix Factorization . . . . . . . . . . . . . 553\n",
      "14.6.1 Archetypal Analysis . . . . . . . . . . . . . . . . 554\n",
      "14.7 Independent Component Analysis\n",
      "and Exploratory Projection Pursuit . . . . . . . . . . . . 557\n",
      "14.7.1 Latent Variables and Factor Analysis . . . . . . 558\n",
      "14.7.2 Independent Component Analysis . . . . . . . . 560\n",
      "14.7.3 Exploratory Projection Pursuit . . . . . . . . . . 565\n",
      "14.7.4 A Direct Approach to ICA . . . . . . . . . . . . 565\n",
      "14.8 Multidimensional Scaling . . . . . . . . . . . . . . . . . . 570\n",
      "14.9 Nonlinear Dimension Reduction\n",
      "and Local Multidimensional Scaling . . . . . . . . . . . . 572\n",
      "14.10 The Google PageRank Algorithm . . . . . . . . . . . . . 576\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 578\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579\"\n",
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      "15 Random Forests 587\n",
      "15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 587\n",
      "15.2 Deﬁnition of Random Forests . . . . . . . . . . . . . . . . 587\n",
      "15.3 Details of Random Forests . . . . . . . . . . . . . . . . . 592\n",
      "15.3.1 Out of Bag Samples . . . . . . . . . . . . . . . . 592\n",
      "15.3.2 Variable Importance . . . . . . . . . . . . . . . . 593\n",
      "15.3.3 Proximity Plots . . . . . . . . . . . . . . . . . . 595\n",
      "15.3.4 Random Forests and Overﬁtting . . . . . . . . . 596\n",
      "15.4 Analysis of Random Forests . . . . . . . . . . . . . . . . . 597\n",
      "15.4.1 Variance and the De-Correlation Eﬀect . . . . . 597\n",
      "15.4.2 Bias . . . . . . . . . . . . . . . . . . . . . . . . . 600\n",
      "15.4.3 Adaptive Nearest Neighbors . . . . . . . . . . . 601\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 602\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603\n",
      "16 Ensemble Learning 605\n",
      "16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 605\n",
      "16.2 Boosting and Regularization Paths . . . . . . . . . . . . . 607\n",
      "16.2.1 Penalized Regression . . . . . . . . . . . . . . . 607\n",
      "16.2.2 The “Bet on Sparsity” Principle . . . . . . . . . 610\n",
      "16.2.3 Regularization Paths, Over-ﬁtting and Margins . 613\n",
      "16.3 Learning Ensembles . . . . . . . . . . . . . . . . . . . . . 616\n",
      "16.3.1 Learning a Good Ensemble . . . . . . . . . . . . 617\n",
      "16.3.2 Rule Ensembles . . . . . . . . . . . . . . . . . . 622\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 623\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624\n",
      "17 Undirected Graphical Models 625\n",
      "17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 625\n",
      "17.2 Markov Graphs and Their Properties . . . . . . . . . . . 627\n",
      "17.3 Undirected Graphical Models for Continuous Variables . 630\n",
      "17.3.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 631\n",
      "17.3.2 Estimation of the Graph Structure . . . . . . . . 635\n",
      "17.4 Undirected Graphical Models for Discrete Variables . . . 638\n",
      "17.4.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 639\n",
      "17.4.2 Hidden Nodes . . . . . . . . . . . . . . . . . . . 641\n",
      "17.4.3 Estimation of the Graph Structure . . . . . . . . 642\n",
      "17.4.4 Restricted Boltzmann Machines . . . . . . . . . 643\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645\n",
      "18 High-Dimensional Problems: p≫N 649\n",
      "18.1 When pis Much Bigger than N. . . . . . . . . . . . . . 649\"\n",
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      "18.2 Diagonal Linear Discriminant Analysis\n",
      "and Nearest Shrunken Centroids . . . . . . . . . . . . . . 651\n",
      "18.3 Linear Classiﬁers with Quadratic Regularization . . . . . 654\n",
      "18.3.1 Regularized Discriminant Analysis . . . . . . . . 656\n",
      "18.3.2 Logistic Regression\n",
      "with Quadratic Regularization . . . . . . . . . . 657\n",
      "18.3.3 The Support Vector Classiﬁer . . . . . . . . . . 657\n",
      "18.3.4 Feature Selection . . . . . . . . . . . . . . . . . . 658\n",
      "18.3.5 Computational Shortcuts When p≫N. . . . . 659\n",
      "18.4 Linear Classiﬁers with L1Regularization . . . . . . . . . 661\n",
      "18.4.1 Application of Lasso\n",
      "to Protein Mass Spectroscopy . . . . . . . . . . 664\n",
      "18.4.2 The Fused Lasso for Functional Data . . . . . . 666\n",
      "18.5 Classiﬁcation When Features are Unavailable . . . . . . . 6 68\n",
      "18.5.1 Example: String Kernels\n",
      "and Protein Classiﬁcation . . . . . . . . . . . . . 668\n",
      "18.5.2 Classiﬁcation and Other Models Using\n",
      "Inner-Product Kernels and Pairwise Distances . 670\n",
      "18.5.3 Example: Abstracts Classiﬁcation . . . . . . . . 672\n",
      "18.6 High-Dimensional Regression:\n",
      "Supervised Principal Components . . . . . . . . . . . . . 674\n",
      "18.6.1 Connection to Latent-Variable Modeling . . . . 678\n",
      "18.6.2 Relationship with Partial Least Squares . . . . . 680\n",
      "18.6.3 Pre-Conditioning for Feature Selection . . . . . 681\n",
      "18.7 Feature Assessment and the Multiple-Testing Problem . . 683\n",
      "18.7.1 The False Discovery Rate . . . . . . . . . . . . . 687\n",
      "18.7.2 Asymmetric Cutpoints and the SAM Procedure 690\n",
      "18.7.3 A Bayesian Interpretation of the FDR . . . . . . 692\n",
      "18.8 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . 693\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694\n",
      "References 699\n",
      "Author Index 729\n",
      "Index 737\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"This is page 1\n",
      "Printer: Opaque this\n",
      "1\n",
      "Introduction\n",
      "Statistical learning plays a key role in many areas of science, ﬁnance and\n",
      "industry. Here are some examples of learning problems:\n",
      "•Predict whether a patient, hospitalized due to a heart attac k, will\n",
      "have a second heart attack. The prediction is to be based on de mo-\n",
      "graphic, diet and clinical measurements for that patient.\n",
      "•Predict the price of a stock in 6 months from now, on the basis o f\n",
      "company performance measures and economic data.\n",
      "•Identify the numbers in a handwritten ZIP code, from a digiti zed\n",
      "image.\n",
      "•Estimate the amount of glucose in the blood of a diabetic pers on,\n",
      "from the infrared absorption spectrum of that person’s bloo d.\n",
      "•Identify the risk factors for prostate cancer, based on clin ical and\n",
      "demographic variables.\n",
      "The science of learning plays a key role in the ﬁelds of statis tics, data\n",
      "mining and artiﬁcial intelligence, intersecting with area s of engineering and\n",
      "other disciplines.\n",
      "This book is about learning from data. In a typical scenario, we have\n",
      "an outcome measurement, usually quantitative (such as a sto ck price) or\n",
      "categorical (such as heart attack/no heart attack), that we wish to predict\n",
      "based on a set of features (such as diet and clinical measurements). We\n",
      "have atraining set of data, in which we observe the outcome and feature\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"The book \"The Elements of Statistical Learning\" provides a comprehensive overview of the important ideas and concepts in data mining, machine learning, and bioinformatics. The authors, Trevor Hastie, Robert Tibshirani, and Jerome Friedman, cover a wide range of topics from supervised to unsupervised learning, including neural networks, support vector machines, and boosting. The second edition of the book includes new topics such as graphical models, random forests, and ensemble methods. The authors are renowned professors of statistics at Stanford University and have made significant contributions to the field.\n",
      "\n",
      "This page is dedicated to the parents and families of the authors, including Valerie and Patrick Hastie, Vera and Sami Tibshirani, and Florence and Harry Friedman. It also mentions specific family members such as Samantha, Timothy, Lynda, Charlie, Ryan, Julie, Cheryl, Melanie, Dora, Monika, and Ildiko.\n",
      "\n",
      "\"vi\" is a text editor commonly used in Unix-like operating systems for editing files.\n",
      "\n",
      "The preface to the second edition of \"The Elements of Statistical Learning\" explains that the popularity of the first edition and the fast pace of research in the field motivated the authors to update the book. They have added four new chapters and made updates to existing chapters while trying to change the layout as little as possible. The preface also clarifies the origin of a quote attributed to William Edwards Deming.\n",
      "\n",
      "The second edition of a book on machine learning includes updates and changes to various chapters. The authors address issues with colorblind readers, change the name of a chapter to avoid confusion, and fix a discussion on error-rate estimation.\n",
      "\n",
      "The preface to the second edition of a book suggests that chapters 15 and 16 should be read after chapter 10. Chapter 17 only discusses undirected graphical models and does not cover directed graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The authors apologize for errors in the first edition and thank those who provided comments and assistance for the new edition. The book is dedicated to the memory of Anna McPhee.\n",
      "\n",
      "The preface to the second edition discusses the updates and changes made in the second edition of the book.\n",
      "\n",
      "The field of Statistics is facing challenges due to the increasing complexity and size of data. The advent of computers and the information age has led to the emergence of data mining and bioinformatics. Learning from data has become crucial, and computation plays a key role in this revolution. The learning problems can be categorized as either supervised or unsupervised, with the goal being to predict outcomes or describe associations and patterns among input measures.\n",
      "\n",
      "This book aims to explain important new ideas in learning using a statistical framework. It focuses on the methods and conceptual underpinnings rather than theoretical properties. The authors hope that the book will be useful not just for statisticians, but also for researchers and practitioners in various fields. The authors acknowledge the contributions of many individuals to the completion of the book, and express gratitude to their families and parents for their support. The book emphasizes the impact of statisticians on changing the ways we reason, experiment, and form opinions.\n",
      "\n",
      "This is page xiii of a book on supervised learning. It includes a preface to the second edition and the first edition. The book covers various topics including an introduction to supervised learning, variable types and terminology, prediction approaches, statistical decision theory, local methods in high dimensions, statistical models, supervised learning, function approximation, and structured regression models.\n",
      "\n",
      "This section discusses different classes of restricted estimators, including roughness penalty and Bayesian methods, kernel methods and local regression, and basis functions and dictionary methods. It also covers model selection and the bias-variance tradeoff. The next section focuses on linear methods for regression, including linear regression models and least squares, subset selection, shrinkage methods such as ridge regression and the lasso, and methods using derived input directions like principal components regression and partial least squares. It also discusses multiple outcome shrinkage and selection, and provides more information on the lasso and related path algorithms. The section concludes with a discussion on computational considerations.\n",
      "\n",
      "The summary includes information about linear methods for classification, such as linear regression, linear discriminant analysis, logistic regression, and separating hyperplanes. It also covers basis expansions and regularization techniques, including piecewise polynomials and splines, filtering and feature extraction, smoothing splines, automatic selection of smoothing parameters, nonparametric logistic regression, multidimensional splines, regularization and reproducing kernel Hilbert spaces, and wavelet smoothing. The appendix provides computational considerations for splines and information about B-splines and computations for smoothing splines.\n",
      "\n",
      "This section of the book covers kernel smoothing methods, including one-dimensional kernel smoothers, selecting the width of the kernel, local regression in IRp, structured local regression models, local likelihood and other models, kernel density estimation and classification, radial basis functions and kernels, mixture models for density estimation and classification, and computational considerations. It also covers model assessment and selection, including bias, variance, and model complexity, the bias-variance decomposition, optimism of the training error rate, estimates of in-sample prediction error, the effective number of parameters, the Bayesian approach and BIC, minimum description length, Vapnik-Chervonenkis dimension, cross-validation, bootstrap methods, and conditional or expected test error. The section concludes with model inference and averaging.\n",
      "\n",
      "This section of the book covers various statistical methods, including the bootstrap and maximum likelihood methods, Bayesian methods, the EM algorithm, MCMC for sampling from the posterior, bagging, model averaging and stacking, and stochastic search. It also discusses additive models, tree-based methods, PRIM, MARS, hierarchical mixtures of experts, and missing data. The section concludes with a discussion of boosting methods.\n",
      "\n",
      "This section of the book covers topics related to boosting and neural networks. It discusses the use of boosting to fit additive models and introduces forward stagewise additive modeling. The concept of exponential loss and its application in AdaBoost is explained. The chapter also explores the reasons behind using exponential loss and the relationship between loss functions and robustness. \"Off-the-shelf\" procedures for data mining are mentioned, along with an example using spam data. The chapter then delves into boosting trees and numerical optimization via gradient boosting. The importance of right-sized trees and regularization techniques, such as shrinkage and subsampling, are discussed. Interpretation methods, such as determining the relative importance of predictor variables and partial dependence plots, are also covered. The chapter concludes with illustrations using various datasets. The following chapter introduces neural networks and explores topics such as projection pursuit regression and fitting neural networks. Issues related to training neural networks, such as starting values, overfitting, scaling of inputs, and determining the number of hidden units and layers, are discussed. Examples using simulated data and ZIP code data are provided. The chapter also touches on Bayesian neural networks and the NIPS 2003 challenge, as well as computational considerations.\n",
      "\n",
      "This section of the book discusses support vector machines and flexible discriminants. It covers topics such as computing the support vector classifier, support vector machines and kernels, function estimation and reproducing kernels, as well as generalizing linear discriminant analysis. It also discusses prototype methods and nearest-neighbor classifiers, including K-means clustering, learning vector quantization, and k-nearest-neighbor classifiers. The chapter concludes with a discussion on computational considerations.\n",
      "\n",
      "This section of the content covers various topics related to unsupervised learning. It includes discussions on association rules, cluster analysis, self-organizing maps, principal components, non-negative matrix factorization, independent component analysis, multidimensional scaling, nonlinear dimension reduction, and the Google PageRank algorithm. The section also includes bibliographic notes and exercises for further practice.\n",
      "\n",
      "The given contents are from a book or article that discusses various topics in machine learning. The topics covered include random forests, ensemble learning, undirected graphical models, and high-dimensional problems. Each section provides an introduction to the topic and explores different aspects and techniques related to it. The contents also include bibliographic notes and exercises for further study and practice.\n",
      "\n",
      "This section of the document discusses various methods for linear discriminant analysis and linear classification with different types of regularization. It also covers feature selection, classification when features are unavailable, high-dimensional regression, feature assessment, and the multiple-testing problem. The section concludes with a bibliography, exercises, and references.\n",
      "\n",
      "This text discusses the importance of statistical learning in various fields and provides examples of learning problems. It emphasizes the role of learning in statistics, data mining, and artificial intelligence. The book focuses on learning from data, specifically predicting outcomes based on features using a training set of data.\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'\"The Elements of Statistical Learning\" is a comprehensive book that covers important concepts in data mining, machine learning, and bioinformatics. The authors provide an overview of various topics, including supervised and unsupervised learning, neural networks, support vector machines, and boosting. The second edition of the book includes new topics such as graphical models, random forests, and ensemble methods. The authors are renowned professors at Stanford University and have made significant contributions to the field. The book is dedicated to the families and parents of the authors. The preface to the second edition explains the updates and changes made to the book, while also addressing issues with colorblind readers and clarifying the origin of a quote. The book aims to explain important new ideas in learning using a statistical framework and hopes to be useful for researchers and practitioners in various fields. The book covers topics such as supervised learning, linear methods, kernel smoothing methods, model assessment and selection, statistical methods, boosting and neural networks, support vector machines, and unsupervised learning. The book provides examples and exercises for further study and practice and emphasizes the importance of statistical learning in various fields.'"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    chain_type=\"map_reduce\",\n",
    "    verbose=True,\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\u001b[1m> Entering new MapReduceDocumentsChain chain...\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Springer Series in Statistics\n",
      "Trevor Hastie\n",
      "Robert TibshiraniJerome FriedmanSpringer Series in Statistics\n",
      "The Elements of\n",
      "Statistical Learning\n",
      "Data Mining, Inference, and Prediction\n",
      "The Elements of Statistical LearningDuring the past decade there has been an explosion in computation and information tech-\n",
      "nology. With it have come vast amounts of data in a variety of fields such as medicine, biolo-gy, finance, and marketing. The challenge of understanding these data has led to the devel-opment of new tools in the field of statistics, and spawned new areas such as data mining,machine learning, and bioinformatics. Many of these tools have common underpinnings butare often expressed with different terminology. This book describes the important ideas inthese areas in a common conceptual framework. While the approach is statistical, theemphasis is on concepts rather than mathematics. Many examples are given, with a liberaluse of color graphics. It should be a valuable resource for statisticians and anyone interestedin data mining in science or industry. The book’s coverage is broad, from supervised learning(prediction) to unsupervised learning. The many topics include neural networks, supportvector machines, classification trees and boosting—the first comprehensive treatment of thistopic in any book.\n",
      "This major new edition features many topics not covered in the original, including graphical\n",
      "models, random forests, ensemble methods, least angle regression & path algorithms for thelasso, non-negative matrix factorization, and spectral clustering. There is also a chapter onmethods for “wide” data (p bigger than n), including multiple testing and false discovery rates.\n",
      "Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at\n",
      "Stanford University. They are prominent researchers in this area: Hastie and Tibshiranideveloped generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS andinvented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of thevery successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.\n",
      "›springer.comSTATISTICS\n",
      "isbn 978-0-387-84857-0Trevor Hastie • Robert Tibshirani • Jerome Friedman\n",
      "The Elements of Statictical Learning\n",
      "Hastie • Tibshirani • Friedman\n",
      "Second Edition\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "This is page v\n",
      "Printer: Opaque this\n",
      "To our parents:\n",
      "Valerie and Patrick Hastie\n",
      "Vera and Sami Tibshirani\n",
      "Florence and Harry Friedman\n",
      "and to our families:\n",
      "Samantha, Timothy, and Lynda\n",
      "Charlie, Ryan, Julie, and Cheryl\n",
      "Melanie, Dora, Monika, and Ildiko\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "vi\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "This is page vii\n",
      "Printer: Opaque this\n",
      "Preface to the Second Edition\n",
      "In God we trust, all others bring data.\n",
      "–William Edwards Deming (1900-1993)1\n",
      "We have been gratiﬁed by the popularity of the ﬁrst edition of The\n",
      "Elements of Statistical Learning. This, along with the fast pace of research\n",
      "in the statistical learning ﬁeld, motivated us to update our book with a\n",
      "second edition.\n",
      "We have added four new chapters and updated some of the existi ng\n",
      "chapters. Because many readers are familiar with the layout of the ﬁrst\n",
      "edition, we have tried to change it as little as possible. Her e is a summary\n",
      "of the main changes:\n",
      "1On the Web, this quote has been widely attributed to both Deming and R obert W.\n",
      "Hayden; however Professor Hayden told us that he can claim no credit for th is quote,\n",
      "and ironically we could ﬁnd no “data” conﬁrming that Deming actual ly said this.\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "viii Preface to the Second Edition\n",
      "Chapter What’s new\n",
      "1.Introduction\n",
      "2.Overview of Supervised Learning\n",
      "3.Linear Methods for Regression LAR algorithm and generaliza tions\n",
      "of the lasso\n",
      "4.Linear Methods for Classiﬁcation Lasso path for logistic re gression\n",
      "5.Basis Expansions and Regulariza-\n",
      "tionAdditional illustrations of RKHS\n",
      "6.Kernel Smoothing Methods\n",
      "7.Model Assessment and Selection Strengths and pitfalls of cr oss-\n",
      "validation\n",
      "8.Model Inference and Averaging\n",
      "9.Additive Models, Trees, and\n",
      "Related Methods\n",
      "10.Boosting and Additive Trees New example from ecology; some\n",
      "material split oﬀ to Chapter 16.\n",
      "11.Neural Networks Bayesian neural nets and the NIPS\n",
      "2003 challenge\n",
      "12.Support Vector Machines and\n",
      "Flexible DiscriminantsPath algorithm for SVM classiﬁer\n",
      "13.Prototype Methods and\n",
      "Nearest-Neighbors\n",
      "14.Unsupervised Learning Spectral clustering, kernel PCA,\n",
      "sparse PCA, non-negative matrix\n",
      "factorization archetypal analysis,\n",
      "nonlinear dimension reduction,\n",
      "Google page rank algorithm, a\n",
      "direct approach to ICA\n",
      "15.Random Forests New\n",
      "16.Ensemble Learning New\n",
      "17.Undirected Graphical Models New\n",
      "18.High-Dimensional Problems New\n",
      "Some further notes:\n",
      "•Our ﬁrst edition was unfriendly to colorblind readers; in pa rticular,\n",
      "we tended to favor red/greencontrasts which are particularly trou-\n",
      "blesome. We have changed the color palette in this edition to a large\n",
      "extent, replacing the above with an orange/bluecontrast.\n",
      "•We have changed the name of Chapter 6 from “Kernel Methods” to\n",
      "“Kernel Smoothing Methods”, to avoid confusion with the mac hine-\n",
      "learningkernelmethodthatisdiscussedinthecontextofsu pportvec-\n",
      "tor machines (Chapter 12) and more generally in Chapters 5 an d 14.\n",
      "•In the ﬁrst edition, the discussion of error-rate estimatio n in Chap-\n",
      "ter 7 was sloppy, as we did not clearly diﬀerentiate the notio ns of\n",
      "conditional error rates (conditional on the training set) a nd uncondi-\n",
      "tional rates. We have ﬁxed this in the new edition.\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Preface to the Second Edition ix\n",
      "•Chapters 15 and 16 follow naturally from Chapter 10, and the c hap-\n",
      "ters are probably best read in that order.\n",
      "•In Chapter 17, we have not attempted a comprehensive treatme nt\n",
      "of graphical models, and discuss only undirected models and some\n",
      "new methods for their estimation. Due to a lack of space, we ha ve\n",
      "speciﬁcally omitted coverage of directed graphical models .\n",
      "•Chapter 18 explores the “ p≫N” problem, which is learning in high-\n",
      "dimensional feature spaces. These problems arise in many ar eas, in-\n",
      "cluding genomic and proteomic studies, and document classi ﬁcation.\n",
      "We thank the many readers who have found the (too numerous) er rors in\n",
      "the ﬁrst edition. We apologize for those and have done our bes t to avoid er-\n",
      "rorsinthisnewedition.WethankMarkSegal,BalaRajaratna m,andLarry\n",
      "Wasserman for comments on some of the new chapters, and many S tanford\n",
      "graduate and post-doctoral students who oﬀered comments, i n particular\n",
      "Mohammed AlQuraishi, John Boik, Holger Hoeﬂing, Arian Male ki, Donal\n",
      "McMahon, Saharon Rosset, Babak Shababa, Daniela Witten, Ji Zhu and\n",
      "Hui Zou. We thank John Kimmel for his patience in guiding us th rough this\n",
      "new edition. RT dedicates this edition to the memory of Anna M cPhee.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "August 2008\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "x Preface to the Second Edition\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "This is page xi\n",
      "Printer: Opaque this\n",
      "Preface to the First Edition\n",
      "We are drowning in information and starving for knowledge.\n",
      "–Rutherford D. Roger\n",
      "The ﬁeld of Statistics is constantly challenged by the probl ems that science\n",
      "andindustrybringstoitsdoor.Intheearlydays,theseprob lemsoftencame\n",
      "from agricultural and industrial experiments and were rela tively small in\n",
      "scope. With the advent of computers and the information age, statistical\n",
      "problems have exploded both in size and complexity. Challen ges in the\n",
      "areas of data storage, organization and searching have led t o the new ﬁeld\n",
      "of “data mining”; statistical and computational problems i n biology and\n",
      "medicine have created “bioinformatics.” Vast amounts of da ta are being\n",
      "generated in many ﬁelds, and the statistician’s job is to mak e sense of it\n",
      "all: to extract important patterns and trends, and understa nd “what the\n",
      "data says.” We call this learning from data .\n",
      "The challenges in learning from data have led to a revolution in the sta-\n",
      "tisticalsciences.Sincecomputationplayssuchakeyrole, itisnotsurprising\n",
      "that much of this new development has been done by researcher s in other\n",
      "ﬁelds such as computer science and engineering.\n",
      "The learning problems that we consider can be roughly catego rized as\n",
      "eithersupervised orunsupervised . In supervised learning, the goal is to pre-\n",
      "dict the value of an outcome measure based on a number of input measures;\n",
      "in unsupervised learning, there is no outcome measure, and t he goal is to\n",
      "describe the associations and patterns among a set of input m easures.\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "xii Preface to the First Edition\n",
      "This book is our attempt to bring together many of the importa nt new\n",
      "ideas in learning, and explain them in a statistical framewo rk. While some\n",
      "mathematical details are needed, we emphasize the methods a nd their con-\n",
      "ceptual underpinnings rather than their theoretical prope rties. As a result,\n",
      "we hope that this book will appeal not just to statisticians b ut also to\n",
      "researchers and practitioners in a wide variety of ﬁelds.\n",
      "Just as we have learned a great deal from researchers outside of the ﬁeld\n",
      "of statistics, our statistical viewpoint may help others to better understand\n",
      "diﬀerent aspects of learning:\n",
      "There is no true interpretation of anything; interpretatio n is a\n",
      "vehicle in the service of human comprehension. The value of\n",
      "interpretation is in enabling others to fruitfully think ab out an\n",
      "idea.\n",
      "–Andreas Buja\n",
      "We would like to acknowledge the contribution of many people to the\n",
      "conception and completion of this book. David Andrews, Leo B reiman,\n",
      "Andreas Buja, John Chambers, Bradley Efron, Geoﬀrey Hinton , Werner\n",
      "Stuetzle, and John Tukey have greatly inﬂuenced our careers . Balasub-\n",
      "ramanian Narasimhan gave us advice and help on many computat ional\n",
      "problems, and maintained an excellent computing environme nt. Shin-Ho\n",
      "Bang helped in the production of a number of the ﬁgures. Lee Wi lkinson\n",
      "gavevaluabletipsoncolorproduction.IlanaBelitskaya,E vaCantoni,Maya\n",
      "Gupta,MichaelJordan,ShantiGopatam,RadfordNeal,Jorge Picazo,Bog-\n",
      "dan Popescu, Olivier Renaud, Saharon Rosset, John Storey, J i Zhu, Mu\n",
      "Zhu, two reviewers and many students read parts of the manusc ript and\n",
      "oﬀered helpful suggestions. John Kimmel was supportive, pa tient and help-\n",
      "ful at every phase; MaryAnn Brickner and Frank Ganz headed a s uperb\n",
      "production team at Springer. Trevor Hastie would like to tha nk the statis-\n",
      "tics department at the University of Cape Town for their hosp itality during\n",
      "the ﬁnal stages of this book. We gratefully acknowledge NSF a nd NIH for\n",
      "their support of this work. Finally, we would like to thank ou r families and\n",
      "our parents for their love and support.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "May 2001\n",
      "The quiet statisticians have changed our world; not by disco v-\n",
      "ering new facts or technical developments, but by changing t he\n",
      "ways that we reason, experiment and form our opinions ....\n",
      "–Ian Hacking\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "This is page xiii\n",
      "Printer: Opaque this\n",
      "Contents\n",
      "Preface to the Second Edition vii\n",
      "Preface to the First Edition xi\n",
      "1 Introduction 1\n",
      "2 Overview of Supervised Learning 9\n",
      "2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9\n",
      "2.2 Variable Types and Terminology . . . . . . . . . . . . . . 9\n",
      "2.3 Two Simple Approaches to Prediction:\n",
      "Least Squares and Nearest Neighbors . . . . . . . . . . . 11\n",
      "2.3.1 Linear Models and Least Squares . . . . . . . . 11\n",
      "2.3.2 Nearest-Neighbor Methods . . . . . . . . . . . . 14\n",
      "2.3.3 From Least Squares to Nearest Neighbors . . . . 16\n",
      "2.4 Statistical Decision Theory . . . . . . . . . . . . . . . . . 18\n",
      "2.5 Local Methods in High Dimensions . . . . . . . . . . . . . 22\n",
      "2.6 Statistical Models, Supervised Learning\n",
      "and Function Approximation . . . . . . . . . . . . . . . . 28\n",
      "2.6.1 A Statistical Model\n",
      "for the Joint Distribution Pr( X,Y) . . . . . . . 28\n",
      "2.6.2 Supervised Learning . . . . . . . . . . . . . . . . 29\n",
      "2.6.3 Function Approximation . . . . . . . . . . . . . 29\n",
      "2.7 Structured Regression Models . . . . . . . . . . . . . . . 32\n",
      "2.7.1 Diﬃculty of the Problem . . . . . . . . . . . . . 32\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "xiv Contents\n",
      "2.8 Classes of Restricted Estimators . . . . . . . . . . . . . . 33\n",
      "2.8.1 Roughness Penalty and Bayesian Methods . . . 34\n",
      "2.8.2 Kernel Methods and Local Regression . . . . . . 34\n",
      "2.8.3 Basis Functions and Dictionary Methods . . . . 35\n",
      "2.9 Model Selection and the Bias–Variance Tradeoﬀ . . . . . 37\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "3 Linear Methods for Regression 43\n",
      "3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43\n",
      "3.2 Linear Regression Models and Least Squares . . . . . . . 44\n",
      "3.2.1 Example: Prostate Cancer . . . . . . . . . . . . 49\n",
      "3.2.2 The Gauss–Markov Theorem . . . . . . . . . . . 51\n",
      "3.2.3 Multiple Regression\n",
      "from Simple Univariate Regression . . . . . . . . 52\n",
      "3.2.4 Multiple Outputs . . . . . . . . . . . . . . . . . 56\n",
      "3.3 Subset Selection . . . . . . . . . . . . . . . . . . . . . . . 57\n",
      "3.3.1 Best-Subset Selection . . . . . . . . . . . . . . . 57\n",
      "3.3.2 Forward- and Backward-Stepwise Selection . . . 58\n",
      "3.3.3 Forward-Stagewise Regression . . . . . . . . . . 60\n",
      "3.3.4 Prostate Cancer Data Example (Continued) . . 61\n",
      "3.4 Shrinkage Methods . . . . . . . . . . . . . . . . . . . . . . 61\n",
      "3.4.1 Ridge Regression . . . . . . . . . . . . . . . . . 61\n",
      "3.4.2 The Lasso . . . . . . . . . . . . . . . . . . . . . 68\n",
      "3.4.3 Discussion: Subset Selection, Ridge Regression\n",
      "and the Lasso . . . . . . . . . . . . . . . . . . . 69\n",
      "3.4.4 Least Angle Regression . . . . . . . . . . . . . . 73\n",
      "3.5 Methods Using Derived Input Directions . . . . . . . . . 79\n",
      "3.5.1 Principal Components Regression . . . . . . . . 79\n",
      "3.5.2 Partial Least Squares . . . . . . . . . . . . . . . 80\n",
      "3.6 Discussion: A Comparison of the Selection\n",
      "and Shrinkage Methods . . . . . . . . . . . . . . . . . . . 82\n",
      "3.7 Multiple Outcome Shrinkage and Selection . . . . . . . . 84\n",
      "3.8 More on the Lasso and Related Path Algorithms . . . . . 86\n",
      "3.8.1 Incremental Forward Stagewise Regression . . . 86\n",
      "3.8.2 Piecewise-Linear Path Algorithms . . . . . . . . 89\n",
      "3.8.3 The Dantzig Selector . . . . . . . . . . . . . . . 89\n",
      "3.8.4 The Grouped Lasso . . . . . . . . . . . . . . . . 90\n",
      "3.8.5 Further Properties of the Lasso . . . . . . . . . . 91\n",
      "3.8.6 Pathwise Coordinate Optimization . . . . . . . . 92\n",
      "3.9 Computational Considerations . . . . . . . . . . . . . . . 93\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Contents xv\n",
      "4 Linear Methods for Classiﬁcation 101\n",
      "4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101\n",
      "4.2 Linear Regression of an Indicator Matrix . . . . . . . . . 103\n",
      "4.3 Linear Discriminant Analysis . . . . . . . . . . . . . . . . 106\n",
      "4.3.1 Regularized Discriminant Analysis . . . . . . . . 112\n",
      "4.3.2 Computations for LDA . . . . . . . . . . . . . . 113\n",
      "4.3.3 Reduced-Rank Linear Discriminant Analysis . . 113\n",
      "4.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 119\n",
      "4.4.1 Fitting Logistic Regression Models . . . . . . . . 120\n",
      "4.4.2 Example: South African Heart Disease . . . . . 122\n",
      "4.4.3 Quadratic Approximations and Inference . . . . 124\n",
      "4.4.4L1Regularized Logistic Regression . . . . . . . . 125\n",
      "4.4.5 Logistic Regression or LDA? . . . . . . . . . . . 127\n",
      "4.5 Separating Hyperplanes . . . . . . . . . . . . . . . . . . . 129\n",
      "4.5.1 Rosenblatt’s Perceptron Learning Algorithm . . 130\n",
      "4.5.2 Optimal Separating Hyperplanes . . . . . . . . . 132\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "5 Basis Expansions and Regularization 139\n",
      "5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 139\n",
      "5.2 Piecewise Polynomials and Splines . . . . . . . . . . . . . 141\n",
      "5.2.1 Natural Cubic Splines . . . . . . . . . . . . . . . 144\n",
      "5.2.2 Example:SouthAfricanHeartDisease(Continued)146\n",
      "5.2.3 Example: Phoneme Recognition . . . . . . . . . 148\n",
      "5.3 Filtering and Feature Extraction . . . . . . . . . . . . . . 150\n",
      "5.4 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . 151\n",
      "5.4.1 Degrees of Freedom and Smoother Matrices . . . 153\n",
      "5.5 Automatic Selection of the Smoothing Parameters . . . . 15 6\n",
      "5.5.1 Fixing the Degrees of Freedom . . . . . . . . . . 158\n",
      "5.5.2 The Bias–Variance Tradeoﬀ . . . . . . . . . . . . 158\n",
      "5.6 Nonparametric Logistic Regression . . . . . . . . . . . . . 161\n",
      "5.7 Multidimensional Splines . . . . . . . . . . . . . . . . . . 162\n",
      "5.8 Regularization and Reproducing Kernel Hilbert Spaces . 167\n",
      "5.8.1 Spaces of Functions Generated by Kernels . . . 168\n",
      "5.8.2 Examples of RKHS . . . . . . . . . . . . . . . . 170\n",
      "5.9 Wavelet Smoothing . . . . . . . . . . . . . . . . . . . . . 174\n",
      "5.9.1 Wavelet Bases and the Wavelet Transform . . . 176\n",
      "5.9.2 Adaptive Wavelet Filtering . . . . . . . . . . . . 179\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Appendix: Computational Considerations for Splines . . . . . . 186\n",
      "Appendix:B-splines . . . . . . . . . . . . . . . . . . . . . 186\n",
      "Appendix: Computations for Smoothing Splines . . . . . 189\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "xvi Contents\n",
      "6 Kernel Smoothing Methods 191\n",
      "6.1 One-Dimensional Kernel Smoothers . . . . . . . . . . . . 192\n",
      "6.1.1 Local Linear Regression . . . . . . . . . . . . . . 194\n",
      "6.1.2 Local Polynomial Regression . . . . . . . . . . . 197\n",
      "6.2 Selecting the Width of the Kernel . . . . . . . . . . . . . 198\n",
      "6.3 Local Regression in IRp. . . . . . . . . . . . . . . . . . . 200\n",
      "6.4 Structured Local Regression Models in IRp. . . . . . . . 201\n",
      "6.4.1 Structured Kernels . . . . . . . . . . . . . . . . . 203\n",
      "6.4.2 Structured Regression Functions . . . . . . . . . 203\n",
      "6.5 Local Likelihood and Other Models . . . . . . . . . . . . 205\n",
      "6.6 Kernel Density Estimation and Classiﬁcation . . . . . . . 20 8\n",
      "6.6.1 Kernel Density Estimation . . . . . . . . . . . . 208\n",
      "6.6.2 Kernel Density Classiﬁcation . . . . . . . . . . . 210\n",
      "6.6.3 The Naive Bayes Classiﬁer . . . . . . . . . . . . 210\n",
      "6.7 Radial Basis Functions and Kernels . . . . . . . . . . . . 212\n",
      "6.8 Mixture Models for Density Estimation and Classiﬁcatio n 214\n",
      "6.9 Computational Considerations . . . . . . . . . . . . . . . 216\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "7 Model Assessment and Selection 219\n",
      "7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 219\n",
      "7.2 Bias, Variance and Model Complexity . . . . . . . . . . . 219\n",
      "7.3 The Bias–Variance Decomposition . . . . . . . . . . . . . 223\n",
      "7.3.1 Example: Bias–Variance Tradeoﬀ . . . . . . . . 226\n",
      "7.4 Optimism of the Training Error Rate . . . . . . . . . . . 228\n",
      "7.5 Estimates of In-Sample Prediction Error . . . . . . . . . . 230\n",
      "7.6 The Eﬀective Number of Parameters . . . . . . . . . . . . 232\n",
      "7.7 The Bayesian Approach and BIC . . . . . . . . . . . . . . 233\n",
      "7.8 Minimum Description Length . . . . . . . . . . . . . . . . 235\n",
      "7.9 Vapnik–Chervonenkis Dimension . . . . . . . . . . . . . . 237\n",
      "7.9.1 Example (Continued) . . . . . . . . . . . . . . . 239\n",
      "7.10 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . 241\n",
      "7.10.1K-Fold Cross-Validation . . . . . . . . . . . . . 241\n",
      "7.10.2 The Wrong and Right Way\n",
      "to Do Cross-validation . . . . . . . . . . . . . . . 245\n",
      "7.10.3 Does Cross-Validation Really Work? . . . . . . . 247\n",
      "7.11 Bootstrap Methods . . . . . . . . . . . . . . . . . . . . . 249\n",
      "7.11.1 Example (Continued) . . . . . . . . . . . . . . . 252\n",
      "7.12 Conditional or Expected Test Error? . . . . . . . . . . . . 254\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "8 Model Inference and Averaging 261\n",
      "8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 261\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Contents xvii\n",
      "8.2 The Bootstrap and Maximum Likelihood Methods . . . . 261\n",
      "8.2.1 A Smoothing Example . . . . . . . . . . . . . . 261\n",
      "8.2.2 Maximum Likelihood Inference . . . . . . . . . . 265\n",
      "8.2.3 Bootstrap versus Maximum Likelihood . . . . . 267\n",
      "8.3 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . 267\n",
      "8.4 Relationship Between the Bootstrap\n",
      "and Bayesian Inference . . . . . . . . . . . . . . . . . . . 271\n",
      "8.5 The EM Algorithm . . . . . . . . . . . . . . . . . . . . . 272\n",
      "8.5.1 Two-Component Mixture Model . . . . . . . . . 272\n",
      "8.5.2 The EM Algorithm in General . . . . . . . . . . 276\n",
      "8.5.3 EM as a Maximization–Maximization Procedure 277\n",
      "8.6 MCMC for Sampling from the Posterior . . . . . . . . . . 279\n",
      "8.7 Bagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282\n",
      "8.7.1 Example: Trees with Simulated Data . . . . . . 283\n",
      "8.8 Model Averaging and Stacking . . . . . . . . . . . . . . . 288\n",
      "8.9 Stochastic Search: Bumping . . . . . . . . . . . . . . . . . 290\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 292\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293\n",
      "9 Additive Models, Trees, and Related Methods 295\n",
      "9.1 Generalized Additive Models . . . . . . . . . . . . . . . . 295\n",
      "9.1.1 Fitting Additive Models . . . . . . . . . . . . . . 297\n",
      "9.1.2 Example: Additive Logistic Regression . . . . . 299\n",
      "9.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . 304\n",
      "9.2 Tree-Based Methods . . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.1 Background . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.2 Regression Trees . . . . . . . . . . . . . . . . . . 307\n",
      "9.2.3 Classiﬁcation Trees . . . . . . . . . . . . . . . . 308\n",
      "9.2.4 Other Issues . . . . . . . . . . . . . . . . . . . . 310\n",
      "9.2.5 Spam Example (Continued) . . . . . . . . . . . 313\n",
      "9.3 PRIM: Bump Hunting . . . . . . . . . . . . . . . . . . . . 317\n",
      "9.3.1 Spam Example (Continued) . . . . . . . . . . . 320\n",
      "9.4 MARS: Multivariate Adaptive Regression Splines . . . . . 3 21\n",
      "9.4.1 Spam Example (Continued) . . . . . . . . . . . 326\n",
      "9.4.2 Example (Simulated Data) . . . . . . . . . . . . 327\n",
      "9.4.3 Other Issues . . . . . . . . . . . . . . . . . . . . 328\n",
      "9.5 Hierarchical Mixtures of Experts . . . . . . . . . . . . . . 329\n",
      "9.6 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . 332\n",
      "9.7 Computational Considerations . . . . . . . . . . . . . . . 334\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 334\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335\n",
      "10 Boosting and Additive Trees 337\n",
      "10.1 Boosting Methods . . . . . . . . . . . . . . . . . . . . . . 337\n",
      "10.1.1 Outline of This Chapter . . . . . . . . . . . . . . 340\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
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      "xviii Contents\n",
      "10.2 Boosting Fits an Additive Model . . . . . . . . . . . . . . 341\n",
      "10.3 Forward Stagewise Additive Modeling . . . . . . . . . . . 342\n",
      "10.4 Exponential Loss and AdaBoost . . . . . . . . . . . . . . 343\n",
      "10.5 Why Exponential Loss? . . . . . . . . . . . . . . . . . . . 345\n",
      "10.6 Loss Functions and Robustness . . . . . . . . . . . . . . . 346\n",
      "10.7 “Oﬀ-the-Shelf” Procedures for Data Mining . . . . . . . . 35 0\n",
      "10.8 Example: Spam Data . . . . . . . . . . . . . . . . . . . . 352\n",
      "10.9 Boosting Trees . . . . . . . . . . . . . . . . . . . . . . . . 353\n",
      "10.10 Numerical Optimization via Gradient Boosting . . . . . . 358\n",
      "10.10.1 Steepest Descent . . . . . . . . . . . . . . . . . . 358\n",
      "10.10.2 Gradient Boosting . . . . . . . . . . . . . . . . . 359\n",
      "10.10.3 Implementations of Gradient Boosting . . . . . . 360\n",
      "10.11 Right-Sized Trees for Boosting . . . . . . . . . . . . . . . 361\n",
      "10.12 Regularization . . . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.1 Shrinkage . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.2 Subsampling . . . . . . . . . . . . . . . . . . . . 365\n",
      "10.13 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 367\n",
      "10.13.1 Relative Importance of Predictor Variables . . . 367\n",
      "10.13.2 Partial Dependence Plots . . . . . . . . . . . . . 369\n",
      "10.14 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . 371\n",
      "10.14.1 California Housing . . . . . . . . . . . . . . . . . 371\n",
      "10.14.2 New Zealand Fish . . . . . . . . . . . . . . . . . 375\n",
      "10.14.3 Demographics Data . . . . . . . . . . . . . . . . 379\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 380\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384\n",
      "11 Neural Networks 389\n",
      "11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 389\n",
      "11.2 Projection Pursuit Regression . . . . . . . . . . . . . . . 389\n",
      "11.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 392\n",
      "11.4 Fitting Neural Networks . . . . . . . . . . . . . . . . . . . 395\n",
      "11.5 Some Issues in Training Neural Networks . . . . . . . . . 397\n",
      "11.5.1 Starting Values . . . . . . . . . . . . . . . . . . . 397\n",
      "11.5.2 Overﬁtting . . . . . . . . . . . . . . . . . . . . . 398\n",
      "11.5.3 Scaling of the Inputs . . . . . . . . . . . . . . . 398\n",
      "11.5.4 Number of Hidden Units and Layers . . . . . . . 400\n",
      "11.5.5 Multiple Minima . . . . . . . . . . . . . . . . . . 400\n",
      "11.6 Example: Simulated Data . . . . . . . . . . . . . . . . . . 401\n",
      "11.7 Example: ZIP Code Data . . . . . . . . . . . . . . . . . . 404\n",
      "11.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 408\n",
      "11.9 Bayesian Neural Nets and the NIPS 2003 Challenge . . . 409\n",
      "11.9.1 Bayes, Boosting and Bagging . . . . . . . . . . . 410\n",
      "11.9.2 Performance Comparisons . . . . . . . . . . . . 412\n",
      "11.10 Computational Considerations . . . . . . . . . . . . . . . 414\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Contents xix\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "12 Support Vector Machines and\n",
      "Flexible Discriminants 417\n",
      "12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 417\n",
      "12.2 The Support Vector Classiﬁer . . . . . . . . . . . . . . . . 417\n",
      "12.2.1 Computing the Support Vector Classiﬁer . . . . 420\n",
      "12.2.2 Mixture Example (Continued) . . . . . . . . . . 421\n",
      "12.3 Support Vector Machines and Kernels . . . . . . . . . . . 423\n",
      "12.3.1 Computing the SVM for Classiﬁcation . . . . . . 423\n",
      "12.3.2 The SVM as a Penalization Method . . . . . . . 426\n",
      "12.3.3 Function Estimation and Reproducing Kernels . 428\n",
      "12.3.4 SVMs and the Curse of Dimensionality . . . . . 431\n",
      "12.3.5 A Path Algorithm for the SVM Classiﬁer . . . . 432\n",
      "12.3.6 Support Vector Machines for Regression . . . . . 434\n",
      "12.3.7 Regression and Kernels . . . . . . . . . . . . . . 436\n",
      "12.3.8 Discussion . . . . . . . . . . . . . . . . . . . . . 438\n",
      "12.4 Generalizing Linear Discriminant Analysis . . . . . . . . 4 38\n",
      "12.5 Flexible Discriminant Analysis . . . . . . . . . . . . . . . 440\n",
      "12.5.1 Computing the FDA Estimates . . . . . . . . . . 444\n",
      "12.6 Penalized Discriminant Analysis . . . . . . . . . . . . . . 446\n",
      "12.7 Mixture Discriminant Analysis . . . . . . . . . . . . . . . 449\n",
      "12.7.1 Example: Waveform Data . . . . . . . . . . . . . 451\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "13 Prototype Methods and Nearest-Neighbors 459\n",
      "13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2 Prototype Methods . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2.1K-means Clustering . . . . . . . . . . . . . . . . 460\n",
      "13.2.2 Learning Vector Quantization . . . . . . . . . . 462\n",
      "13.2.3 Gaussian Mixtures . . . . . . . . . . . . . . . . . 463\n",
      "13.3k-Nearest-Neighbor Classiﬁers . . . . . . . . . . . . . . . 463\n",
      "13.3.1 Example: A Comparative Study . . . . . . . . . 468\n",
      "13.3.2 Example: k-Nearest-Neighbors\n",
      "and Image Scene Classiﬁcation . . . . . . . . . . 470\n",
      "13.3.3 Invariant Metrics and Tangent Distance . . . . . 471\n",
      "13.4 Adaptive Nearest-Neighbor Methods . . . . . . . . . . . . 475\n",
      "13.4.1 Example . . . . . . . . . . . . . . . . . . . . . . 478\n",
      "13.4.2 Global Dimension Reduction\n",
      "for Nearest-Neighbors . . . . . . . . . . . . . . . 479\n",
      "13.5 Computational Considerations . . . . . . . . . . . . . . . 480\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "xx Contents\n",
      "14 Unsupervised Learning 485\n",
      "14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 485\n",
      "14.2 Association Rules . . . . . . . . . . . . . . . . . . . . . . 487\n",
      "14.2.1 Market Basket Analysis . . . . . . . . . . . . . . 488\n",
      "14.2.2 The Apriori Algorithm . . . . . . . . . . . . . . 489\n",
      "14.2.3 Example: Market Basket Analysis . . . . . . . . 492\n",
      "14.2.4 Unsupervised as Supervised Learning . . . . . . 495\n",
      "14.2.5 Generalized Association Rules . . . . . . . . . . 497\n",
      "14.2.6 Choice of Supervised Learning Method . . . . . 499\n",
      "14.2.7 Example: Market Basket Analysis (Continued) . 499\n",
      "14.3 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . 501\n",
      "14.3.1 Proximity Matrices . . . . . . . . . . . . . . . . 503\n",
      "14.3.2 Dissimilarities Based on Attributes . . . . . . . 503\n",
      "14.3.3 Object Dissimilarity . . . . . . . . . . . . . . . . 505\n",
      "14.3.4 Clustering Algorithms . . . . . . . . . . . . . . . 507\n",
      "14.3.5 Combinatorial Algorithms . . . . . . . . . . . . 507\n",
      "14.3.6K-means . . . . . . . . . . . . . . . . . . . . . . 509\n",
      "14.3.7 Gaussian Mixtures as Soft K-means Clustering . 510\n",
      "14.3.8 Example: Human Tumor Microarray Data . . . 512\n",
      "14.3.9 Vector Quantization . . . . . . . . . . . . . . . . 514\n",
      "14.3.10K-medoids . . . . . . . . . . . . . . . . . . . . . 515\n",
      "14.3.11 Practical Issues . . . . . . . . . . . . . . . . . . 518\n",
      "14.3.12 Hierarchical Clustering . . . . . . . . . . . . . . 520\n",
      "14.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . 528\n",
      "14.5 Principal Components, Curves and Surfaces . . . . . . . . 53 4\n",
      "14.5.1 Principal Components . . . . . . . . . . . . . . . 534\n",
      "14.5.2 Principal Curves and Surfaces . . . . . . . . . . 541\n",
      "14.5.3 Spectral Clustering . . . . . . . . . . . . . . . . 544\n",
      "14.5.4 Kernel Principal Components . . . . . . . . . . . 547\n",
      "14.5.5 Sparse Principal Components . . . . . . . . . . . 550\n",
      "14.6 Non-negative Matrix Factorization . . . . . . . . . . . . . 553\n",
      "14.6.1 Archetypal Analysis . . . . . . . . . . . . . . . . 554\n",
      "14.7 Independent Component Analysis\n",
      "and Exploratory Projection Pursuit . . . . . . . . . . . . 557\n",
      "14.7.1 Latent Variables and Factor Analysis . . . . . . 558\n",
      "14.7.2 Independent Component Analysis . . . . . . . . 560\n",
      "14.7.3 Exploratory Projection Pursuit . . . . . . . . . . 565\n",
      "14.7.4 A Direct Approach to ICA . . . . . . . . . . . . 565\n",
      "14.8 Multidimensional Scaling . . . . . . . . . . . . . . . . . . 570\n",
      "14.9 Nonlinear Dimension Reduction\n",
      "and Local Multidimensional Scaling . . . . . . . . . . . . 572\n",
      "14.10 The Google PageRank Algorithm . . . . . . . . . . . . . 576\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 578\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "Contents xxi\n",
      "15 Random Forests 587\n",
      "15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 587\n",
      "15.2 Deﬁnition of Random Forests . . . . . . . . . . . . . . . . 587\n",
      "15.3 Details of Random Forests . . . . . . . . . . . . . . . . . 592\n",
      "15.3.1 Out of Bag Samples . . . . . . . . . . . . . . . . 592\n",
      "15.3.2 Variable Importance . . . . . . . . . . . . . . . . 593\n",
      "15.3.3 Proximity Plots . . . . . . . . . . . . . . . . . . 595\n",
      "15.3.4 Random Forests and Overﬁtting . . . . . . . . . 596\n",
      "15.4 Analysis of Random Forests . . . . . . . . . . . . . . . . . 597\n",
      "15.4.1 Variance and the De-Correlation Eﬀect . . . . . 597\n",
      "15.4.2 Bias . . . . . . . . . . . . . . . . . . . . . . . . . 600\n",
      "15.4.3 Adaptive Nearest Neighbors . . . . . . . . . . . 601\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 602\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603\n",
      "16 Ensemble Learning 605\n",
      "16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 605\n",
      "16.2 Boosting and Regularization Paths . . . . . . . . . . . . . 607\n",
      "16.2.1 Penalized Regression . . . . . . . . . . . . . . . 607\n",
      "16.2.2 The “Bet on Sparsity” Principle . . . . . . . . . 610\n",
      "16.2.3 Regularization Paths, Over-ﬁtting and Margins . 613\n",
      "16.3 Learning Ensembles . . . . . . . . . . . . . . . . . . . . . 616\n",
      "16.3.1 Learning a Good Ensemble . . . . . . . . . . . . 617\n",
      "16.3.2 Rule Ensembles . . . . . . . . . . . . . . . . . . 622\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 623\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624\n",
      "17 Undirected Graphical Models 625\n",
      "17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 625\n",
      "17.2 Markov Graphs and Their Properties . . . . . . . . . . . 627\n",
      "17.3 Undirected Graphical Models for Continuous Variables . 630\n",
      "17.3.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 631\n",
      "17.3.2 Estimation of the Graph Structure . . . . . . . . 635\n",
      "17.4 Undirected Graphical Models for Discrete Variables . . . 638\n",
      "17.4.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 639\n",
      "17.4.2 Hidden Nodes . . . . . . . . . . . . . . . . . . . 641\n",
      "17.4.3 Estimation of the Graph Structure . . . . . . . . 642\n",
      "17.4.4 Restricted Boltzmann Machines . . . . . . . . . 643\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645\n",
      "18 High-Dimensional Problems: p≫N 649\n",
      "18.1 When pis Much Bigger than N. . . . . . . . . . . . . . 649\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "xxii Contents\n",
      "18.2 Diagonal Linear Discriminant Analysis\n",
      "and Nearest Shrunken Centroids . . . . . . . . . . . . . . 651\n",
      "18.3 Linear Classiﬁers with Quadratic Regularization . . . . . 654\n",
      "18.3.1 Regularized Discriminant Analysis . . . . . . . . 656\n",
      "18.3.2 Logistic Regression\n",
      "with Quadratic Regularization . . . . . . . . . . 657\n",
      "18.3.3 The Support Vector Classiﬁer . . . . . . . . . . 657\n",
      "18.3.4 Feature Selection . . . . . . . . . . . . . . . . . . 658\n",
      "18.3.5 Computational Shortcuts When p≫N. . . . . 659\n",
      "18.4 Linear Classiﬁers with L1Regularization . . . . . . . . . 661\n",
      "18.4.1 Application of Lasso\n",
      "to Protein Mass Spectroscopy . . . . . . . . . . 664\n",
      "18.4.2 The Fused Lasso for Functional Data . . . . . . 666\n",
      "18.5 Classiﬁcation When Features are Unavailable . . . . . . . 6 68\n",
      "18.5.1 Example: String Kernels\n",
      "and Protein Classiﬁcation . . . . . . . . . . . . . 668\n",
      "18.5.2 Classiﬁcation and Other Models Using\n",
      "Inner-Product Kernels and Pairwise Distances . 670\n",
      "18.5.3 Example: Abstracts Classiﬁcation . . . . . . . . 672\n",
      "18.6 High-Dimensional Regression:\n",
      "Supervised Principal Components . . . . . . . . . . . . . 674\n",
      "18.6.1 Connection to Latent-Variable Modeling . . . . 678\n",
      "18.6.2 Relationship with Partial Least Squares . . . . . 680\n",
      "18.6.3 Pre-Conditioning for Feature Selection . . . . . 681\n",
      "18.7 Feature Assessment and the Multiple-Testing Problem . . 683\n",
      "18.7.1 The False Discovery Rate . . . . . . . . . . . . . 687\n",
      "18.7.2 Asymmetric Cutpoints and the SAM Procedure 690\n",
      "18.7.3 A Bayesian Interpretation of the FDR . . . . . . 692\n",
      "18.8 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . 693\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694\n",
      "References 699\n",
      "Author Index 729\n",
      "Index 737\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of documents\n",
      "\n",
      "This is page 1\n",
      "Printer: Opaque this\n",
      "1\n",
      "Introduction\n",
      "Statistical learning plays a key role in many areas of science, ﬁnance and\n",
      "industry. Here are some examples of learning problems:\n",
      "•Predict whether a patient, hospitalized due to a heart attac k, will\n",
      "have a second heart attack. The prediction is to be based on de mo-\n",
      "graphic, diet and clinical measurements for that patient.\n",
      "•Predict the price of a stock in 6 months from now, on the basis o f\n",
      "company performance measures and economic data.\n",
      "•Identify the numbers in a handwritten ZIP code, from a digiti zed\n",
      "image.\n",
      "•Estimate the amount of glucose in the blood of a diabetic pers on,\n",
      "from the infrared absorption spectrum of that person’s bloo d.\n",
      "•Identify the risk factors for prostate cancer, based on clin ical and\n",
      "demographic variables.\n",
      "The science of learning plays a key role in the ﬁelds of statis tics, data\n",
      "mining and artiﬁcial intelligence, intersecting with area s of engineering and\n",
      "other disciplines.\n",
      "This book is about learning from data. In a typical scenario, we have\n",
      "an outcome measurement, usually quantitative (such as a sto ck price) or\n",
      "categorical (such as heart attack/no heart attack), that we wish to predict\n",
      "based on a set of features (such as diet and clinical measurements). We\n",
      "have atraining set of data, in which we observe the outcome and feature\n",
      "\n",
      "Based on this list of docs, please identify the main themes\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "The following is a set of summaries:\n",
      "\n",
      "The main themes in this set of documents are:\n",
      "\n",
      "1. Statistics: The documents discuss the field of statistics and its importance in understanding and analyzing vast amounts of data in various fields.\n",
      "\n",
      "2. Data Mining and Machine Learning: The documents highlight the development of new tools and areas such as data mining and machine learning, which are used to extract insights and patterns from large datasets.\n",
      "\n",
      "3. Conceptual Framework: The emphasis is on understanding key concepts rather than focusing on mathematical details.\n",
      "\n",
      "4. Topics and Techniques: The documents mention several topics and techniques used in statistical learning, such as neural networks, support vector machines, classification trees, boosting, graphical models, random forests, ensemble methods, and more.\n",
      "\n",
      "5. Authors' Background: The authors' expertise and contributions in the field of statistics and data mining are mentioned, including their work on generalized additive models, the lasso, statistical modeling software, and various data-mining tools.\n",
      "\n",
      "Based on the list of documents provided, the main themes that can be identified are:\n",
      "\n",
      "1. Acknowledgement and gratitude towards parents: The first document is addressed to the parents of the individuals mentioned, expressing thanks and appreciation.\n",
      "\n",
      "2. Acknowledgement and gratitude towards families: The second document extends thanks to the broader family, specifically mentioning the names of individuals within each family.\n",
      "\n",
      "3. Familial relationships: The names mentioned in both documents indicate a focus on family connections and relationships.\n",
      "\n",
      "4. Personal connections and relationships: The second document mentions the names of individuals within each family, suggesting a focus on personal connections and relationships within the broader family context.\n",
      "\n",
      "Overall, the main themes revolve around appreciation for and recognition of familial and personal relationships.\n",
      "\n",
      "Unfortunately, without any content or information about the documents, it is not possible to identify the main themes. Could you please provide more details or context about the documents?\n",
      "\n",
      "Based on the provided documents, the main themes can be identified as follows:\n",
      "1. The popularity of the first edition of \"The Elements of Statistical Learning\" and the motivation to update it with a second edition.\n",
      "2. The fast pace of research in the statistical learning field.\n",
      "3. The addition of four new chapters and updates to existing chapters in the second edition.\n",
      "4. The attempt to keep the layout of the first edition as unchanged as possible.\n",
      "5. The quote by William Edwards Deming about trusting in God and bringing data.\n",
      "\n",
      "Based on the list of documents, the main themes are:\n",
      "1. Introduction and overview of supervised learning\n",
      "2. Linear methods for regression and classification\n",
      "3. Basis expansions and regularization techniques\n",
      "4. Kernel smoothing methods\n",
      "5. Model assessment and selection\n",
      "6. Model inference and averaging\n",
      "7. Additive models, trees, and related methods\n",
      "8. Boosting and additive trees\n",
      "9. Neural networks\n",
      "10. Support vector machines and flexible discriminants\n",
      "11. Prototype methods and nearest-neighbors\n",
      "12. Unsupervised learning\n",
      "13. Random forests\n",
      "14. Ensemble learning\n",
      "15. Undirected graphical models\n",
      "16. High-dimensional problems\n",
      "\n",
      "Some additional notes:\n",
      "- Color palette changes for better readability for colorblind readers\n",
      "- Renaming of a chapter to avoid confusion with another method\n",
      "- Corrections made to error-rate estimation discussion in the first edition\n",
      "\n",
      "Based on this list of documents, the main themes of the book appear to be:\n",
      "\n",
      "1. Sequential order of chapters: The preface mentions that Chapters 15 and 16 follow naturally from Chapter 10 and it is recommended to read the chapters in that order. This suggests that the book follows a sequential structure in presenting its content.\n",
      "\n",
      "2. Graphical models: Chapter 17 discusses graphical models, specifically undirected models, and some new methods for their estimation. The mention of a lack of space and omission of coverage of directed graphical models implies that graphical models are an important theme in the book.\n",
      "\n",
      "3. High-dimensional feature spaces: Chapter 18 explores the \"p≫N\" problem, which refers to learning in high-dimensional feature spaces. This problem is relevant in various areas such as genomic and proteomic studies, and document classification. Therefore, high-dimensional feature spaces and the challenges associated with them are another main theme of the book.\n",
      "\n",
      "4. Acknowledgments and errors: The preface also includes acknowledgments to readers who found errors in the first edition and an apology for those errors. This suggests that the book aims to provide accurate and error-free information.\n",
      "\n",
      "Overall, the main themes of the book seem to be the sequential order of chapters, graphical models, high-dimensional feature spaces, and the importance of accuracy in the content.\n",
      "\n",
      "Without the actual content of the documents, it is impossible to determine the main themes. The titles provided only indicate the order or organization of the documents, but do not provide any information about their subject matter.\n",
      "\n",
      "1. The challenges and complexities of statistical problems in the information age.\n",
      "2. The emergence of new fields such as data mining and bioinformatics.\n",
      "3. The importance of learning from data and extracting patterns and trends.\n",
      "4. The revolution in the statistical sciences and the role of computation.\n",
      "5. The distinction between supervised and unsupervised learning.\n",
      "\n",
      "1) The main theme of the first document is the attempt to bring together important new ideas in learning and explain them in a statistical framework. It emphasizes the methods and conceptual underpinnings of learning rather than theoretical properties.\n",
      "2) The main theme of the second document is the acknowledgement of the contribution of various individuals to the conception and completion of a book on learning. It also expresses gratitude to funding agencies and family members for their support.\n",
      "3) The main theme of the third document is the impact of statisticians on changing the ways we reason, experiment, and form opinions. It highlights the role of statisticians in shaping our understanding and perspectives.\n",
      "\n",
      "Based on the list of documents, the main themes appear to be:\n",
      "1. Introduction to the topic\n",
      "2. Overview of supervised learning\n",
      "3. Variable types and terminology\n",
      "4. Two simple approaches to prediction: Least Squares and Nearest Neighbors\n",
      "5. Statistical decision theory\n",
      "6. Local methods in high dimensions\n",
      "7. Statistical models, supervised learning, and function approximation\n",
      "8. Structured regression models\n",
      "\n",
      "Based on this list of documents, the main themes are:\n",
      "\n",
      "1. Classes of Restricted Estimators\n",
      "2. Model Selection and the Bias-Variance Tradeoff\n",
      "3. Linear Methods for Regression\n",
      "4. Subset Selection\n",
      "5. Shrinkage Methods\n",
      "6. Methods Using Derived Input Directions\n",
      "7. Multiple Outcome Shrinkage and Selection\n",
      "8. More on the Lasso and Related Path Algorithms\n",
      "9. Computational Considerations\n",
      "\n",
      "Based on the list of documents, the main themes are:\n",
      "\n",
      "1. Linear methods for classification:\n",
      "- Linear Regression of an Indicator Matrix\n",
      "- Linear Discriminant Analysis\n",
      "- Regularized Discriminant Analysis\n",
      "- Reduced-Rank Linear Discriminant Analysis\n",
      "- Logistic Regression\n",
      "- Fitting Logistic Regression Models\n",
      "- Quadratic Approximations and Inference\n",
      "- L1 Regularized Logistic Regression\n",
      "- Logistic Regression or LDA?\n",
      "- Separating Hyperplanes\n",
      "- Rosenblatt’s Perceptron Learning Algorithm\n",
      "- Optimal Separating Hyperplanes\n",
      "\n",
      "2. Basis Expansions and Regularization:\n",
      "- Piecewise Polynomials and Splines\n",
      "- Natural Cubic Splines\n",
      "- Example: South African Heart Disease (Continued)\n",
      "- Example: Phoneme Recognition\n",
      "- Filtering and Feature Extraction\n",
      "- Smoothing Splines\n",
      "- Degrees of Freedom and Smoother Matrices\n",
      "- Automatic Selection of the Smoothing Parameters\n",
      "- Fixing the Degrees of Freedom\n",
      "- The Bias–Variance Tradeoff\n",
      "- Nonparametric Logistic Regression\n",
      "- Multidimensional Splines\n",
      "- Regularization and Reproducing Kernel Hilbert Spaces\n",
      "- Spaces of Functions Generated by Kernels\n",
      "- Examples of RKHS\n",
      "- Wavelet Smoothing\n",
      "- Wavelet Bases and the Wavelet Transform\n",
      "- Adaptive Wavelet Filtering\n",
      "\n",
      "These themes cover various linear and non-linear classification methods, as well as techniques for basis expansions and regularization.\n",
      "\n",
      "Based on the list of documents, the main themes appear to be kernel smoothing methods, model assessment and selection, and model inference and averaging.\n",
      "\n",
      "Based on the list of documents, the main themes are:\n",
      "\n",
      "1. Bootstrap and Maximum Likelihood Methods\n",
      "2. Bayesian Methods\n",
      "3. The EM Algorithm\n",
      "4. MCMC for Sampling from the Posterior\n",
      "5. Bagging\n",
      "6. Model Averaging and Stacking\n",
      "7. Stochastic Search: Bumping\n",
      "8. Additive Models, Trees, and Related Methods\n",
      "9. Generalized Additive Models\n",
      "10. Tree-Based Methods\n",
      "11. PRIM: Bump Hunting\n",
      "12. MARS: Multivariate Adaptive Regression Splines\n",
      "13. Hierarchical Mixtures of Experts\n",
      "14. Missing Data\n",
      "15. Computational Considerations\n",
      "16. Boosting Methods\n",
      "\n",
      "Based on the list of documents provided, the main themes are:\n",
      "\n",
      "1. Boosting:\n",
      "- Boosting Fits an Additive Model\n",
      "- Forward Stagewise Additive Modeling\n",
      "- Exponential Loss and AdaBoost\n",
      "- Why Exponential Loss?\n",
      "- Loss Functions and Robustness\n",
      "- \"Off-the-Shelf\" Procedures for Data Mining\n",
      "- Boosting Trees\n",
      "- Numerical Optimization via Gradient Boosting\n",
      "- Right-Sized Trees for Boosting\n",
      "- Regularization\n",
      "- Interpretation\n",
      "\n",
      "2. Neural Networks:\n",
      "- Introduction\n",
      "- Projection Pursuit Regression\n",
      "- Neural Networks\n",
      "- Fitting Neural Networks\n",
      "- Some Issues in Training Neural Networks\n",
      "- Example: Simulated Data\n",
      "- Example: ZIP Code Data\n",
      "- Discussion\n",
      "- Bayesian Neural Nets and the NIPS 2003 Challenge\n",
      "- Computational Considerations\n",
      "\n",
      "3. Other:\n",
      "- Bibliographic Notes\n",
      "- Exercises\n",
      "\n",
      "These themes suggest that the documents are likely related to machine learning techniques such as boosting and neural networks, with some additional sections for references and exercises.\n",
      "\n",
      "Based on this list of documents, the main themes can be identified as follows:\n",
      "\n",
      "1. Support Vector Machines and Flexible Discriminants\n",
      "2. Prototype Methods and Nearest-Neighbors\n",
      "\n",
      "Based on this list of documents, the main themes are:\n",
      "\n",
      "1. Unsupervised Learning: This theme includes topics such as association rules, market basket analysis, the Apriori algorithm, generalized association rules, and choice of supervised learning method.\n",
      "\n",
      "2. Cluster Analysis: This theme covers topics like proximity matrices, dissimilarities based on attributes, clustering algorithms, K-means, Gaussian mixtures as soft K-means clustering, vector quantization, K-medoids, practical issues, and hierarchical clustering.\n",
      "\n",
      "3. Self-Organizing Maps: This theme focuses on self-organizing maps.\n",
      "\n",
      "4. Principal Components, Curves, and Surfaces: This theme includes topics such as principal components, principal curves and surfaces, spectral clustering, kernel principal components, and sparse principal components.\n",
      "\n",
      "5. Non-negative Matrix Factorization: This theme covers non-negative matrix factorization and archetypal analysis.\n",
      "\n",
      "6. Independent Component Analysis and Exploratory Projection Pursuit: This theme includes topics such as latent variables and factor analysis, independent component analysis, and exploratory projection pursuit.\n",
      "\n",
      "7. Multidimensional Scaling: This theme focuses on multidimensional scaling.\n",
      "\n",
      "8. Nonlinear Dimension Reduction and Local Multidimensional Scaling: This theme covers nonlinear dimension reduction and local multidimensional scaling.\n",
      "\n",
      "9. The Google PageRank Algorithm: This theme specifically focuses on the Google PageRank algorithm.\n",
      "\n",
      "Based on this list of documents, the main themes are:\n",
      "\n",
      "1. Random Forests (documents 15 and 15.1-15.4): This theme discusses the concept and details of random forests, including out-of-bag samples, variable importance, proximity plots, overfitting, and analysis of random forests.\n",
      "\n",
      "2. Ensemble Learning (document 16 and 16.1-16.3): This theme focuses on ensemble learning techniques, such as boosting and regularization paths, learning ensembles, and rule ensembles.\n",
      "\n",
      "3. Undirected Graphical Models (document 17 and 17.1-17.4): This theme explores undirected graphical models for both continuous and discrete variables, including the estimation of parameters and graph structure. It also introduces restricted Boltzmann machines.\n",
      "\n",
      "4. High-Dimensional Problems (document 18): This theme specifically addresses high-dimensional problems where the number of variables (p) is much larger than the number of samples (N).\n",
      "\n",
      "Based on the list of documents, the main themes appear to be:\n",
      "\n",
      "1. Linear Discriminant Analysis and Nearest Shrunken Centroids\n",
      "2. Linear Classifiers with Quadratic Regularization\n",
      "3. Regularized Discriminant Analysis\n",
      "4. Logistic Regression with Quadratic Regularization\n",
      "5. Support Vector Classifier\n",
      "6. Feature Selection\n",
      "7. Linear Classifiers with L1 Regularization (Lasso)\n",
      "8. Application of Lasso to Protein Mass Spectroscopy\n",
      "9. The Fused Lasso for Functional Data\n",
      "10. Classification When Features are Unavailable\n",
      "11. High-Dimensional Regression: Supervised Principal Components\n",
      "12. Connection to Latent-Variable Modeling\n",
      "13. Relationship with Partial Least Squares\n",
      "14. Pre-Conditioning for Feature Selection\n",
      "15. Feature Assessment and the Multiple-Testing Problem\n",
      "16. The False Discovery Rate\n",
      "17. Asymmetric Cutpoints and the SAM Procedure\n",
      "18. A Bayesian Interpretation of the FDR\n",
      "19. Bibliographic Notes\n",
      "20. Exercises\n",
      "21. References\n",
      "22. Author Index\n",
      "23. Index\n",
      "\n",
      "Based on the list of documents, the main themes are:\n",
      "1. Statistical learning in various fields such as science, finance, and industry.\n",
      "2. Examples of learning problems, including predicting health conditions, stock prices, and identifying patterns in data.\n",
      "3. The intersection of statistical learning with fields like data mining, artificial intelligence, and engineering.\n",
      "4. Learning from data, where outcomes are predicted based on features using a training set of data.\n",
      "\n",
      "Take these and distill it into a final, consolidated list\n",
      "of the main themes.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "Helpful Answer:\n",
      "\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'Statistics, Data Mining and Machine Learning, Conceptual Framework, Topics and Techniques, Authors\\' Background, Acknowledgement and gratitude towards parents, Acknowledgement and gratitude towards families, Familial relationships, Personal connections and relationships, Popularity and motivation for updating \"The Elements of Statistical Learning\", Fast pace of research in statistical learning, New chapters and updates in the second edition, Attempt to keep layout of first edition unchanged, Quote about trusting in God and bringing data, Introduction and overview of supervised learning, Linear methods for regression and classification, Basis expansions and regularization techniques, Kernel smoothing methods, Model assessment and selection, Model inference and averaging, Additive models, trees, and related methods, Boosting and additive trees, Neural networks, Support vector machines and flexible discriminants, Prototype methods and nearest-neighbors, Unsupervised learning, Random forests, Ensemble learning, Undirected graphical models, High-dimensional problems, Sequential order of chapters, Graphical models, High-dimensional feature spaces, Acknowledgments and errors, Introduction and overview of supervised learning, Linear methods for regression and classification, Basis expansions and regularization techniques, Kernel smoothing methods, Model assessment and selection, Model inference and averaging, Additive models, trees, and related methods, Boosting and additive trees, Neural networks, Support vector machines and flexible discriminants, Prototype methods and nearest-neighbors, Unsupervised learning, Random forests, Ensemble learning, Undirected graphical models, High-dimensional problems, Bootstrap and Maximum Likelihood Methods, Bayesian Methods, The EM Algorithm, MCMC for Sampling from the Posterior, Bagging, Model Averaging and Stacking, Stochastic Search: Bumping, Additive Models, Trees, and Related Methods, Generalized Additive Models, Tree-Based Methods, PRIM: Bump Hunting, MARS: Multivariate Adaptive Regression Splines, Hierarchical Mixtures of Experts, Missing Data, Computational Considerations, Boosting, Neural Networks, Other, Support Vector Machines and Flexible Discriminants, Prototype Methods and Nearest-Neighbors, Unsupervised Learning, Cluster Analysis, Self-Organizing Maps, Principal Components, Curves, and Surfaces, Non-negative Matrix Factorization, Independent Component Analysis and Exploratory Projection Pursuit, Multidimensional Scaling, Nonlinear Dimension Reduction and Local Multidimensional Scaling, The Google PageRank Algorithm, Random Forests, Ensemble Learning, Undirected Graphical Models, High-Dimensional Problems, Linear Discriminant Analysis and Nearest Shrunken Centroids, Linear Classifiers with Quadratic Regularization, Regularized Discriminant Analysis, Logistic Regression with Quadratic Regularization, Support Vector Classifier, Feature Selection, Linear Classifiers with L1 Regularization (Lasso), Application of Lasso to Protein Mass Spectroscopy, The Fused Lasso for Functional Data, Classification When Features are Unavailable, High-Dimensional Regression: Supervised Principal Components, Connection to Latent-Variable Modeling, Relationship with Partial Least Squares, Pre-Conditioning for Feature Selection, Feature Assessment and the Multiple-Testing Problem, The False Discovery Rate, Asymmetric Cutpoints and the SAM Procedure, A Bayesian Interpretation of the FDR'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map_template_example = \"\"\"\n",
    "The following is a set of documents\n",
    "\n",
    "{text}\n",
    "\n",
    "Based on this list of docs, please identify the main themes\n",
    "\n",
    "Helpful Answer:\n",
    "\"\"\"\n",
    "\n",
    "combine_template_example = \"\"\"\n",
    "The following is a set of summaries:\n",
    "\n",
    "{text}\n",
    "\n",
    "Take these and distill it into a final, consolidated list\n",
    "of the main themes.\n",
    "\n",
    "Return that list as a comma separated list.\n",
    "\n",
    "Helpful Answer:\n",
    "\"\"\"\n",
    "\n",
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    map_prompt=PromptTemplate.from_template(map_template_example),\n",
    "    combine_prompt=PromptTemplate.from_template(combine_template_example),\n",
    "    chain_type=\"map_reduce\",\n",
    "    verbose=True,\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Refine chain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\u001b[1m> Entering new RefineDocumentsChain chain...\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mWrite a concise summary of the following:\n",
      "\n",
      "\n",
      "\"Springer Series in Statistics\n",
      "Trevor Hastie\n",
      "Robert TibshiraniJerome FriedmanSpringer Series in Statistics\n",
      "The Elements of\n",
      "Statistical Learning\n",
      "Data Mining, Inference, and Prediction\n",
      "The Elements of Statistical LearningDuring the past decade there has been an explosion in computation and information tech-\n",
      "nology. With it have come vast amounts of data in a variety of fields such as medicine, biolo-gy, finance, and marketing. The challenge of understanding these data has led to the devel-opment of new tools in the field of statistics, and spawned new areas such as data mining,machine learning, and bioinformatics. Many of these tools have common underpinnings butare often expressed with different terminology. This book describes the important ideas inthese areas in a common conceptual framework. While the approach is statistical, theemphasis is on concepts rather than mathematics. Many examples are given, with a liberaluse of color graphics. It should be a valuable resource for statisticians and anyone interestedin data mining in science or industry. The book’s coverage is broad, from supervised learning(prediction) to unsupervised learning. The many topics include neural networks, supportvector machines, classification trees and boosting—the first comprehensive treatment of thistopic in any book.\n",
      "This major new edition features many topics not covered in the original, including graphical\n",
      "models, random forests, ensemble methods, least angle regression & path algorithms for thelasso, non-negative matrix factorization, and spectral clustering. There is also a chapter onmethods for “wide” data (p bigger than n), including multiple testing and false discovery rates.\n",
      "Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at\n",
      "Stanford University. They are prominent researchers in this area: Hastie and Tibshiranideveloped generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS andinvented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of thevery successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.\n",
      "›springer.comSTATISTICS\n",
      "isbn 978-0-387-84857-0Trevor Hastie • Robert Tibshirani • Jerome Friedman\n",
      "The Elements of Statictical Learning\n",
      "Hastie • Tibshirani • Friedman\n",
      "Second Edition\"\n",
      "\n",
      "\n",
      "CONCISE SUMMARY:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The book \"The Elements of Statistical Learning\" is a comprehensive resource that explores various concepts and tools in data mining, machine learning, and bioinformatics. Written by experts in the field, the book covers topics such as neural networks, support vector machines, and classification trees. The second edition includes additional topics such as graphical models and random forests. The authors are professors of statistics at Stanford University and have made significant contributions to the field.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "This is page v\n",
      "Printer: Opaque this\n",
      "To our parents:\n",
      "Valerie and Patrick Hastie\n",
      "Vera and Sami Tibshirani\n",
      "Florence and Harry Friedman\n",
      "and to our families:\n",
      "Samantha, Timothy, and Lynda\n",
      "Charlie, Ryan, Julie, and Cheryl\n",
      "Melanie, Dora, Monika, and Ildiko\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The existing summary does not need to be refined with the new context provided.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "vi\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The original summary does not need to be refined with the new context provided.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "This is page vii\n",
      "Printer: Opaque this\n",
      "Preface to the Second Edition\n",
      "In God we trust, all others bring data.\n",
      "–William Edwards Deming (1900-1993)1\n",
      "We have been gratiﬁed by the popularity of the ﬁrst edition of The\n",
      "Elements of Statistical Learning. This, along with the fast pace of research\n",
      "in the statistical learning ﬁeld, motivated us to update our book with a\n",
      "second edition.\n",
      "We have added four new chapters and updated some of the existi ng\n",
      "chapters. Because many readers are familiar with the layout of the ﬁrst\n",
      "edition, we have tried to change it as little as possible. Her e is a summary\n",
      "of the main changes:\n",
      "1On the Web, this quote has been widely attributed to both Deming and R obert W.\n",
      "Hayden; however Professor Hayden told us that he can claim no credit for th is quote,\n",
      "and ironically we could ﬁnd no “data” conﬁrming that Deming actual ly said this.\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: We have added four new chapters and updated some of the existing chapters in the second edition of The Elements of Statistical Learning. We have tried to change the layout as little as possible to accommodate readers familiar with the first edition.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "viii Preface to the Second Edition\n",
      "Chapter What’s new\n",
      "1.Introduction\n",
      "2.Overview of Supervised Learning\n",
      "3.Linear Methods for Regression LAR algorithm and generaliza tions\n",
      "of the lasso\n",
      "4.Linear Methods for Classiﬁcation Lasso path for logistic re gression\n",
      "5.Basis Expansions and Regulariza-\n",
      "tionAdditional illustrations of RKHS\n",
      "6.Kernel Smoothing Methods\n",
      "7.Model Assessment and Selection Strengths and pitfalls of cr oss-\n",
      "validation\n",
      "8.Model Inference and Averaging\n",
      "9.Additive Models, Trees, and\n",
      "Related Methods\n",
      "10.Boosting and Additive Trees New example from ecology; some\n",
      "material split oﬀ to Chapter 16.\n",
      "11.Neural Networks Bayesian neural nets and the NIPS\n",
      "2003 challenge\n",
      "12.Support Vector Machines and\n",
      "Flexible DiscriminantsPath algorithm for SVM classiﬁer\n",
      "13.Prototype Methods and\n",
      "Nearest-Neighbors\n",
      "14.Unsupervised Learning Spectral clustering, kernel PCA,\n",
      "sparse PCA, non-negative matrix\n",
      "factorization archetypal analysis,\n",
      "nonlinear dimension reduction,\n",
      "Google page rank algorithm, a\n",
      "direct approach to ICA\n",
      "15.Random Forests New\n",
      "16.Ensemble Learning New\n",
      "17.Undirected Graphical Models New\n",
      "18.High-Dimensional Problems New\n",
      "Some further notes:\n",
      "•Our ﬁrst edition was unfriendly to colorblind readers; in pa rticular,\n",
      "we tended to favor red/greencontrasts which are particularly trou-\n",
      "blesome. We have changed the color palette in this edition to a large\n",
      "extent, replacing the above with an orange/bluecontrast.\n",
      "•We have changed the name of Chapter 6 from “Kernel Methods” to\n",
      "“Kernel Smoothing Methods”, to avoid confusion with the mac hine-\n",
      "learningkernelmethodthatisdiscussedinthecontextofsu pportvec-\n",
      "tor machines (Chapter 12) and more generally in Chapters 5 an d 14.\n",
      "•In the ﬁrst edition, the discussion of error-rate estimatio n in Chap-\n",
      "ter 7 was sloppy, as we did not clearly diﬀerentiate the notio ns of\n",
      "conditional error rates (conditional on the training set) a nd uncondi-\n",
      "tional rates. We have ﬁxed this in the new edition.\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been kept as similar as possible to accommodate readers familiar with the first edition. Changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved in the new edition.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "Preface to the Second Edition ix\n",
      "•Chapters 15 and 16 follow naturally from Chapter 10, and the c hap-\n",
      "ters are probably best read in that order.\n",
      "•In Chapter 17, we have not attempted a comprehensive treatme nt\n",
      "of graphical models, and discuss only undirected models and some\n",
      "new methods for their estimation. Due to a lack of space, we ha ve\n",
      "speciﬁcally omitted coverage of directed graphical models .\n",
      "•Chapter 18 explores the “ p≫N” problem, which is learning in high-\n",
      "dimensional feature spaces. These problems arise in many ar eas, in-\n",
      "cluding genomic and proteomic studies, and document classi ﬁcation.\n",
      "We thank the many readers who have found the (too numerous) er rors in\n",
      "the ﬁrst edition. We apologize for those and have done our bes t to avoid er-\n",
      "rorsinthisnewedition.WethankMarkSegal,BalaRajaratna m,andLarry\n",
      "Wasserman for comments on some of the new chapters, and many S tanford\n",
      "graduate and post-doctoral students who oﬀered comments, i n particular\n",
      "Mohammed AlQuraishi, John Boik, Holger Hoeﬂing, Arian Male ki, Donal\n",
      "McMahon, Saharon Rosset, Babak Shababa, Daniela Witten, Ji Zhu and\n",
      "Hui Zou. We thank John Kimmel for his patience in guiding us th rough this\n",
      "new edition. RT dedicates this edition to the memory of Anna M cPhee.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "August 2008\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been kept as similar as possible to accommodate readers familiar with the first edition. Changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved in the new edition. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "x Preface to the Second Edition\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters, with a layout that accommodates readers familiar with the first edition. Changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "This is page xi\n",
      "Printer: Opaque this\n",
      "Preface to the First Edition\n",
      "We are drowning in information and starving for knowledge.\n",
      "–Rutherford D. Roger\n",
      "The ﬁeld of Statistics is constantly challenged by the probl ems that science\n",
      "andindustrybringstoitsdoor.Intheearlydays,theseprob lemsoftencame\n",
      "from agricultural and industrial experiments and were rela tively small in\n",
      "scope. With the advent of computers and the information age, statistical\n",
      "problems have exploded both in size and complexity. Challen ges in the\n",
      "areas of data storage, organization and searching have led t o the new ﬁeld\n",
      "of “data mining”; statistical and computational problems i n biology and\n",
      "medicine have created “bioinformatics.” Vast amounts of da ta are being\n",
      "generated in many ﬁelds, and the statistician’s job is to mak e sense of it\n",
      "all: to extract important patterns and trends, and understa nd “what the\n",
      "data says.” We call this learning from data .\n",
      "The challenges in learning from data have led to a revolution in the sta-\n",
      "tisticalsciences.Sincecomputationplayssuchakeyrole, itisnotsurprising\n",
      "that much of this new development has been done by researcher s in other\n",
      "ﬁelds such as computer science and engineering.\n",
      "The learning problems that we consider can be roughly catego rized as\n",
      "eithersupervised orunsupervised . In supervised learning, the goal is to pre-\n",
      "dict the value of an outcome measure based on a number of input measures;\n",
      "in unsupervised learning, there is no outcome measure, and t he goal is to\n",
      "describe the associations and patterns among a set of input m easures.\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout is designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xii Preface to the First Edition\n",
      "This book is our attempt to bring together many of the importa nt new\n",
      "ideas in learning, and explain them in a statistical framewo rk. While some\n",
      "mathematical details are needed, we emphasize the methods a nd their con-\n",
      "ceptual underpinnings rather than their theoretical prope rties. As a result,\n",
      "we hope that this book will appeal not just to statisticians b ut also to\n",
      "researchers and practitioners in a wide variety of ﬁelds.\n",
      "Just as we have learned a great deal from researchers outside of the ﬁeld\n",
      "of statistics, our statistical viewpoint may help others to better understand\n",
      "diﬀerent aspects of learning:\n",
      "There is no true interpretation of anything; interpretatio n is a\n",
      "vehicle in the service of human comprehension. The value of\n",
      "interpretation is in enabling others to fruitfully think ab out an\n",
      "idea.\n",
      "–Andreas Buja\n",
      "We would like to acknowledge the contribution of many people to the\n",
      "conception and completion of this book. David Andrews, Leo B reiman,\n",
      "Andreas Buja, John Chambers, Bradley Efron, Geoﬀrey Hinton , Werner\n",
      "Stuetzle, and John Tukey have greatly inﬂuenced our careers . Balasub-\n",
      "ramanian Narasimhan gave us advice and help on many computat ional\n",
      "problems, and maintained an excellent computing environme nt. Shin-Ho\n",
      "Bang helped in the production of a number of the ﬁgures. Lee Wi lkinson\n",
      "gavevaluabletipsoncolorproduction.IlanaBelitskaya,E vaCantoni,Maya\n",
      "Gupta,MichaelJordan,ShantiGopatam,RadfordNeal,Jorge Picazo,Bog-\n",
      "dan Popescu, Olivier Renaud, Saharon Rosset, John Storey, J i Zhu, Mu\n",
      "Zhu, two reviewers and many students read parts of the manusc ript and\n",
      "oﬀered helpful suggestions. John Kimmel was supportive, pa tient and help-\n",
      "ful at every phase; MaryAnn Brickner and Frank Ganz headed a s uperb\n",
      "production team at Springer. Trevor Hastie would like to tha nk the statis-\n",
      "tics department at the University of Cape Town for their hosp itality during\n",
      "the ﬁnal stages of this book. We gratefully acknowledge NSF a nd NIH for\n",
      "their support of this work. Finally, we would like to thank ou r families and\n",
      "our parents for their love and support.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "May 2001\n",
      "The quiet statisticians have changed our world; not by disco v-\n",
      "ering new facts or technical developments, but by changing t he\n",
      "ways that we reason, experiment and form our opinions ....\n",
      "–Ian Hacking\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout is designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised. The preface to the first edition acknowledges the contribution of many people to the conception and completion of the book, and expresses gratitude to the statistics department at the University of Cape Town for their hospitality during the final stages of the book's creation. The authors also thank their families and parents for their love and support.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "This is page xiii\n",
      "Printer: Opaque this\n",
      "Contents\n",
      "Preface to the Second Edition vii\n",
      "Preface to the First Edition xi\n",
      "1 Introduction 1\n",
      "2 Overview of Supervised Learning 9\n",
      "2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9\n",
      "2.2 Variable Types and Terminology . . . . . . . . . . . . . . 9\n",
      "2.3 Two Simple Approaches to Prediction:\n",
      "Least Squares and Nearest Neighbors . . . . . . . . . . . 11\n",
      "2.3.1 Linear Models and Least Squares . . . . . . . . 11\n",
      "2.3.2 Nearest-Neighbor Methods . . . . . . . . . . . . 14\n",
      "2.3.3 From Least Squares to Nearest Neighbors . . . . 16\n",
      "2.4 Statistical Decision Theory . . . . . . . . . . . . . . . . . 18\n",
      "2.5 Local Methods in High Dimensions . . . . . . . . . . . . . 22\n",
      "2.6 Statistical Models, Supervised Learning\n",
      "and Function Approximation . . . . . . . . . . . . . . . . 28\n",
      "2.6.1 A Statistical Model\n",
      "for the Joint Distribution Pr( X,Y) . . . . . . . 28\n",
      "2.6.2 Supervised Learning . . . . . . . . . . . . . . . . 29\n",
      "2.6.3 Function Approximation . . . . . . . . . . . . . 29\n",
      "2.7 Structured Regression Models . . . . . . . . . . . . . . . 32\n",
      "2.7.1 Diﬃculty of the Problem . . . . . . . . . . . . . 32\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout is designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised. The preface to the first edition acknowledges the contribution of many people to the conception and completion of the book, and expresses gratitude to the statistics department at the University of Cape Town for their hospitality during the final stages of the book's creation. The authors also thank their families and parents for their love and support. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xiv Contents\n",
      "2.8 Classes of Restricted Estimators . . . . . . . . . . . . . . 33\n",
      "2.8.1 Roughness Penalty and Bayesian Methods . . . 34\n",
      "2.8.2 Kernel Methods and Local Regression . . . . . . 34\n",
      "2.8.3 Basis Functions and Dictionary Methods . . . . 35\n",
      "2.9 Model Selection and the Bias–Variance Tradeoﬀ . . . . . 37\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "3 Linear Methods for Regression 43\n",
      "3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43\n",
      "3.2 Linear Regression Models and Least Squares . . . . . . . 44\n",
      "3.2.1 Example: Prostate Cancer . . . . . . . . . . . . 49\n",
      "3.2.2 The Gauss–Markov Theorem . . . . . . . . . . . 51\n",
      "3.2.3 Multiple Regression\n",
      "from Simple Univariate Regression . . . . . . . . 52\n",
      "3.2.4 Multiple Outputs . . . . . . . . . . . . . . . . . 56\n",
      "3.3 Subset Selection . . . . . . . . . . . . . . . . . . . . . . . 57\n",
      "3.3.1 Best-Subset Selection . . . . . . . . . . . . . . . 57\n",
      "3.3.2 Forward- and Backward-Stepwise Selection . . . 58\n",
      "3.3.3 Forward-Stagewise Regression . . . . . . . . . . 60\n",
      "3.3.4 Prostate Cancer Data Example (Continued) . . 61\n",
      "3.4 Shrinkage Methods . . . . . . . . . . . . . . . . . . . . . . 61\n",
      "3.4.1 Ridge Regression . . . . . . . . . . . . . . . . . 61\n",
      "3.4.2 The Lasso . . . . . . . . . . . . . . . . . . . . . 68\n",
      "3.4.3 Discussion: Subset Selection, Ridge Regression\n",
      "and the Lasso . . . . . . . . . . . . . . . . . . . 69\n",
      "3.4.4 Least Angle Regression . . . . . . . . . . . . . . 73\n",
      "3.5 Methods Using Derived Input Directions . . . . . . . . . 79\n",
      "3.5.1 Principal Components Regression . . . . . . . . 79\n",
      "3.5.2 Partial Least Squares . . . . . . . . . . . . . . . 80\n",
      "3.6 Discussion: A Comparison of the Selection\n",
      "and Shrinkage Methods . . . . . . . . . . . . . . . . . . . 82\n",
      "3.7 Multiple Outcome Shrinkage and Selection . . . . . . . . 84\n",
      "3.8 More on the Lasso and Related Path Algorithms . . . . . 86\n",
      "3.8.1 Incremental Forward Stagewise Regression . . . 86\n",
      "3.8.2 Piecewise-Linear Path Algorithms . . . . . . . . 89\n",
      "3.8.3 The Dantzig Selector . . . . . . . . . . . . . . . 89\n",
      "3.8.4 The Grouped Lasso . . . . . . . . . . . . . . . . 90\n",
      "3.8.5 Further Properties of the Lasso . . . . . . . . . . 91\n",
      "3.8.6 Pathwise Coordinate Optimization . . . . . . . . 92\n",
      "3.9 Computational Considerations . . . . . . . . . . . . . . . 93\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout is designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised. The preface to the first edition acknowledges the contribution of many people to the conception and completion of the book, and expresses gratitude to the statistics department at the University of Cape Town for their hospitality during the final stages of the book's creation. The authors also thank their families and parents for their love and support. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. The book also covers linear methods for regression, including topics such as subset selection, shrinkage methods, methods using derived input directions, and computational considerations.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "Contents xv\n",
      "4 Linear Methods for Classiﬁcation 101\n",
      "4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101\n",
      "4.2 Linear Regression of an Indicator Matrix . . . . . . . . . 103\n",
      "4.3 Linear Discriminant Analysis . . . . . . . . . . . . . . . . 106\n",
      "4.3.1 Regularized Discriminant Analysis . . . . . . . . 112\n",
      "4.3.2 Computations for LDA . . . . . . . . . . . . . . 113\n",
      "4.3.3 Reduced-Rank Linear Discriminant Analysis . . 113\n",
      "4.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 119\n",
      "4.4.1 Fitting Logistic Regression Models . . . . . . . . 120\n",
      "4.4.2 Example: South African Heart Disease . . . . . 122\n",
      "4.4.3 Quadratic Approximations and Inference . . . . 124\n",
      "4.4.4L1Regularized Logistic Regression . . . . . . . . 125\n",
      "4.4.5 Logistic Regression or LDA? . . . . . . . . . . . 127\n",
      "4.5 Separating Hyperplanes . . . . . . . . . . . . . . . . . . . 129\n",
      "4.5.1 Rosenblatt’s Perceptron Learning Algorithm . . 130\n",
      "4.5.2 Optimal Separating Hyperplanes . . . . . . . . . 132\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "5 Basis Expansions and Regularization 139\n",
      "5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 139\n",
      "5.2 Piecewise Polynomials and Splines . . . . . . . . . . . . . 141\n",
      "5.2.1 Natural Cubic Splines . . . . . . . . . . . . . . . 144\n",
      "5.2.2 Example:SouthAfricanHeartDisease(Continued)146\n",
      "5.2.3 Example: Phoneme Recognition . . . . . . . . . 148\n",
      "5.3 Filtering and Feature Extraction . . . . . . . . . . . . . . 150\n",
      "5.4 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . 151\n",
      "5.4.1 Degrees of Freedom and Smoother Matrices . . . 153\n",
      "5.5 Automatic Selection of the Smoothing Parameters . . . . 15 6\n",
      "5.5.1 Fixing the Degrees of Freedom . . . . . . . . . . 158\n",
      "5.5.2 The Bias–Variance Tradeoﬀ . . . . . . . . . . . . 158\n",
      "5.6 Nonparametric Logistic Regression . . . . . . . . . . . . . 161\n",
      "5.7 Multidimensional Splines . . . . . . . . . . . . . . . . . . 162\n",
      "5.8 Regularization and Reproducing Kernel Hilbert Spaces . 167\n",
      "5.8.1 Spaces of Functions Generated by Kernels . . . 168\n",
      "5.8.2 Examples of RKHS . . . . . . . . . . . . . . . . 170\n",
      "5.9 Wavelet Smoothing . . . . . . . . . . . . . . . . . . . . . 174\n",
      "5.9.1 Wavelet Bases and the Wavelet Transform . . . 176\n",
      "5.9.2 Adaptive Wavelet Filtering . . . . . . . . . . . . 179\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Appendix: Computational Considerations for Splines . . . . . . 186\n",
      "Appendix:B-splines . . . . . . . . . . . . . . . . . . . . . 186\n",
      "Appendix: Computations for Smoothing Splines . . . . . 189\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. The book also covers linear methods for regression, including topics such as subset selection, shrinkage methods, methods using derived input directions, and computational considerations. Additionally, the book covers linear methods for classification, such as linear regression of an indicator matrix, linear discriminant analysis, regularized discriminant analysis, logistic regression, and separating hyperplanes. It also covers basis expansions and regularization techniques, including piecewise polynomials and splines, filtering and feature extraction, smoothing splines, automatic selection of smoothing parameters, nonparametric logistic regression, multidimensional splines, regularization and reproducing kernel Hilbert spaces, and wavelet smoothing. The book provides insights into computational considerations for splines and includes appendices on B-splines and computations for smoothing splines.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xvi Contents\n",
      "6 Kernel Smoothing Methods 191\n",
      "6.1 One-Dimensional Kernel Smoothers . . . . . . . . . . . . 192\n",
      "6.1.1 Local Linear Regression . . . . . . . . . . . . . . 194\n",
      "6.1.2 Local Polynomial Regression . . . . . . . . . . . 197\n",
      "6.2 Selecting the Width of the Kernel . . . . . . . . . . . . . 198\n",
      "6.3 Local Regression in IRp. . . . . . . . . . . . . . . . . . . 200\n",
      "6.4 Structured Local Regression Models in IRp. . . . . . . . 201\n",
      "6.4.1 Structured Kernels . . . . . . . . . . . . . . . . . 203\n",
      "6.4.2 Structured Regression Functions . . . . . . . . . 203\n",
      "6.5 Local Likelihood and Other Models . . . . . . . . . . . . 205\n",
      "6.6 Kernel Density Estimation and Classiﬁcation . . . . . . . 20 8\n",
      "6.6.1 Kernel Density Estimation . . . . . . . . . . . . 208\n",
      "6.6.2 Kernel Density Classiﬁcation . . . . . . . . . . . 210\n",
      "6.6.3 The Naive Bayes Classiﬁer . . . . . . . . . . . . 210\n",
      "6.7 Radial Basis Functions and Kernels . . . . . . . . . . . . 212\n",
      "6.8 Mixture Models for Density Estimation and Classiﬁcatio n 214\n",
      "6.9 Computational Considerations . . . . . . . . . . . . . . . 216\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "7 Model Assessment and Selection 219\n",
      "7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 219\n",
      "7.2 Bias, Variance and Model Complexity . . . . . . . . . . . 219\n",
      "7.3 The Bias–Variance Decomposition . . . . . . . . . . . . . 223\n",
      "7.3.1 Example: Bias–Variance Tradeoﬀ . . . . . . . . 226\n",
      "7.4 Optimism of the Training Error Rate . . . . . . . . . . . 228\n",
      "7.5 Estimates of In-Sample Prediction Error . . . . . . . . . . 230\n",
      "7.6 The Eﬀective Number of Parameters . . . . . . . . . . . . 232\n",
      "7.7 The Bayesian Approach and BIC . . . . . . . . . . . . . . 233\n",
      "7.8 Minimum Description Length . . . . . . . . . . . . . . . . 235\n",
      "7.9 Vapnik–Chervonenkis Dimension . . . . . . . . . . . . . . 237\n",
      "7.9.1 Example (Continued) . . . . . . . . . . . . . . . 239\n",
      "7.10 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . 241\n",
      "7.10.1K-Fold Cross-Validation . . . . . . . . . . . . . 241\n",
      "7.10.2 The Wrong and Right Way\n",
      "to Do Cross-validation . . . . . . . . . . . . . . . 245\n",
      "7.10.3 Does Cross-Validation Really Work? . . . . . . . 247\n",
      "7.11 Bootstrap Methods . . . . . . . . . . . . . . . . . . . . . 249\n",
      "7.11.1 Example (Continued) . . . . . . . . . . . . . . . 252\n",
      "7.12 Conditional or Expected Test Error? . . . . . . . . . . . . 254\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "8 Model Inference and Averaging 261\n",
      "8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 261\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed to accommodate readers familiar with the first edition, and changes have been made to the color palette to be more inclusive for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion with other machine learning methods. The discussion of error-rate estimation has been improved. Additionally, Chapters 15 and 16 are best read in order after Chapter 10, while Chapter 17 focuses on undirected graphical models and excludes coverage of directed models. Chapter 18 explores learning in high-dimensional feature spaces. The authors express gratitude to readers who identified errors in the first edition and apologize for any mistakes. They also acknowledge individuals who provided comments and guidance throughout the creation of the new edition. The edition is dedicated to the memory of Anna McPhee. The challenges in learning from data have led to a revolution in the statistical sciences, with much of the development being done by researchers in other fields such as computer science and engineering. The learning problems considered in the book can be categorized as either supervised or unsupervised. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. The book also covers linear methods for regression, including topics such as subset selection, shrinkage methods, methods using derived input directions, and computational considerations. Additionally, the book covers linear methods for classification, such as linear regression of an indicator matrix, linear discriminant analysis, regularized discriminant analysis, logistic regression, and separating hyperplanes. It also covers basis expansions and regularization techniques, including piecewise polynomials and splines, filtering and feature extraction, smoothing splines, automatic selection of smoothing parameters, nonparametric logistic regression, multidimensional splines, regularization and reproducing kernel Hilbert spaces, and wavelet smoothing. The book provides insights into computational considerations for splines and includes appendices on B-splines and computations for smoothing splines. The new context describes the additional content in Chapter 6 on kernel smoothing methods, including local regression, selecting the width of the kernel, structured local regression models, kernel density estimation and classification, and radial basis functions and kernels. Chapter 7 focuses on model assessment and selection, discussing bias, variance, model complexity, the bias-variance decomposition, estimates of in-sample prediction error, the effective number of parameters, the Bayesian approach, minimum description length, Vapnik-Chervonenkis dimension, cross-validation, bootstrap methods, and conditional or expected test error. Chapter 8 is about model inference and averaging.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "Contents xvii\n",
      "8.2 The Bootstrap and Maximum Likelihood Methods . . . . 261\n",
      "8.2.1 A Smoothing Example . . . . . . . . . . . . . . 261\n",
      "8.2.2 Maximum Likelihood Inference . . . . . . . . . . 265\n",
      "8.2.3 Bootstrap versus Maximum Likelihood . . . . . 267\n",
      "8.3 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . 267\n",
      "8.4 Relationship Between the Bootstrap\n",
      "and Bayesian Inference . . . . . . . . . . . . . . . . . . . 271\n",
      "8.5 The EM Algorithm . . . . . . . . . . . . . . . . . . . . . 272\n",
      "8.5.1 Two-Component Mixture Model . . . . . . . . . 272\n",
      "8.5.2 The EM Algorithm in General . . . . . . . . . . 276\n",
      "8.5.3 EM as a Maximization–Maximization Procedure 277\n",
      "8.6 MCMC for Sampling from the Posterior . . . . . . . . . . 279\n",
      "8.7 Bagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282\n",
      "8.7.1 Example: Trees with Simulated Data . . . . . . 283\n",
      "8.8 Model Averaging and Stacking . . . . . . . . . . . . . . . 288\n",
      "8.9 Stochastic Search: Bumping . . . . . . . . . . . . . . . . . 290\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 292\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293\n",
      "9 Additive Models, Trees, and Related Methods 295\n",
      "9.1 Generalized Additive Models . . . . . . . . . . . . . . . . 295\n",
      "9.1.1 Fitting Additive Models . . . . . . . . . . . . . . 297\n",
      "9.1.2 Example: Additive Logistic Regression . . . . . 299\n",
      "9.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . 304\n",
      "9.2 Tree-Based Methods . . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.1 Background . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.2 Regression Trees . . . . . . . . . . . . . . . . . . 307\n",
      "9.2.3 Classiﬁcation Trees . . . . . . . . . . . . . . . . 308\n",
      "9.2.4 Other Issues . . . . . . . . . . . . . . . . . . . . 310\n",
      "9.2.5 Spam Example (Continued) . . . . . . . . . . . 313\n",
      "9.3 PRIM: Bump Hunting . . . . . . . . . . . . . . . . . . . . 317\n",
      "9.3.1 Spam Example (Continued) . . . . . . . . . . . 320\n",
      "9.4 MARS: Multivariate Adaptive Regression Splines . . . . . 3 21\n",
      "9.4.1 Spam Example (Continued) . . . . . . . . . . . 326\n",
      "9.4.2 Example (Simulated Data) . . . . . . . . . . . . 327\n",
      "9.4.3 Other Issues . . . . . . . . . . . . . . . . . . . . 328\n",
      "9.5 Hierarchical Mixtures of Experts . . . . . . . . . . . . . . 329\n",
      "9.6 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . 332\n",
      "9.7 Computational Considerations . . . . . . . . . . . . . . . 334\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 334\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335\n",
      "10 Boosting and Additive Trees 337\n",
      "10.1 Boosting Methods . . . . . . . . . . . . . . . . . . . . . . 337\n",
      "10.1.1 Outline of This Chapter . . . . . . . . . . . . . . 340\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed for readers familiar with the first edition and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. The new context describes additional content on the bootstrap and maximum likelihood methods, Bayesian methods, the EM algorithm, bagging, model averaging and stacking, and stochastic search. Chapter 9 covers additive models, trees, and related methods such as generalized additive models, tree-based methods, bump hunting, multivariate adaptive regression splines, hierarchical mixtures of experts, and missing data. Chapter 10 focuses on boosting methods.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xviii Contents\n",
      "10.2 Boosting Fits an Additive Model . . . . . . . . . . . . . . 341\n",
      "10.3 Forward Stagewise Additive Modeling . . . . . . . . . . . 342\n",
      "10.4 Exponential Loss and AdaBoost . . . . . . . . . . . . . . 343\n",
      "10.5 Why Exponential Loss? . . . . . . . . . . . . . . . . . . . 345\n",
      "10.6 Loss Functions and Robustness . . . . . . . . . . . . . . . 346\n",
      "10.7 “Oﬀ-the-Shelf” Procedures for Data Mining . . . . . . . . 35 0\n",
      "10.8 Example: Spam Data . . . . . . . . . . . . . . . . . . . . 352\n",
      "10.9 Boosting Trees . . . . . . . . . . . . . . . . . . . . . . . . 353\n",
      "10.10 Numerical Optimization via Gradient Boosting . . . . . . 358\n",
      "10.10.1 Steepest Descent . . . . . . . . . . . . . . . . . . 358\n",
      "10.10.2 Gradient Boosting . . . . . . . . . . . . . . . . . 359\n",
      "10.10.3 Implementations of Gradient Boosting . . . . . . 360\n",
      "10.11 Right-Sized Trees for Boosting . . . . . . . . . . . . . . . 361\n",
      "10.12 Regularization . . . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.1 Shrinkage . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.2 Subsampling . . . . . . . . . . . . . . . . . . . . 365\n",
      "10.13 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 367\n",
      "10.13.1 Relative Importance of Predictor Variables . . . 367\n",
      "10.13.2 Partial Dependence Plots . . . . . . . . . . . . . 369\n",
      "10.14 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . 371\n",
      "10.14.1 California Housing . . . . . . . . . . . . . . . . . 371\n",
      "10.14.2 New Zealand Fish . . . . . . . . . . . . . . . . . 375\n",
      "10.14.3 Demographics Data . . . . . . . . . . . . . . . . 379\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 380\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384\n",
      "11 Neural Networks 389\n",
      "11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 389\n",
      "11.2 Projection Pursuit Regression . . . . . . . . . . . . . . . 389\n",
      "11.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 392\n",
      "11.4 Fitting Neural Networks . . . . . . . . . . . . . . . . . . . 395\n",
      "11.5 Some Issues in Training Neural Networks . . . . . . . . . 397\n",
      "11.5.1 Starting Values . . . . . . . . . . . . . . . . . . . 397\n",
      "11.5.2 Overﬁtting . . . . . . . . . . . . . . . . . . . . . 398\n",
      "11.5.3 Scaling of the Inputs . . . . . . . . . . . . . . . 398\n",
      "11.5.4 Number of Hidden Units and Layers . . . . . . . 400\n",
      "11.5.5 Multiple Minima . . . . . . . . . . . . . . . . . . 400\n",
      "11.6 Example: Simulated Data . . . . . . . . . . . . . . . . . . 401\n",
      "11.7 Example: ZIP Code Data . . . . . . . . . . . . . . . . . . 404\n",
      "11.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 408\n",
      "11.9 Bayesian Neural Nets and the NIPS 2003 Challenge . . . 409\n",
      "11.9.1 Bayes, Boosting and Bagging . . . . . . . . . . . 410\n",
      "11.9.2 Performance Comparisons . . . . . . . . . . . . 412\n",
      "11.10 Computational Considerations . . . . . . . . . . . . . . . 414\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed for readers familiar with the first edition and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. The new context describes additional content on the bootstrap and maximum likelihood methods, Bayesian methods, the EM algorithm, bagging, model averaging and stacking, and stochastic search. Chapter 9 covers additive models, trees, and related methods such as generalized additive models, tree-based methods, bump hunting, multivariate adaptive regression splines, hierarchical mixtures of experts, and missing data. Chapter 10 focuses on boosting methods, including forward stagewise additive modeling, exponential loss and AdaBoost, and numerical optimization via gradient boosting. Chapter 11 introduces neural networks and covers topics such as projection pursuit regression, fitting neural networks, and issues in training neural networks.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "Contents xix\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "12 Support Vector Machines and\n",
      "Flexible Discriminants 417\n",
      "12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 417\n",
      "12.2 The Support Vector Classiﬁer . . . . . . . . . . . . . . . . 417\n",
      "12.2.1 Computing the Support Vector Classiﬁer . . . . 420\n",
      "12.2.2 Mixture Example (Continued) . . . . . . . . . . 421\n",
      "12.3 Support Vector Machines and Kernels . . . . . . . . . . . 423\n",
      "12.3.1 Computing the SVM for Classiﬁcation . . . . . . 423\n",
      "12.3.2 The SVM as a Penalization Method . . . . . . . 426\n",
      "12.3.3 Function Estimation and Reproducing Kernels . 428\n",
      "12.3.4 SVMs and the Curse of Dimensionality . . . . . 431\n",
      "12.3.5 A Path Algorithm for the SVM Classiﬁer . . . . 432\n",
      "12.3.6 Support Vector Machines for Regression . . . . . 434\n",
      "12.3.7 Regression and Kernels . . . . . . . . . . . . . . 436\n",
      "12.3.8 Discussion . . . . . . . . . . . . . . . . . . . . . 438\n",
      "12.4 Generalizing Linear Discriminant Analysis . . . . . . . . 4 38\n",
      "12.5 Flexible Discriminant Analysis . . . . . . . . . . . . . . . 440\n",
      "12.5.1 Computing the FDA Estimates . . . . . . . . . . 444\n",
      "12.6 Penalized Discriminant Analysis . . . . . . . . . . . . . . 446\n",
      "12.7 Mixture Discriminant Analysis . . . . . . . . . . . . . . . 449\n",
      "12.7.1 Example: Waveform Data . . . . . . . . . . . . . 451\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "13 Prototype Methods and Nearest-Neighbors 459\n",
      "13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2 Prototype Methods . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2.1K-means Clustering . . . . . . . . . . . . . . . . 460\n",
      "13.2.2 Learning Vector Quantization . . . . . . . . . . 462\n",
      "13.2.3 Gaussian Mixtures . . . . . . . . . . . . . . . . . 463\n",
      "13.3k-Nearest-Neighbor Classiﬁers . . . . . . . . . . . . . . . 463\n",
      "13.3.1 Example: A Comparative Study . . . . . . . . . 468\n",
      "13.3.2 Example: k-Nearest-Neighbors\n",
      "and Image Scene Classiﬁcation . . . . . . . . . . 470\n",
      "13.3.3 Invariant Metrics and Tangent Distance . . . . . 471\n",
      "13.4 Adaptive Nearest-Neighbor Methods . . . . . . . . . . . . 475\n",
      "13.4.1 Example . . . . . . . . . . . . . . . . . . . . . . 478\n",
      "13.4.2 Global Dimension Reduction\n",
      "for Nearest-Neighbors . . . . . . . . . . . . . . . 479\n",
      "13.5 Computational Considerations . . . . . . . . . . . . . . . 480\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed for readers familiar with the first edition and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. The new context describes additional content on support vector machines and flexible discriminants in Chapter 12, and prototype methods and nearest-neighbors in Chapter 13.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xx Contents\n",
      "14 Unsupervised Learning 485\n",
      "14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 485\n",
      "14.2 Association Rules . . . . . . . . . . . . . . . . . . . . . . 487\n",
      "14.2.1 Market Basket Analysis . . . . . . . . . . . . . . 488\n",
      "14.2.2 The Apriori Algorithm . . . . . . . . . . . . . . 489\n",
      "14.2.3 Example: Market Basket Analysis . . . . . . . . 492\n",
      "14.2.4 Unsupervised as Supervised Learning . . . . . . 495\n",
      "14.2.5 Generalized Association Rules . . . . . . . . . . 497\n",
      "14.2.6 Choice of Supervised Learning Method . . . . . 499\n",
      "14.2.7 Example: Market Basket Analysis (Continued) . 499\n",
      "14.3 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . 501\n",
      "14.3.1 Proximity Matrices . . . . . . . . . . . . . . . . 503\n",
      "14.3.2 Dissimilarities Based on Attributes . . . . . . . 503\n",
      "14.3.3 Object Dissimilarity . . . . . . . . . . . . . . . . 505\n",
      "14.3.4 Clustering Algorithms . . . . . . . . . . . . . . . 507\n",
      "14.3.5 Combinatorial Algorithms . . . . . . . . . . . . 507\n",
      "14.3.6K-means . . . . . . . . . . . . . . . . . . . . . . 509\n",
      "14.3.7 Gaussian Mixtures as Soft K-means Clustering . 510\n",
      "14.3.8 Example: Human Tumor Microarray Data . . . 512\n",
      "14.3.9 Vector Quantization . . . . . . . . . . . . . . . . 514\n",
      "14.3.10K-medoids . . . . . . . . . . . . . . . . . . . . . 515\n",
      "14.3.11 Practical Issues . . . . . . . . . . . . . . . . . . 518\n",
      "14.3.12 Hierarchical Clustering . . . . . . . . . . . . . . 520\n",
      "14.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . 528\n",
      "14.5 Principal Components, Curves and Surfaces . . . . . . . . 53 4\n",
      "14.5.1 Principal Components . . . . . . . . . . . . . . . 534\n",
      "14.5.2 Principal Curves and Surfaces . . . . . . . . . . 541\n",
      "14.5.3 Spectral Clustering . . . . . . . . . . . . . . . . 544\n",
      "14.5.4 Kernel Principal Components . . . . . . . . . . . 547\n",
      "14.5.5 Sparse Principal Components . . . . . . . . . . . 550\n",
      "14.6 Non-negative Matrix Factorization . . . . . . . . . . . . . 553\n",
      "14.6.1 Archetypal Analysis . . . . . . . . . . . . . . . . 554\n",
      "14.7 Independent Component Analysis\n",
      "and Exploratory Projection Pursuit . . . . . . . . . . . . 557\n",
      "14.7.1 Latent Variables and Factor Analysis . . . . . . 558\n",
      "14.7.2 Independent Component Analysis . . . . . . . . 560\n",
      "14.7.3 Exploratory Projection Pursuit . . . . . . . . . . 565\n",
      "14.7.4 A Direct Approach to ICA . . . . . . . . . . . . 565\n",
      "14.8 Multidimensional Scaling . . . . . . . . . . . . . . . . . . 570\n",
      "14.9 Nonlinear Dimension Reduction\n",
      "and Local Multidimensional Scaling . . . . . . . . . . . . 572\n",
      "14.10 The Google PageRank Algorithm . . . . . . . . . . . . . 576\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 578\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed for readers familiar with the first edition and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. The new context describes additional content on support vector machines and flexible discriminants in Chapter 12, and prototype methods and nearest-neighbors in Chapter 13. Additionally, the book includes chapters on unsupervised learning, such as association rules, cluster analysis, self-organizing maps, principal components, non-negative matrix factorization, independent component analysis, multidimensional scaling, and the Google PageRank algorithm.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "Contents xxi\n",
      "15 Random Forests 587\n",
      "15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 587\n",
      "15.2 Deﬁnition of Random Forests . . . . . . . . . . . . . . . . 587\n",
      "15.3 Details of Random Forests . . . . . . . . . . . . . . . . . 592\n",
      "15.3.1 Out of Bag Samples . . . . . . . . . . . . . . . . 592\n",
      "15.3.2 Variable Importance . . . . . . . . . . . . . . . . 593\n",
      "15.3.3 Proximity Plots . . . . . . . . . . . . . . . . . . 595\n",
      "15.3.4 Random Forests and Overﬁtting . . . . . . . . . 596\n",
      "15.4 Analysis of Random Forests . . . . . . . . . . . . . . . . . 597\n",
      "15.4.1 Variance and the De-Correlation Eﬀect . . . . . 597\n",
      "15.4.2 Bias . . . . . . . . . . . . . . . . . . . . . . . . . 600\n",
      "15.4.3 Adaptive Nearest Neighbors . . . . . . . . . . . 601\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 602\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603\n",
      "16 Ensemble Learning 605\n",
      "16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 605\n",
      "16.2 Boosting and Regularization Paths . . . . . . . . . . . . . 607\n",
      "16.2.1 Penalized Regression . . . . . . . . . . . . . . . 607\n",
      "16.2.2 The “Bet on Sparsity” Principle . . . . . . . . . 610\n",
      "16.2.3 Regularization Paths, Over-ﬁtting and Margins . 613\n",
      "16.3 Learning Ensembles . . . . . . . . . . . . . . . . . . . . . 616\n",
      "16.3.1 Learning a Good Ensemble . . . . . . . . . . . . 617\n",
      "16.3.2 Rule Ensembles . . . . . . . . . . . . . . . . . . 622\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 623\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624\n",
      "17 Undirected Graphical Models 625\n",
      "17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 625\n",
      "17.2 Markov Graphs and Their Properties . . . . . . . . . . . 627\n",
      "17.3 Undirected Graphical Models for Continuous Variables . 630\n",
      "17.3.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 631\n",
      "17.3.2 Estimation of the Graph Structure . . . . . . . . 635\n",
      "17.4 Undirected Graphical Models for Discrete Variables . . . 638\n",
      "17.4.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 639\n",
      "17.4.2 Hidden Nodes . . . . . . . . . . . . . . . . . . . 641\n",
      "17.4.3 Estimation of the Graph Structure . . . . . . . . 642\n",
      "17.4.4 Restricted Boltzmann Machines . . . . . . . . . 643\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645\n",
      "18 High-Dimensional Problems: p≫N 649\n",
      "18.1 When pis Much Bigger than N. . . . . . . . . . . . . . 649\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters and updates to existing chapters. The layout has been designed for readers familiar with the first edition and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces. The book covers various topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. The new context describes additional content on support vector machines and flexible discriminants in Chapter 12, and prototype methods and nearest-neighbors in Chapter 13. Additionally, the book includes chapters on unsupervised learning, such as association rules, cluster analysis, self-organizing maps, principal components, non-negative matrix factorization, independent component analysis, multidimensional scaling, and the Google PageRank algorithm. The new chapters added in the second edition include Random Forests, Ensemble Learning, Undirected Graphical Models, and High-Dimensional Problems.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "xxii Contents\n",
      "18.2 Diagonal Linear Discriminant Analysis\n",
      "and Nearest Shrunken Centroids . . . . . . . . . . . . . . 651\n",
      "18.3 Linear Classiﬁers with Quadratic Regularization . . . . . 654\n",
      "18.3.1 Regularized Discriminant Analysis . . . . . . . . 656\n",
      "18.3.2 Logistic Regression\n",
      "with Quadratic Regularization . . . . . . . . . . 657\n",
      "18.3.3 The Support Vector Classiﬁer . . . . . . . . . . 657\n",
      "18.3.4 Feature Selection . . . . . . . . . . . . . . . . . . 658\n",
      "18.3.5 Computational Shortcuts When p≫N. . . . . 659\n",
      "18.4 Linear Classiﬁers with L1Regularization . . . . . . . . . 661\n",
      "18.4.1 Application of Lasso\n",
      "to Protein Mass Spectroscopy . . . . . . . . . . 664\n",
      "18.4.2 The Fused Lasso for Functional Data . . . . . . 666\n",
      "18.5 Classiﬁcation When Features are Unavailable . . . . . . . 6 68\n",
      "18.5.1 Example: String Kernels\n",
      "and Protein Classiﬁcation . . . . . . . . . . . . . 668\n",
      "18.5.2 Classiﬁcation and Other Models Using\n",
      "Inner-Product Kernels and Pairwise Distances . 670\n",
      "18.5.3 Example: Abstracts Classiﬁcation . . . . . . . . 672\n",
      "18.6 High-Dimensional Regression:\n",
      "Supervised Principal Components . . . . . . . . . . . . . 674\n",
      "18.6.1 Connection to Latent-Variable Modeling . . . . 678\n",
      "18.6.2 Relationship with Partial Least Squares . . . . . 680\n",
      "18.6.3 Pre-Conditioning for Feature Selection . . . . . 681\n",
      "18.7 Feature Assessment and the Multiple-Testing Problem . . 683\n",
      "18.7.1 The False Discovery Rate . . . . . . . . . . . . . 687\n",
      "18.7.2 Asymmetric Cutpoints and the SAM Procedure 690\n",
      "18.7.3 A Bayesian Interpretation of the FDR . . . . . . 692\n",
      "18.8 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . 693\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694\n",
      "References 699\n",
      "Author Index 729\n",
      "Index 737\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3mYour job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: The second edition of \"The Elements of Statistical Learning\" includes four new chapters: Random Forests, Ensemble Learning, Undirected Graphical Models, and High-Dimensional Problems. The layout has been designed for readers familiar with the first edition, and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces and covers topics such as diagonal linear discriminant analysis, nearest shrunken centroids, linear classifiers with quadratic regularization, logistic regression with quadratic regularization, the support vector classifier, feature selection, linear classifiers with L1 regularization, classification when features are unavailable, high-dimensional regression with supervised principal components, feature assessment, and the multiple-testing problem. The book also covers various other topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. It also covers linear methods for regression and classification, basis expansions and regularization techniques, smoothing splines, and wavelet smoothing. Additionally, the book includes chapters on unsupervised learning, such as association rules, cluster analysis, self-organizing maps, principal components, non-negative matrix factorization, independent component analysis, multidimensional scaling, and the Google PageRank algorithm.\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "This is page 1\n",
      "Printer: Opaque this\n",
      "1\n",
      "Introduction\n",
      "Statistical learning plays a key role in many areas of science, ﬁnance and\n",
      "industry. Here are some examples of learning problems:\n",
      "•Predict whether a patient, hospitalized due to a heart attac k, will\n",
      "have a second heart attack. The prediction is to be based on de mo-\n",
      "graphic, diet and clinical measurements for that patient.\n",
      "•Predict the price of a stock in 6 months from now, on the basis o f\n",
      "company performance measures and economic data.\n",
      "•Identify the numbers in a handwritten ZIP code, from a digiti zed\n",
      "image.\n",
      "•Estimate the amount of glucose in the blood of a diabetic pers on,\n",
      "from the infrared absorption spectrum of that person’s bloo d.\n",
      "•Identify the risk factors for prostate cancer, based on clin ical and\n",
      "demographic variables.\n",
      "The science of learning plays a key role in the ﬁelds of statis tics, data\n",
      "mining and artiﬁcial intelligence, intersecting with area s of engineering and\n",
      "other disciplines.\n",
      "This book is about learning from data. In a typical scenario, we have\n",
      "an outcome measurement, usually quantitative (such as a sto ck price) or\n",
      "categorical (such as heart attack/no heart attack), that we wish to predict\n",
      "based on a set of features (such as diet and clinical measurements). We\n",
      "have atraining set of data, in which we observe the outcome and feature\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'The second edition of \"The Elements of Statistical Learning\" includes four new chapters: Random Forests, Ensemble Learning, Undirected Graphical Models, and High-Dimensional Problems. The layout has been designed for readers familiar with the first edition, and changes have been made to the color palette for colorblind readers. The name of Chapter 6 has been changed to \"Kernel Smoothing Methods\" to avoid confusion. The discussion of error-rate estimation has been improved. Chapters 15 and 16 should be read after Chapter 10, and Chapter 17 focuses on undirected graphical models. Chapter 18 explores learning in high-dimensional feature spaces and covers topics such as diagonal linear discriminant analysis, nearest shrunken centroids, linear classifiers with quadratic regularization, logistic regression with quadratic regularization, the support vector classifier, feature selection, linear classifiers with L1 regularization, classification when features are unavailable, high-dimensional regression with supervised principal components, feature assessment, and the multiple-testing problem. The book also covers various other topics including variable types, statistical decision theory, local methods in high dimensions, function approximation, and structured regression models. Additionally, the book includes chapters on unsupervised learning, such as association rules, cluster analysis, self-organizing maps, principal components, non-negative matrix factorization, independent component analysis, multidimensional scaling, and the Google PageRank algorithm. The book is about learning from data and covers various real-life examples of learning problems in fields such as healthcare, finance, and industry.'"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    chain_type=\"refine\",\n",
    "    verbose=True,\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your job is to produce a final summary.\n",
      "We have provided an existing summary up to a certain point: {existing_answer}\n",
      "We have the opportunity to refine the existing summary (only if needed) with some more context below.\n",
      "------------\n",
      "{text}\n",
      "------------\n",
      "Given the new context, refine the original summary.\n",
      "If the context isn't useful, return the original summary.\n"
     ]
    }
   ],
   "source": [
    "print(chain.refine_llm_chain.prompt.template)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\u001b[1m> Entering new RefineDocumentsChain chain...\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Extract the most relevant themes from the following:\n",
      "\n",
      "\"Springer Series in Statistics\n",
      "Trevor Hastie\n",
      "Robert TibshiraniJerome FriedmanSpringer Series in Statistics\n",
      "The Elements of\n",
      "Statistical Learning\n",
      "Data Mining, Inference, and Prediction\n",
      "The Elements of Statistical LearningDuring the past decade there has been an explosion in computation and information tech-\n",
      "nology. With it have come vast amounts of data in a variety of fields such as medicine, biolo-gy, finance, and marketing. The challenge of understanding these data has led to the devel-opment of new tools in the field of statistics, and spawned new areas such as data mining,machine learning, and bioinformatics. Many of these tools have common underpinnings butare often expressed with different terminology. This book describes the important ideas inthese areas in a common conceptual framework. While the approach is statistical, theemphasis is on concepts rather than mathematics. Many examples are given, with a liberaluse of color graphics. It should be a valuable resource for statisticians and anyone interestedin data mining in science or industry. The book’s coverage is broad, from supervised learning(prediction) to unsupervised learning. The many topics include neural networks, supportvector machines, classification trees and boosting—the first comprehensive treatment of thistopic in any book.\n",
      "This major new edition features many topics not covered in the original, including graphical\n",
      "models, random forests, ensemble methods, least angle regression & path algorithms for thelasso, non-negative matrix factorization, and spectral clustering. There is also a chapter onmethods for “wide” data (p bigger than n), including multiple testing and false discovery rates.\n",
      "Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at\n",
      "Stanford University. They are prominent researchers in this area: Hastie and Tibshiranideveloped generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS andinvented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of thevery successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.\n",
      "›springer.comSTATISTICS\n",
      "isbn 978-0-387-84857-0Trevor Hastie • Robert Tibshirani • Jerome Friedman\n",
      "The Elements of Statictical Learning\n",
      "Hastie • Tibshirani • Friedman\n",
      "Second Edition\"\n",
      "\n",
      "THEMES:\n",
      "\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: 1. Computation and information technology: The text mentions the explosion in computation and information technology, which has resulted in vast amounts of data in various fields. This theme highlights the importance of technological advancements in the field of statistics.\n",
      "\n",
      "2. Data analysis and understanding: The challenge of understanding large amounts of data has led to the development of new tools in statistics, such as data mining, machine learning, and bioinformatics. This theme emphasizes the importance of data analysis and interpretation.\n",
      "\n",
      "3. Statistical concepts and frameworks: The book aims to describe important ideas in statistics, data mining, and machine learning in a common conceptual framework. The emphasis is on concepts rather than mathematics, suggesting a focus on understanding the underlying principles.\n",
      "\n",
      "4. Broad coverage of topics: The book covers a wide range of topics, including supervised and unsupervised learning, neural networks, support vector machines, classification trees, boosting, graphical models, random forests, ensemble methods, and more. This theme highlights the breadth of topics covered in the book.\n",
      "\n",
      "5. Prominent researchers and their contributions: The authors of the book, Trevor Hastie, Robert Tibshirani, and Jerome Friedman, are professors of statistics at Stanford University and have made significant contributions to the field. This theme emphasizes the expertise and credibility of the authors.\n",
      "\n",
      "6. Updated edition: The text mentions that this edition includes new topics not covered in the original, such as graphical models, random forests, ensemble methods, and more. This theme suggests that the book is up-to-date and incorporates the latest developments in the field.\n",
      "\n",
      "7. Practical applications: The book is described as a valuable resource for statisticians and anyone interested in data mining in science or industry. This theme highlights the practical applications of the concepts and tools discussed in the book.\n",
      "\n",
      "8. Use of examples and graphics: The book includes many examples and uses color graphics to enhance understanding. This theme emphasizes the use of visual aids to illustrate concepts and enhance the learning experience.\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "This is page v\n",
      "Printer: Opaque this\n",
      "To our parents:\n",
      "Valerie and Patrick Hastie\n",
      "Vera and Sami Tibshirani\n",
      "Florence and Harry Friedman\n",
      "and to our families:\n",
      "Samantha, Timothy, and Lynda\n",
      "Charlie, Ryan, Julie, and Cheryl\n",
      "Melanie, Dora, Monika, and Ildiko\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "vi\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "This is page vii\n",
      "Printer: Opaque this\n",
      "Preface to the Second Edition\n",
      "In God we trust, all others bring data.\n",
      "–William Edwards Deming (1900-1993)1\n",
      "We have been gratiﬁed by the popularity of the ﬁrst edition of The\n",
      "Elements of Statistical Learning. This, along with the fast pace of research\n",
      "in the statistical learning ﬁeld, motivated us to update our book with a\n",
      "second edition.\n",
      "We have added four new chapters and updated some of the existi ng\n",
      "chapters. Because many readers are familiar with the layout of the ﬁrst\n",
      "edition, we have tried to change it as little as possible. Her e is a summary\n",
      "of the main changes:\n",
      "1On the Web, this quote has been widely attributed to both Deming and R obert W.\n",
      "Hayden; however Professor Hayden told us that he can claim no credit for th is quote,\n",
      "and ironically we could ﬁnd no “data” conﬁrming that Deming actual ly said this.\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "viii Preface to the Second Edition\n",
      "Chapter What’s new\n",
      "1.Introduction\n",
      "2.Overview of Supervised Learning\n",
      "3.Linear Methods for Regression LAR algorithm and generaliza tions\n",
      "of the lasso\n",
      "4.Linear Methods for Classiﬁcation Lasso path for logistic re gression\n",
      "5.Basis Expansions and Regulariza-\n",
      "tionAdditional illustrations of RKHS\n",
      "6.Kernel Smoothing Methods\n",
      "7.Model Assessment and Selection Strengths and pitfalls of cr oss-\n",
      "validation\n",
      "8.Model Inference and Averaging\n",
      "9.Additive Models, Trees, and\n",
      "Related Methods\n",
      "10.Boosting and Additive Trees New example from ecology; some\n",
      "material split oﬀ to Chapter 16.\n",
      "11.Neural Networks Bayesian neural nets and the NIPS\n",
      "2003 challenge\n",
      "12.Support Vector Machines and\n",
      "Flexible DiscriminantsPath algorithm for SVM classiﬁer\n",
      "13.Prototype Methods and\n",
      "Nearest-Neighbors\n",
      "14.Unsupervised Learning Spectral clustering, kernel PCA,\n",
      "sparse PCA, non-negative matrix\n",
      "factorization archetypal analysis,\n",
      "nonlinear dimension reduction,\n",
      "Google page rank algorithm, a\n",
      "direct approach to ICA\n",
      "15.Random Forests New\n",
      "16.Ensemble Learning New\n",
      "17.Undirected Graphical Models New\n",
      "18.High-Dimensional Problems New\n",
      "Some further notes:\n",
      "•Our ﬁrst edition was unfriendly to colorblind readers; in pa rticular,\n",
      "we tended to favor red/greencontrasts which are particularly trou-\n",
      "blesome. We have changed the color palette in this edition to a large\n",
      "extent, replacing the above with an orange/bluecontrast.\n",
      "•We have changed the name of Chapter 6 from “Kernel Methods” to\n",
      "“Kernel Smoothing Methods”, to avoid confusion with the mac hine-\n",
      "learningkernelmethodthatisdiscussedinthecontextofsu pportvec-\n",
      "tor machines (Chapter 12) and more generally in Chapters 5 an d 14.\n",
      "•In the ﬁrst edition, the discussion of error-rate estimatio n in Chap-\n",
      "ter 7 was sloppy, as we did not clearly diﬀerentiate the notio ns of\n",
      "conditional error rates (conditional on the training set) a nd uncondi-\n",
      "tional rates. We have ﬁxed this in the new edition.\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "Preface to the Second Edition ix\n",
      "•Chapters 15 and 16 follow naturally from Chapter 10, and the c hap-\n",
      "ters are probably best read in that order.\n",
      "•In Chapter 17, we have not attempted a comprehensive treatme nt\n",
      "of graphical models, and discuss only undirected models and some\n",
      "new methods for their estimation. Due to a lack of space, we ha ve\n",
      "speciﬁcally omitted coverage of directed graphical models .\n",
      "•Chapter 18 explores the “ p≫N” problem, which is learning in high-\n",
      "dimensional feature spaces. These problems arise in many ar eas, in-\n",
      "cluding genomic and proteomic studies, and document classi ﬁcation.\n",
      "We thank the many readers who have found the (too numerous) er rors in\n",
      "the ﬁrst edition. We apologize for those and have done our bes t to avoid er-\n",
      "rorsinthisnewedition.WethankMarkSegal,BalaRajaratna m,andLarry\n",
      "Wasserman for comments on some of the new chapters, and many S tanford\n",
      "graduate and post-doctoral students who oﬀered comments, i n particular\n",
      "Mohammed AlQuraishi, John Boik, Holger Hoeﬂing, Arian Male ki, Donal\n",
      "McMahon, Saharon Rosset, Babak Shababa, Daniela Witten, Ji Zhu and\n",
      "Hui Zou. We thank John Kimmel for his patience in guiding us th rough this\n",
      "new edition. RT dedicates this edition to the memory of Anna M cPhee.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "August 2008\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "x Preface to the Second Edition\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "This is page xi\n",
      "Printer: Opaque this\n",
      "Preface to the First Edition\n",
      "We are drowning in information and starving for knowledge.\n",
      "–Rutherford D. Roger\n",
      "The ﬁeld of Statistics is constantly challenged by the probl ems that science\n",
      "andindustrybringstoitsdoor.Intheearlydays,theseprob lemsoftencame\n",
      "from agricultural and industrial experiments and were rela tively small in\n",
      "scope. With the advent of computers and the information age, statistical\n",
      "problems have exploded both in size and complexity. Challen ges in the\n",
      "areas of data storage, organization and searching have led t o the new ﬁeld\n",
      "of “data mining”; statistical and computational problems i n biology and\n",
      "medicine have created “bioinformatics.” Vast amounts of da ta are being\n",
      "generated in many ﬁelds, and the statistician’s job is to mak e sense of it\n",
      "all: to extract important patterns and trends, and understa nd “what the\n",
      "data says.” We call this learning from data .\n",
      "The challenges in learning from data have led to a revolution in the sta-\n",
      "tisticalsciences.Sincecomputationplayssuchakeyrole, itisnotsurprising\n",
      "that much of this new development has been done by researcher s in other\n",
      "ﬁelds such as computer science and engineering.\n",
      "The learning problems that we consider can be roughly catego rized as\n",
      "eithersupervised orunsupervised . In supervised learning, the goal is to pre-\n",
      "dict the value of an outcome measure based on a number of input measures;\n",
      "in unsupervised learning, there is no outcome measure, and t he goal is to\n",
      "describe the associations and patterns among a set of input m easures.\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xii Preface to the First Edition\n",
      "This book is our attempt to bring together many of the importa nt new\n",
      "ideas in learning, and explain them in a statistical framewo rk. While some\n",
      "mathematical details are needed, we emphasize the methods a nd their con-\n",
      "ceptual underpinnings rather than their theoretical prope rties. As a result,\n",
      "we hope that this book will appeal not just to statisticians b ut also to\n",
      "researchers and practitioners in a wide variety of ﬁelds.\n",
      "Just as we have learned a great deal from researchers outside of the ﬁeld\n",
      "of statistics, our statistical viewpoint may help others to better understand\n",
      "diﬀerent aspects of learning:\n",
      "There is no true interpretation of anything; interpretatio n is a\n",
      "vehicle in the service of human comprehension. The value of\n",
      "interpretation is in enabling others to fruitfully think ab out an\n",
      "idea.\n",
      "–Andreas Buja\n",
      "We would like to acknowledge the contribution of many people to the\n",
      "conception and completion of this book. David Andrews, Leo B reiman,\n",
      "Andreas Buja, John Chambers, Bradley Efron, Geoﬀrey Hinton , Werner\n",
      "Stuetzle, and John Tukey have greatly inﬂuenced our careers . Balasub-\n",
      "ramanian Narasimhan gave us advice and help on many computat ional\n",
      "problems, and maintained an excellent computing environme nt. Shin-Ho\n",
      "Bang helped in the production of a number of the ﬁgures. Lee Wi lkinson\n",
      "gavevaluabletipsoncolorproduction.IlanaBelitskaya,E vaCantoni,Maya\n",
      "Gupta,MichaelJordan,ShantiGopatam,RadfordNeal,Jorge Picazo,Bog-\n",
      "dan Popescu, Olivier Renaud, Saharon Rosset, John Storey, J i Zhu, Mu\n",
      "Zhu, two reviewers and many students read parts of the manusc ript and\n",
      "oﬀered helpful suggestions. John Kimmel was supportive, pa tient and help-\n",
      "ful at every phase; MaryAnn Brickner and Frank Ganz headed a s uperb\n",
      "production team at Springer. Trevor Hastie would like to tha nk the statis-\n",
      "tics department at the University of Cape Town for their hosp itality during\n",
      "the ﬁnal stages of this book. We gratefully acknowledge NSF a nd NIH for\n",
      "their support of this work. Finally, we would like to thank ou r families and\n",
      "our parents for their love and support.\n",
      "Trevor Hastie\n",
      "Robert Tibshirani\n",
      "Jerome Friedman\n",
      "Stanford, California\n",
      "May 2001\n",
      "The quiet statisticians have changed our world; not by disco v-\n",
      "ering new facts or technical developments, but by changing t he\n",
      "ways that we reason, experiment and form our opinions ....\n",
      "–Ian Hacking\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "This is page xiii\n",
      "Printer: Opaque this\n",
      "Contents\n",
      "Preface to the Second Edition vii\n",
      "Preface to the First Edition xi\n",
      "1 Introduction 1\n",
      "2 Overview of Supervised Learning 9\n",
      "2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 9\n",
      "2.2 Variable Types and Terminology . . . . . . . . . . . . . . 9\n",
      "2.3 Two Simple Approaches to Prediction:\n",
      "Least Squares and Nearest Neighbors . . . . . . . . . . . 11\n",
      "2.3.1 Linear Models and Least Squares . . . . . . . . 11\n",
      "2.3.2 Nearest-Neighbor Methods . . . . . . . . . . . . 14\n",
      "2.3.3 From Least Squares to Nearest Neighbors . . . . 16\n",
      "2.4 Statistical Decision Theory . . . . . . . . . . . . . . . . . 18\n",
      "2.5 Local Methods in High Dimensions . . . . . . . . . . . . . 22\n",
      "2.6 Statistical Models, Supervised Learning\n",
      "and Function Approximation . . . . . . . . . . . . . . . . 28\n",
      "2.6.1 A Statistical Model\n",
      "for the Joint Distribution Pr( X,Y) . . . . . . . 28\n",
      "2.6.2 Supervised Learning . . . . . . . . . . . . . . . . 29\n",
      "2.6.3 Function Approximation . . . . . . . . . . . . . 29\n",
      "2.7 Structured Regression Models . . . . . . . . . . . . . . . 32\n",
      "2.7.1 Diﬃculty of the Problem . . . . . . . . . . . . . 32\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xiv Contents\n",
      "2.8 Classes of Restricted Estimators . . . . . . . . . . . . . . 33\n",
      "2.8.1 Roughness Penalty and Bayesian Methods . . . 34\n",
      "2.8.2 Kernel Methods and Local Regression . . . . . . 34\n",
      "2.8.3 Basis Functions and Dictionary Methods . . . . 35\n",
      "2.9 Model Selection and the Bias–Variance Tradeoﬀ . . . . . 37\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39\n",
      "3 Linear Methods for Regression 43\n",
      "3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43\n",
      "3.2 Linear Regression Models and Least Squares . . . . . . . 44\n",
      "3.2.1 Example: Prostate Cancer . . . . . . . . . . . . 49\n",
      "3.2.2 The Gauss–Markov Theorem . . . . . . . . . . . 51\n",
      "3.2.3 Multiple Regression\n",
      "from Simple Univariate Regression . . . . . . . . 52\n",
      "3.2.4 Multiple Outputs . . . . . . . . . . . . . . . . . 56\n",
      "3.3 Subset Selection . . . . . . . . . . . . . . . . . . . . . . . 57\n",
      "3.3.1 Best-Subset Selection . . . . . . . . . . . . . . . 57\n",
      "3.3.2 Forward- and Backward-Stepwise Selection . . . 58\n",
      "3.3.3 Forward-Stagewise Regression . . . . . . . . . . 60\n",
      "3.3.4 Prostate Cancer Data Example (Continued) . . 61\n",
      "3.4 Shrinkage Methods . . . . . . . . . . . . . . . . . . . . . . 61\n",
      "3.4.1 Ridge Regression . . . . . . . . . . . . . . . . . 61\n",
      "3.4.2 The Lasso . . . . . . . . . . . . . . . . . . . . . 68\n",
      "3.4.3 Discussion: Subset Selection, Ridge Regression\n",
      "and the Lasso . . . . . . . . . . . . . . . . . . . 69\n",
      "3.4.4 Least Angle Regression . . . . . . . . . . . . . . 73\n",
      "3.5 Methods Using Derived Input Directions . . . . . . . . . 79\n",
      "3.5.1 Principal Components Regression . . . . . . . . 79\n",
      "3.5.2 Partial Least Squares . . . . . . . . . . . . . . . 80\n",
      "3.6 Discussion: A Comparison of the Selection\n",
      "and Shrinkage Methods . . . . . . . . . . . . . . . . . . . 82\n",
      "3.7 Multiple Outcome Shrinkage and Selection . . . . . . . . 84\n",
      "3.8 More on the Lasso and Related Path Algorithms . . . . . 86\n",
      "3.8.1 Incremental Forward Stagewise Regression . . . 86\n",
      "3.8.2 Piecewise-Linear Path Algorithms . . . . . . . . 89\n",
      "3.8.3 The Dantzig Selector . . . . . . . . . . . . . . . 89\n",
      "3.8.4 The Grouped Lasso . . . . . . . . . . . . . . . . 90\n",
      "3.8.5 Further Properties of the Lasso . . . . . . . . . . 91\n",
      "3.8.6 Pathwise Coordinate Optimization . . . . . . . . 92\n",
      "3.9 Computational Considerations . . . . . . . . . . . . . . . 93\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "Contents xv\n",
      "4 Linear Methods for Classiﬁcation 101\n",
      "4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 101\n",
      "4.2 Linear Regression of an Indicator Matrix . . . . . . . . . 103\n",
      "4.3 Linear Discriminant Analysis . . . . . . . . . . . . . . . . 106\n",
      "4.3.1 Regularized Discriminant Analysis . . . . . . . . 112\n",
      "4.3.2 Computations for LDA . . . . . . . . . . . . . . 113\n",
      "4.3.3 Reduced-Rank Linear Discriminant Analysis . . 113\n",
      "4.4 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . 119\n",
      "4.4.1 Fitting Logistic Regression Models . . . . . . . . 120\n",
      "4.4.2 Example: South African Heart Disease . . . . . 122\n",
      "4.4.3 Quadratic Approximations and Inference . . . . 124\n",
      "4.4.4L1Regularized Logistic Regression . . . . . . . . 125\n",
      "4.4.5 Logistic Regression or LDA? . . . . . . . . . . . 127\n",
      "4.5 Separating Hyperplanes . . . . . . . . . . . . . . . . . . . 129\n",
      "4.5.1 Rosenblatt’s Perceptron Learning Algorithm . . 130\n",
      "4.5.2 Optimal Separating Hyperplanes . . . . . . . . . 132\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135\n",
      "5 Basis Expansions and Regularization 139\n",
      "5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 139\n",
      "5.2 Piecewise Polynomials and Splines . . . . . . . . . . . . . 141\n",
      "5.2.1 Natural Cubic Splines . . . . . . . . . . . . . . . 144\n",
      "5.2.2 Example:SouthAfricanHeartDisease(Continued)146\n",
      "5.2.3 Example: Phoneme Recognition . . . . . . . . . 148\n",
      "5.3 Filtering and Feature Extraction . . . . . . . . . . . . . . 150\n",
      "5.4 Smoothing Splines . . . . . . . . . . . . . . . . . . . . . . 151\n",
      "5.4.1 Degrees of Freedom and Smoother Matrices . . . 153\n",
      "5.5 Automatic Selection of the Smoothing Parameters . . . . 15 6\n",
      "5.5.1 Fixing the Degrees of Freedom . . . . . . . . . . 158\n",
      "5.5.2 The Bias–Variance Tradeoﬀ . . . . . . . . . . . . 158\n",
      "5.6 Nonparametric Logistic Regression . . . . . . . . . . . . . 161\n",
      "5.7 Multidimensional Splines . . . . . . . . . . . . . . . . . . 162\n",
      "5.8 Regularization and Reproducing Kernel Hilbert Spaces . 167\n",
      "5.8.1 Spaces of Functions Generated by Kernels . . . 168\n",
      "5.8.2 Examples of RKHS . . . . . . . . . . . . . . . . 170\n",
      "5.9 Wavelet Smoothing . . . . . . . . . . . . . . . . . . . . . 174\n",
      "5.9.1 Wavelet Bases and the Wavelet Transform . . . 176\n",
      "5.9.2 Adaptive Wavelet Filtering . . . . . . . . . . . . 179\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181\n",
      "Appendix: Computational Considerations for Splines . . . . . . 186\n",
      "Appendix:B-splines . . . . . . . . . . . . . . . . . . . . . 186\n",
      "Appendix: Computations for Smoothing Splines . . . . . 189\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xvi Contents\n",
      "6 Kernel Smoothing Methods 191\n",
      "6.1 One-Dimensional Kernel Smoothers . . . . . . . . . . . . 192\n",
      "6.1.1 Local Linear Regression . . . . . . . . . . . . . . 194\n",
      "6.1.2 Local Polynomial Regression . . . . . . . . . . . 197\n",
      "6.2 Selecting the Width of the Kernel . . . . . . . . . . . . . 198\n",
      "6.3 Local Regression in IRp. . . . . . . . . . . . . . . . . . . 200\n",
      "6.4 Structured Local Regression Models in IRp. . . . . . . . 201\n",
      "6.4.1 Structured Kernels . . . . . . . . . . . . . . . . . 203\n",
      "6.4.2 Structured Regression Functions . . . . . . . . . 203\n",
      "6.5 Local Likelihood and Other Models . . . . . . . . . . . . 205\n",
      "6.6 Kernel Density Estimation and Classiﬁcation . . . . . . . 20 8\n",
      "6.6.1 Kernel Density Estimation . . . . . . . . . . . . 208\n",
      "6.6.2 Kernel Density Classiﬁcation . . . . . . . . . . . 210\n",
      "6.6.3 The Naive Bayes Classiﬁer . . . . . . . . . . . . 210\n",
      "6.7 Radial Basis Functions and Kernels . . . . . . . . . . . . 212\n",
      "6.8 Mixture Models for Density Estimation and Classiﬁcatio n 214\n",
      "6.9 Computational Considerations . . . . . . . . . . . . . . . 216\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216\n",
      "7 Model Assessment and Selection 219\n",
      "7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 219\n",
      "7.2 Bias, Variance and Model Complexity . . . . . . . . . . . 219\n",
      "7.3 The Bias–Variance Decomposition . . . . . . . . . . . . . 223\n",
      "7.3.1 Example: Bias–Variance Tradeoﬀ . . . . . . . . 226\n",
      "7.4 Optimism of the Training Error Rate . . . . . . . . . . . 228\n",
      "7.5 Estimates of In-Sample Prediction Error . . . . . . . . . . 230\n",
      "7.6 The Eﬀective Number of Parameters . . . . . . . . . . . . 232\n",
      "7.7 The Bayesian Approach and BIC . . . . . . . . . . . . . . 233\n",
      "7.8 Minimum Description Length . . . . . . . . . . . . . . . . 235\n",
      "7.9 Vapnik–Chervonenkis Dimension . . . . . . . . . . . . . . 237\n",
      "7.9.1 Example (Continued) . . . . . . . . . . . . . . . 239\n",
      "7.10 Cross-Validation . . . . . . . . . . . . . . . . . . . . . . . 241\n",
      "7.10.1K-Fold Cross-Validation . . . . . . . . . . . . . 241\n",
      "7.10.2 The Wrong and Right Way\n",
      "to Do Cross-validation . . . . . . . . . . . . . . . 245\n",
      "7.10.3 Does Cross-Validation Really Work? . . . . . . . 247\n",
      "7.11 Bootstrap Methods . . . . . . . . . . . . . . . . . . . . . 249\n",
      "7.11.1 Example (Continued) . . . . . . . . . . . . . . . 252\n",
      "7.12 Conditional or Expected Test Error? . . . . . . . . . . . . 254\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257\n",
      "8 Model Inference and Averaging 261\n",
      "8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 261\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "Contents xvii\n",
      "8.2 The Bootstrap and Maximum Likelihood Methods . . . . 261\n",
      "8.2.1 A Smoothing Example . . . . . . . . . . . . . . 261\n",
      "8.2.2 Maximum Likelihood Inference . . . . . . . . . . 265\n",
      "8.2.3 Bootstrap versus Maximum Likelihood . . . . . 267\n",
      "8.3 Bayesian Methods . . . . . . . . . . . . . . . . . . . . . . 267\n",
      "8.4 Relationship Between the Bootstrap\n",
      "and Bayesian Inference . . . . . . . . . . . . . . . . . . . 271\n",
      "8.5 The EM Algorithm . . . . . . . . . . . . . . . . . . . . . 272\n",
      "8.5.1 Two-Component Mixture Model . . . . . . . . . 272\n",
      "8.5.2 The EM Algorithm in General . . . . . . . . . . 276\n",
      "8.5.3 EM as a Maximization–Maximization Procedure 277\n",
      "8.6 MCMC for Sampling from the Posterior . . . . . . . . . . 279\n",
      "8.7 Bagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282\n",
      "8.7.1 Example: Trees with Simulated Data . . . . . . 283\n",
      "8.8 Model Averaging and Stacking . . . . . . . . . . . . . . . 288\n",
      "8.9 Stochastic Search: Bumping . . . . . . . . . . . . . . . . . 290\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 292\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293\n",
      "9 Additive Models, Trees, and Related Methods 295\n",
      "9.1 Generalized Additive Models . . . . . . . . . . . . . . . . 295\n",
      "9.1.1 Fitting Additive Models . . . . . . . . . . . . . . 297\n",
      "9.1.2 Example: Additive Logistic Regression . . . . . 299\n",
      "9.1.3 Summary . . . . . . . . . . . . . . . . . . . . . . 304\n",
      "9.2 Tree-Based Methods . . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.1 Background . . . . . . . . . . . . . . . . . . . . 305\n",
      "9.2.2 Regression Trees . . . . . . . . . . . . . . . . . . 307\n",
      "9.2.3 Classiﬁcation Trees . . . . . . . . . . . . . . . . 308\n",
      "9.2.4 Other Issues . . . . . . . . . . . . . . . . . . . . 310\n",
      "9.2.5 Spam Example (Continued) . . . . . . . . . . . 313\n",
      "9.3 PRIM: Bump Hunting . . . . . . . . . . . . . . . . . . . . 317\n",
      "9.3.1 Spam Example (Continued) . . . . . . . . . . . 320\n",
      "9.4 MARS: Multivariate Adaptive Regression Splines . . . . . 3 21\n",
      "9.4.1 Spam Example (Continued) . . . . . . . . . . . 326\n",
      "9.4.2 Example (Simulated Data) . . . . . . . . . . . . 327\n",
      "9.4.3 Other Issues . . . . . . . . . . . . . . . . . . . . 328\n",
      "9.5 Hierarchical Mixtures of Experts . . . . . . . . . . . . . . 329\n",
      "9.6 Missing Data . . . . . . . . . . . . . . . . . . . . . . . . . 332\n",
      "9.7 Computational Considerations . . . . . . . . . . . . . . . 334\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 334\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335\n",
      "10 Boosting and Additive Trees 337\n",
      "10.1 Boosting Methods . . . . . . . . . . . . . . . . . . . . . . 337\n",
      "10.1.1 Outline of This Chapter . . . . . . . . . . . . . . 340\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xviii Contents\n",
      "10.2 Boosting Fits an Additive Model . . . . . . . . . . . . . . 341\n",
      "10.3 Forward Stagewise Additive Modeling . . . . . . . . . . . 342\n",
      "10.4 Exponential Loss and AdaBoost . . . . . . . . . . . . . . 343\n",
      "10.5 Why Exponential Loss? . . . . . . . . . . . . . . . . . . . 345\n",
      "10.6 Loss Functions and Robustness . . . . . . . . . . . . . . . 346\n",
      "10.7 “Oﬀ-the-Shelf” Procedures for Data Mining . . . . . . . . 35 0\n",
      "10.8 Example: Spam Data . . . . . . . . . . . . . . . . . . . . 352\n",
      "10.9 Boosting Trees . . . . . . . . . . . . . . . . . . . . . . . . 353\n",
      "10.10 Numerical Optimization via Gradient Boosting . . . . . . 358\n",
      "10.10.1 Steepest Descent . . . . . . . . . . . . . . . . . . 358\n",
      "10.10.2 Gradient Boosting . . . . . . . . . . . . . . . . . 359\n",
      "10.10.3 Implementations of Gradient Boosting . . . . . . 360\n",
      "10.11 Right-Sized Trees for Boosting . . . . . . . . . . . . . . . 361\n",
      "10.12 Regularization . . . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.1 Shrinkage . . . . . . . . . . . . . . . . . . . . . . 364\n",
      "10.12.2 Subsampling . . . . . . . . . . . . . . . . . . . . 365\n",
      "10.13 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . 367\n",
      "10.13.1 Relative Importance of Predictor Variables . . . 367\n",
      "10.13.2 Partial Dependence Plots . . . . . . . . . . . . . 369\n",
      "10.14 Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . 371\n",
      "10.14.1 California Housing . . . . . . . . . . . . . . . . . 371\n",
      "10.14.2 New Zealand Fish . . . . . . . . . . . . . . . . . 375\n",
      "10.14.3 Demographics Data . . . . . . . . . . . . . . . . 379\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 380\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384\n",
      "11 Neural Networks 389\n",
      "11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 389\n",
      "11.2 Projection Pursuit Regression . . . . . . . . . . . . . . . 389\n",
      "11.3 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 392\n",
      "11.4 Fitting Neural Networks . . . . . . . . . . . . . . . . . . . 395\n",
      "11.5 Some Issues in Training Neural Networks . . . . . . . . . 397\n",
      "11.5.1 Starting Values . . . . . . . . . . . . . . . . . . . 397\n",
      "11.5.2 Overﬁtting . . . . . . . . . . . . . . . . . . . . . 398\n",
      "11.5.3 Scaling of the Inputs . . . . . . . . . . . . . . . 398\n",
      "11.5.4 Number of Hidden Units and Layers . . . . . . . 400\n",
      "11.5.5 Multiple Minima . . . . . . . . . . . . . . . . . . 400\n",
      "11.6 Example: Simulated Data . . . . . . . . . . . . . . . . . . 401\n",
      "11.7 Example: ZIP Code Data . . . . . . . . . . . . . . . . . . 404\n",
      "11.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 408\n",
      "11.9 Bayesian Neural Nets and the NIPS 2003 Challenge . . . 409\n",
      "11.9.1 Bayes, Boosting and Bagging . . . . . . . . . . . 410\n",
      "11.9.2 Performance Comparisons . . . . . . . . . . . . 412\n",
      "11.10 Computational Considerations . . . . . . . . . . . . . . . 414\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "Contents xix\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415\n",
      "12 Support Vector Machines and\n",
      "Flexible Discriminants 417\n",
      "12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 417\n",
      "12.2 The Support Vector Classiﬁer . . . . . . . . . . . . . . . . 417\n",
      "12.2.1 Computing the Support Vector Classiﬁer . . . . 420\n",
      "12.2.2 Mixture Example (Continued) . . . . . . . . . . 421\n",
      "12.3 Support Vector Machines and Kernels . . . . . . . . . . . 423\n",
      "12.3.1 Computing the SVM for Classiﬁcation . . . . . . 423\n",
      "12.3.2 The SVM as a Penalization Method . . . . . . . 426\n",
      "12.3.3 Function Estimation and Reproducing Kernels . 428\n",
      "12.3.4 SVMs and the Curse of Dimensionality . . . . . 431\n",
      "12.3.5 A Path Algorithm for the SVM Classiﬁer . . . . 432\n",
      "12.3.6 Support Vector Machines for Regression . . . . . 434\n",
      "12.3.7 Regression and Kernels . . . . . . . . . . . . . . 436\n",
      "12.3.8 Discussion . . . . . . . . . . . . . . . . . . . . . 438\n",
      "12.4 Generalizing Linear Discriminant Analysis . . . . . . . . 4 38\n",
      "12.5 Flexible Discriminant Analysis . . . . . . . . . . . . . . . 440\n",
      "12.5.1 Computing the FDA Estimates . . . . . . . . . . 444\n",
      "12.6 Penalized Discriminant Analysis . . . . . . . . . . . . . . 446\n",
      "12.7 Mixture Discriminant Analysis . . . . . . . . . . . . . . . 449\n",
      "12.7.1 Example: Waveform Data . . . . . . . . . . . . . 451\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455\n",
      "13 Prototype Methods and Nearest-Neighbors 459\n",
      "13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2 Prototype Methods . . . . . . . . . . . . . . . . . . . . . 459\n",
      "13.2.1K-means Clustering . . . . . . . . . . . . . . . . 460\n",
      "13.2.2 Learning Vector Quantization . . . . . . . . . . 462\n",
      "13.2.3 Gaussian Mixtures . . . . . . . . . . . . . . . . . 463\n",
      "13.3k-Nearest-Neighbor Classiﬁers . . . . . . . . . . . . . . . 463\n",
      "13.3.1 Example: A Comparative Study . . . . . . . . . 468\n",
      "13.3.2 Example: k-Nearest-Neighbors\n",
      "and Image Scene Classiﬁcation . . . . . . . . . . 470\n",
      "13.3.3 Invariant Metrics and Tangent Distance . . . . . 471\n",
      "13.4 Adaptive Nearest-Neighbor Methods . . . . . . . . . . . . 475\n",
      "13.4.1 Example . . . . . . . . . . . . . . . . . . . . . . 478\n",
      "13.4.2 Global Dimension Reduction\n",
      "for Nearest-Neighbors . . . . . . . . . . . . . . . 479\n",
      "13.5 Computational Considerations . . . . . . . . . . . . . . . 480\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xx Contents\n",
      "14 Unsupervised Learning 485\n",
      "14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 485\n",
      "14.2 Association Rules . . . . . . . . . . . . . . . . . . . . . . 487\n",
      "14.2.1 Market Basket Analysis . . . . . . . . . . . . . . 488\n",
      "14.2.2 The Apriori Algorithm . . . . . . . . . . . . . . 489\n",
      "14.2.3 Example: Market Basket Analysis . . . . . . . . 492\n",
      "14.2.4 Unsupervised as Supervised Learning . . . . . . 495\n",
      "14.2.5 Generalized Association Rules . . . . . . . . . . 497\n",
      "14.2.6 Choice of Supervised Learning Method . . . . . 499\n",
      "14.2.7 Example: Market Basket Analysis (Continued) . 499\n",
      "14.3 Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . 501\n",
      "14.3.1 Proximity Matrices . . . . . . . . . . . . . . . . 503\n",
      "14.3.2 Dissimilarities Based on Attributes . . . . . . . 503\n",
      "14.3.3 Object Dissimilarity . . . . . . . . . . . . . . . . 505\n",
      "14.3.4 Clustering Algorithms . . . . . . . . . . . . . . . 507\n",
      "14.3.5 Combinatorial Algorithms . . . . . . . . . . . . 507\n",
      "14.3.6K-means . . . . . . . . . . . . . . . . . . . . . . 509\n",
      "14.3.7 Gaussian Mixtures as Soft K-means Clustering . 510\n",
      "14.3.8 Example: Human Tumor Microarray Data . . . 512\n",
      "14.3.9 Vector Quantization . . . . . . . . . . . . . . . . 514\n",
      "14.3.10K-medoids . . . . . . . . . . . . . . . . . . . . . 515\n",
      "14.3.11 Practical Issues . . . . . . . . . . . . . . . . . . 518\n",
      "14.3.12 Hierarchical Clustering . . . . . . . . . . . . . . 520\n",
      "14.4 Self-Organizing Maps . . . . . . . . . . . . . . . . . . . . 528\n",
      "14.5 Principal Components, Curves and Surfaces . . . . . . . . 53 4\n",
      "14.5.1 Principal Components . . . . . . . . . . . . . . . 534\n",
      "14.5.2 Principal Curves and Surfaces . . . . . . . . . . 541\n",
      "14.5.3 Spectral Clustering . . . . . . . . . . . . . . . . 544\n",
      "14.5.4 Kernel Principal Components . . . . . . . . . . . 547\n",
      "14.5.5 Sparse Principal Components . . . . . . . . . . . 550\n",
      "14.6 Non-negative Matrix Factorization . . . . . . . . . . . . . 553\n",
      "14.6.1 Archetypal Analysis . . . . . . . . . . . . . . . . 554\n",
      "14.7 Independent Component Analysis\n",
      "and Exploratory Projection Pursuit . . . . . . . . . . . . 557\n",
      "14.7.1 Latent Variables and Factor Analysis . . . . . . 558\n",
      "14.7.2 Independent Component Analysis . . . . . . . . 560\n",
      "14.7.3 Exploratory Projection Pursuit . . . . . . . . . . 565\n",
      "14.7.4 A Direct Approach to ICA . . . . . . . . . . . . 565\n",
      "14.8 Multidimensional Scaling . . . . . . . . . . . . . . . . . . 570\n",
      "14.9 Nonlinear Dimension Reduction\n",
      "and Local Multidimensional Scaling . . . . . . . . . . . . 572\n",
      "14.10 The Google PageRank Algorithm . . . . . . . . . . . . . 576\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 578\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "Contents xxi\n",
      "15 Random Forests 587\n",
      "15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 587\n",
      "15.2 Deﬁnition of Random Forests . . . . . . . . . . . . . . . . 587\n",
      "15.3 Details of Random Forests . . . . . . . . . . . . . . . . . 592\n",
      "15.3.1 Out of Bag Samples . . . . . . . . . . . . . . . . 592\n",
      "15.3.2 Variable Importance . . . . . . . . . . . . . . . . 593\n",
      "15.3.3 Proximity Plots . . . . . . . . . . . . . . . . . . 595\n",
      "15.3.4 Random Forests and Overﬁtting . . . . . . . . . 596\n",
      "15.4 Analysis of Random Forests . . . . . . . . . . . . . . . . . 597\n",
      "15.4.1 Variance and the De-Correlation Eﬀect . . . . . 597\n",
      "15.4.2 Bias . . . . . . . . . . . . . . . . . . . . . . . . . 600\n",
      "15.4.3 Adaptive Nearest Neighbors . . . . . . . . . . . 601\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 602\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603\n",
      "16 Ensemble Learning 605\n",
      "16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 605\n",
      "16.2 Boosting and Regularization Paths . . . . . . . . . . . . . 607\n",
      "16.2.1 Penalized Regression . . . . . . . . . . . . . . . 607\n",
      "16.2.2 The “Bet on Sparsity” Principle . . . . . . . . . 610\n",
      "16.2.3 Regularization Paths, Over-ﬁtting and Margins . 613\n",
      "16.3 Learning Ensembles . . . . . . . . . . . . . . . . . . . . . 616\n",
      "16.3.1 Learning a Good Ensemble . . . . . . . . . . . . 617\n",
      "16.3.2 Rule Ensembles . . . . . . . . . . . . . . . . . . 622\n",
      "Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . . . . . 623\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624\n",
      "17 Undirected Graphical Models 625\n",
      "17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 625\n",
      "17.2 Markov Graphs and Their Properties . . . . . . . . . . . 627\n",
      "17.3 Undirected Graphical Models for Continuous Variables . 630\n",
      "17.3.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 631\n",
      "17.3.2 Estimation of the Graph Structure . . . . . . . . 635\n",
      "17.4 Undirected Graphical Models for Discrete Variables . . . 638\n",
      "17.4.1 Estimation of the Parameters\n",
      "when the Graph Structure is Known . . . . . . . 639\n",
      "17.4.2 Hidden Nodes . . . . . . . . . . . . . . . . . . . 641\n",
      "17.4.3 Estimation of the Graph Structure . . . . . . . . 642\n",
      "17.4.4 Restricted Boltzmann Machines . . . . . . . . . 643\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645\n",
      "18 High-Dimensional Problems: p≫N 649\n",
      "18.1 When pis Much Bigger than N. . . . . . . . . . . . . . 649\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "xxii Contents\n",
      "18.2 Diagonal Linear Discriminant Analysis\n",
      "and Nearest Shrunken Centroids . . . . . . . . . . . . . . 651\n",
      "18.3 Linear Classiﬁers with Quadratic Regularization . . . . . 654\n",
      "18.3.1 Regularized Discriminant Analysis . . . . . . . . 656\n",
      "18.3.2 Logistic Regression\n",
      "with Quadratic Regularization . . . . . . . . . . 657\n",
      "18.3.3 The Support Vector Classiﬁer . . . . . . . . . . 657\n",
      "18.3.4 Feature Selection . . . . . . . . . . . . . . . . . . 658\n",
      "18.3.5 Computational Shortcuts When p≫N. . . . . 659\n",
      "18.4 Linear Classiﬁers with L1Regularization . . . . . . . . . 661\n",
      "18.4.1 Application of Lasso\n",
      "to Protein Mass Spectroscopy . . . . . . . . . . 664\n",
      "18.4.2 The Fused Lasso for Functional Data . . . . . . 666\n",
      "18.5 Classiﬁcation When Features are Unavailable . . . . . . . 6 68\n",
      "18.5.1 Example: String Kernels\n",
      "and Protein Classiﬁcation . . . . . . . . . . . . . 668\n",
      "18.5.2 Classiﬁcation and Other Models Using\n",
      "Inner-Product Kernels and Pairwise Distances . 670\n",
      "18.5.3 Example: Abstracts Classiﬁcation . . . . . . . . 672\n",
      "18.6 High-Dimensional Regression:\n",
      "Supervised Principal Components . . . . . . . . . . . . . 674\n",
      "18.6.1 Connection to Latent-Variable Modeling . . . . 678\n",
      "18.6.2 Relationship with Partial Least Squares . . . . . 680\n",
      "18.6.3 Pre-Conditioning for Feature Selection . . . . . 681\n",
      "18.7 Feature Assessment and the Multiple-Testing Problem . . 683\n",
      "18.7.1 The False Discovery Rate . . . . . . . . . . . . . 687\n",
      "18.7.2 Asymmetric Cutpoints and the SAM Procedure 690\n",
      "18.7.3 A Bayesian Interpretation of the FDR . . . . . . 692\n",
      "18.8 Bibliographic Notes . . . . . . . . . . . . . . . . . . . . . 693\n",
      "Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694\n",
      "References 699\n",
      "Author Index 729\n",
      "Index 737\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\n",
      "\u001b[1m> Entering new LLMChain chain...\u001b[0m\n",
      "Prompt after formatting:\n",
      "\u001b[32;1m\u001b[1;3m\n",
      "Your job is to extract the most relevant themes\n",
      "We have provided you with the list of themes up to a certain point: Computation and information technology, Data analysis and understanding, Statistical concepts and frameworks, Broad coverage of topics, Prominent researchers and their contributions, Updated edition, Practical applications, Use of examples and graphics\n",
      "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
      "\n",
      "----------\n",
      "This is page 1\n",
      "Printer: Opaque this\n",
      "1\n",
      "Introduction\n",
      "Statistical learning plays a key role in many areas of science, ﬁnance and\n",
      "industry. Here are some examples of learning problems:\n",
      "•Predict whether a patient, hospitalized due to a heart attac k, will\n",
      "have a second heart attack. The prediction is to be based on de mo-\n",
      "graphic, diet and clinical measurements for that patient.\n",
      "•Predict the price of a stock in 6 months from now, on the basis o f\n",
      "company performance measures and economic data.\n",
      "•Identify the numbers in a handwritten ZIP code, from a digiti zed\n",
      "image.\n",
      "•Estimate the amount of glucose in the blood of a diabetic pers on,\n",
      "from the infrared absorption spectrum of that person’s bloo d.\n",
      "•Identify the risk factors for prostate cancer, based on clin ical and\n",
      "demographic variables.\n",
      "The science of learning plays a key role in the ﬁelds of statis tics, data\n",
      "mining and artiﬁcial intelligence, intersecting with area s of engineering and\n",
      "other disciplines.\n",
      "This book is about learning from data. In a typical scenario, we have\n",
      "an outcome measurement, usually quantitative (such as a sto ck price) or\n",
      "categorical (such as heart attack/no heart attack), that we wish to predict\n",
      "based on a set of features (such as diet and clinical measurements). We\n",
      "have atraining set of data, in which we observe the outcome and feature\n",
      "----------\n",
      "\n",
      "Given the new context, refine the original list\n",
      "If the context isn't useful, return the original list, and ONLY the original list.\n",
      "\n",
      "Return that list as a comma separated list.\n",
      "\n",
      "LIST:\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n",
      "\n",
      "\u001b[1m> Finished chain.\u001b[0m\n"
     ]
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   ],
   "source": [
    "initial_template_example = \"\"\"\n",
    "Extract the most relevant themes from the following:\n",
    "\n",
    "\"{text}\"\n",
    "\n",
    "THEMES:\n",
    "\"\"\"\n",
    "\n",
    "refine_template_example = \"\"\"\n",
    "Your job is to extract the most relevant themes\n",
    "We have provided you with the list of themes up to a certain point: {existing_answer}\n",
    "We have the opportunity to refine the existing list(only if needed) with some more context bellow:\n",
    "\n",
    "----------\n",
    "{text}\n",
    "----------\n",
    "\n",
    "Given the new context, refine the original list\n",
    "If the context isn't useful, return the original list, and ONLY the original list.\n",
    "\n",
    "Return that list as a comma separated list.\n",
    "\n",
    "LIST:\"\"\"\n",
    "\n",
    "chain = load_summarize_chain(\n",
    "    llm=llm,\n",
    "    question_prompt=PromptTemplate.from_template(initial_template_example),\n",
    "    refine_prompt=PromptTemplate.from_template(refine_template_example),\n",
    "    chain_type=\"refine\",\n",
    "    verbose=True,\n",
    ")\n",
    "\n",
    "chain.run(sl_data[:20])"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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