DS_Lecture8.ipynb

{
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   "attachments": {},
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   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Advanced Topics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "%precision 3\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import datasets\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-Nearest Neighbors (KNN)\n",
    "\n",
    "<img src=\"./figures/irisDataCampKNN.jpeg\" width=600>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "KNeighborsClassifier(n_neighbors=6)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = datasets.load_iris()\n",
    "knn = KNeighborsClassifier(n_neighbors=6)\n",
    "knn.fit(iris['data'], iris['target'])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Task: Split the iris data into training and test. Predict on test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "# Split into training and test set\n",
    "X = iris['data']\n",
    "y = iris['target']\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state=42)\n",
    "\n",
    "# Create a k-NN classifier with 7 neighbors: knn\n",
    "knn = KNeighborsClassifier(n_neighbors=6)\n",
    "\n",
    "# Fit the classifier to the training data\n",
    "knn.fit(X_train, y_train)\n",
    "\n",
    "# Print the accuracy\n",
    "print(knn.score(X_test, y_test))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple Idea, no modeling assumptions at all !!\n",
    "Think about the following:\n",
    "\n",
    "- What is \"the model\", i.e. what needs to be stored ? (coefficients, functions, ...)\n",
    "- What is the model complexity ?\n",
    "- Does this only work for classification ? What would be the regression analogy ?\n",
    "- What improvements could we make to the simple idea ?\n",
    "- In the modeling world:\n",
    "    * linear ?\n",
    "    * local vs. global\n",
    "    * memory/CPU requirements\n",
    "    * wide versus tall data ?\n",
    "\n",
    "\n",
    "#### Handwritten Digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 640x480 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits = datasets.load_digits()\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#how can I improve the plots ? (i..e no margins, box around plot...)\n",
    "plt.figure(1)\n",
    "\n",
    "for i in np.arange(10)+1:\n",
    "    plt.subplot(2, 5, i)\n",
    "    plt.axis('off')\n",
    "    #plt.gray() \n",
    "    #plt.matshow(digits.images[i-1]) \n",
    "    plt.imshow(digits.images[i-1], cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show() \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9833333333333333\n"
     ]
    }
   ],
   "source": [
    "# Create feature and target arrays\n",
    "X = digits.data\n",
    "y = digits.target\n",
    "\n",
    "# Split into training and test set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state=42, stratify=y)\n",
    "\n",
    "# Create a k-NN classifier with 7 neighbors: knn\n",
    "knn = KNeighborsClassifier(n_neighbors=7)\n",
    "\n",
    "# Fit the classifier to the training data\n",
    "knn.fit(X_train, y_train)\n",
    "\n",
    "# Print the accuracy\n",
    "print(knn.score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "col_0   0   1   2   3   4   5   6   7   8   9\n",
       "row_0                                        \n",
       "0      36   0   0   0   0   0   0   0   0   0\n",
       "1       0  36   0   0   0   0   0   0   2   0\n",
       "2       0   0  35   0   0   0   0   0   0   0\n",
       "3       0   0   0  37   0   0   0   0   0   0\n",
       "4       0   0   0   0  36   0   0   0   0   1\n",
       "5       0   0   0   0   0  37   0   0   0   0\n",
       "6       0   0   0   0   0   0  35   0   0   0\n",
       "7       0   0   0   0   0   0   0  36   1   0\n",
       "8       0   0   0   0   0   0   1   0  32   1\n",
       "9       0   0   0   0   0   0   0   0   0  34"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Big Confusion Matrix\n",
    "preds = knn.predict(X_test)\n",
    "\n",
    "pd.crosstab(preds,y_test)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**\n",
    "\n",
    "Construct a model complexity curve for the digits dataset! In this exercise, you will compute and plot the training and testing accuracy scores for a variety of different neighbor values. By observing how the accuracy scores differ for the training and testing sets with different values of k, you will develop your intuition for overfitting and underfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Setup arrays to store train and test accuracies\n",
    "# neighbors = np.arange(1, 20)\n",
    "# train_accuracy = np.empty(len(neighbors))\n",
    "# test_accuracy = np.empty(len(neighbors))\n",
    "# \n",
    "# # Loop over different values of k\n",
    "# for i, k in enumerate(neighbors):\n",
    "#     # Setup a k-NN Classifier with k neighbors: knn\n",
    "#     knn = KNeighborsClassifier(___)\n",
    "# \n",
    "#     # Fit the classifier to the training data\n",
    "#     ___\n",
    "#     \n",
    "#     #Compute accuracy on the training set\n",
    "#     train_accuracy[i] = ___\n",
    "# \n",
    "#     #Compute accuracy on the testing set\n",
    "#     test_accuracy[i] = ___\n",
    "# \n",
    "# # Generate plot\n",
    "# plt.title('k-NN: Varying Number of Neighbors')\n",
    "# plt.plot(___, label = 'Testing Accuracy')\n",
    "# plt.plot(___, label = 'Training Accuracy')\n",
    "# plt.legend()\n",
    "# plt.xlabel('Number of Neighbors')\n",
    "# plt.ylabel('Accuracy')\n",
    "# plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multinomial Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.25859359e-01, 7.39618434e-02, 1.78797175e-04],\n",
       "       [9.25859359e-01, 7.39618434e-02, 1.78797175e-04],\n",
       "       [9.25859359e-01, 7.39618434e-02, 1.78797175e-04],\n",
       "       [9.25859359e-01, 7.39618434e-02, 1.78797175e-04]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "log_reg = LogisticRegression(multi_class='multinomial',solver='sag', max_iter=100, random_state=42)\n",
    "log_reg.fit(iris[\"data\"][:,3:],iris[\"target\"])\n",
    "    \n",
    "preds = log_reg.predict_proba(iris[\"data\"][:,3:])\n",
    "\n",
    "preds[1:5,:]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Compute a confusion matrix\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Further Reading and Explorations:**\n",
    "* Read about \"one versus all\" pitted against multinomial. Check out this [notebook](plot_logistic_multinomial.ipynb).\n",
    "* Read about [marginal probabilities](http://data.princeton.edu/wws509/stata/mlogit.html)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ROC Curves\n",
    "\n",
    "Simplest to go back to 2 labels from lesson 7:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[24  8]\n",
      " [ 0 13]]\n",
      "[[32  0]\n",
      " [ 0 13]]\n",
      "[[32  0]\n",
      " [ 4  9]]\n"
     ]
    }
   ],
   "source": [
    "iris = datasets.load_iris()\n",
    "X = iris[\"data\"][:,3:]\n",
    "y = (iris[\"target\"]==2).astype(int)\n",
    "# Split into training and test set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state=42)\n",
    "\n",
    "log_reg = LogisticRegression()\n",
    "log_reg.fit(X_train,y_train)\n",
    "\n",
    "y_pred = log_reg.predict_proba(X_test) \n",
    "y_pred_prob = y_pred[:,1]\n",
    "\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "print(confusion_matrix(y_test, y_pred_prob > 0.25 ))\n",
    "\n",
    "print(confusion_matrix(y_test, y_pred_prob > 0.5 ))\n",
    "\n",
    "print(confusion_matrix(y_test, y_pred_prob > 0.75 ))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The need for more sophisticated metrics than accuracy and single thresholding**\n",
    "\n",
    "This is particularly relevant for imbalanced classes, example: Emails\n",
    "\n",
    "- Spam classification\n",
    "    * 99% of emails are real; 1% of emails are spam\n",
    "- Could build a classifier that predicts ALL emails as real\n",
    "    * 99% accurate!\n",
    "    * But horrible at actually classifying spam\n",
    "    * Fails at its original purpose\n",
    "<table> \n",
    "<tr>\n",
    "    <td><img src=\"./figures/ISLR-Table4.7.png\" width=600></td>\n",
    "</tr>\n",
    "</table>\n",
    "\n",
    " \n",
    " **Metrics from CM**\n",
    " \n",
    "- Precision: $\\frac{TP}{TP+FP}$\n",
    "- Recall: $\\frac{TP}{TP+FN}$\n",
    "- F1 score: $2 \\cdot \\frac{precision \\cdot recall}{precision + recall}$\n",
    "\n",
    "The F1 score is the harmonic average of the precision and recall, where an F1 score reaches its best value at 1 (perfect precision and recall) and worst at 0. ()\n",
    "- High precision: Not many real emails predicted as spam\n",
    "- High recall: Predicted most spam emails correctly\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00        32\n",
      "           1       1.00      1.00      1.00        13\n",
      "\n",
      "    accuracy                           1.00        45\n",
      "   macro avg       1.00      1.00      1.00        45\n",
      "weighted avg       1.00      1.00      1.00        45\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(y_test, y_pred_prob > 0.5 ))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But we still need to fix a threshold for any of the metrics above to work !\n",
    "\n",
    "Wouldn't it be best to communicate the prediction quality over a wide range (all!) of thresholds and enable the user to choose the most suitable one for his/her application !\n",
    "That is the idea of the **Receiver Operating Characteristic (ROC)** curve!\n",
    "\n",
    "<img src=\"./figures/DataCampROCexample.png\" width=600>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true
   },
   "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>pregnant</th>\n",
       "      <th>glucose</th>\n",
       "      <th>bp</th>\n",
       "      <th>skin</th>\n",
       "      <th>insulin</th>\n",
       "      <th>bmi</th>\n",
       "      <th>pedigree</th>\n",
       "      <th>age</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>148</td>\n",
       "      <td>72</td>\n",
       "      <td>35</td>\n",
       "      <td>0</td>\n",
       "      <td>33.6</td>\n",
       "      <td>0.627</td>\n",
       "      <td>50</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>85</td>\n",
       "      <td>66</td>\n",
       "      <td>29</td>\n",
       "      <td>0</td>\n",
       "      <td>26.6</td>\n",
       "      <td>0.351</td>\n",
       "      <td>31</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>183</td>\n",
       "      <td>64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>23.3</td>\n",
       "      <td>0.672</td>\n",
       "      <td>32</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>89</td>\n",
       "      <td>66</td>\n",
       "      <td>23</td>\n",
       "      <td>94</td>\n",
       "      <td>28.1</td>\n",
       "      <td>0.167</td>\n",
       "      <td>21</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>137</td>\n",
       "      <td>40</td>\n",
       "      <td>35</td>\n",
       "      <td>168</td>\n",
       "      <td>43.1</td>\n",
       "      <td>2.288</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   pregnant  glucose  bp  skin  insulin   bmi  pedigree  age  label\n",
       "0         6      148  72    35        0  33.6     0.627   50      1\n",
       "1         1       85  66    29        0  26.6     0.351   31      0\n",
       "2         8      183  64     0        0  23.3     0.672   32      1\n",
       "3         1       89  66    23       94  28.1     0.167   21      0\n",
       "4         0      137  40    35      168  43.1     2.288   33      1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The pima-indians- diabetes data:\n",
    "#  https://www.kaggle.com/uciml/pima-indians-diabetes-database#diabetes.csv\n",
    "\n",
    "col_names = ['pregnant', 'glucose', 'bp', 'skin', 'insulin', 'bmi', 'pedigree', 'age', 'label']\n",
    "# load dataset\n",
    "pima = pd.read_csv(\"../data/diabetes.csv\", header=None, names=col_names,skiprows=[0])\n",
    "pima.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 768 entries, 0 to 767\n",
      "Data columns (total 9 columns):\n",
      " #   Column    Non-Null Count  Dtype  \n",
      "---  ------    --------------  -----  \n",
      " 0   pregnant  768 non-null    int64  \n",
      " 1   glucose   768 non-null    int64  \n",
      " 2   bp        768 non-null    int64  \n",
      " 3   skin      768 non-null    int64  \n",
      " 4   insulin   768 non-null    int64  \n",
      " 5   bmi       768 non-null    float64\n",
      " 6   pedigree  768 non-null    float64\n",
      " 7   age       768 non-null    int64  \n",
      " 8   label     768 non-null    int64  \n",
      "dtypes: float64(2), int64(7)\n",
      "memory usage: 54.1 KB\n"
     ]
    }
   ],
   "source": [
    "pima.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1,2,3]\n",
    "b = [*a]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "#split dataset in features and target variable\n",
    "feature_cols = ['pregnant', 'insulin', 'bmi', 'age','glucose','bp','pedigree']\n",
    "X = pima[feature_cols] # Features\n",
    "y = pima.label # Target variable\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_reg = LogisticRegression(max_iter=200)\n",
    "log_reg.fit(X_train,y_train)\n",
    "\n",
    "y_pred = log_reg.predict_proba(X_test) \n",
    "y_pred_prob = y_pred[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(y_test, y_pred_prob)\n",
    "plt.plot([0, 1], [0, 1], 'k--')\n",
    "plt.plot(fpr, tpr, label='Logistic Regression')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('Logistic Regression ROC Curve')\n",
    "plt.show();"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Area under the ROC curve (AUC)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.797"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score\n",
    "\n",
    "roc_auc_score(y_test, y_pred_prob)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**AUC using cross-validation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.78888889 0.83037037 0.83777778 0.77333333 0.81111111 0.84814815\n",
      " 0.81925926 0.92148148 0.85692308 0.83307692]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "cv_scores = cross_val_score(log_reg, X, y, cv=10, scoring='roc_auc')\n",
    "\n",
    "print(cv_scores)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------------------------\n",
    "\n",
    "### Regularized Regression\n",
    "\n",
    "We will illustrate the concepts on the Boston housing data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "boston = pd.read_csv('../data/boston.csv')\n",
    "#print(boston.head())\n",
    "X = boston.drop('medv', axis=1).values\n",
    "y = boston['medv'].values"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variable Selection**\n",
    "\n",
    "[ISLR slides on model selection](../figures/model_selection.pdf)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  L2 Regression\n",
    "\n",
    "Recall: Linear regression minimizes a loss function\n",
    "- It chooses a coefficient for each feature variable\n",
    "- Large coefficients can lead to overfitting\n",
    "- Penalizing large coefficients: Regularization\n",
    "\n",
    "**Detour: $L_p$ norms**\n",
    "\n",
    "http://mathworld.wolfram.com/VectorNorm.html\n",
    "\n",
    "Our new penalty term in finding the coefficients $\\beta_j$ is the minimization\n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^n{\\left( y_i - \\beta_0 - \\sum_{j=1}^p{\\beta_j x_{ij}} \\right)^2} + \\lambda \\sum_{j=1}^p{\\beta_j^2} = RSS + \\lambda \\sum_{j=1}^p{\\beta_j^2}\n",
    "$$\n",
    "\n",
    "Instead of obtaining **one** set of coefficients we have a dependency of $\\beta_j$  on $\\lambda$:\n",
    "\n",
    "<img src=\"./figures/RidgeCoefficients1.jpg\" width=600>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([28.59300181, 36.45275937, 15.30416262, 25.37120109, 18.91168087])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y,test_size = 0.3, random_state=42)\n",
    "\n",
    "ridge = Ridge(alpha=0.1)#, normalize=True)\n",
    "ridge.fit(X_train, y_train)\n",
    "ridge_pred = ridge.predict(X_test)#?does this automatically take care of nromalization ??\n",
    "#Returns the coefficient of determination R^2 of the prediction.\n",
    "ridge.score(X_test, y_test)\n",
    "ridge_pred[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.32535034e-01,  3.59944827e-02,  4.38480378e-02,  3.09567615e+00,\n",
       "       -1.40625952e+01,  4.06131940e+00, -1.20010626e-02, -1.36547356e+00,\n",
       "        2.39463689e-01, -8.81732204e-03, -8.95518536e-01,  1.18278475e-02,\n",
       "       -5.49776010e-01])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2 = Ridge(alpha=0.1)#, normalize=False)\n",
    "ridge2.fit(X_train, y_train)\n",
    "ridge2_pred = ridge2.predict(X_test)\n",
    "ridge2_pred[0:5]\n",
    "ridge2.coef_"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  L1 Regression\n",
    "\n",
    "Our penalty termy looks slightly different (with big consequences for **sparsity**)\n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^n{\\left( y_i - \\beta_0 - \\sum_{j=1}^p{\\beta_j x_{ij}} \\right)^2} + \\lambda \\sum_{j=1}^p{| \\beta_j |} = RSS + \\lambda \\sum_{j=1}^p{| \\beta_j |}\n",
    "$$\n",
    "\n",
    "<img src=\"./figures/LassoCoefficients1.png\" width=600>\n",
    "\n",
    "(Comment: *LASSO* = \"least absolute shrinkage and selection operator\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.22854422e-01,  3.86385849e-02, -4.97188385e-04,  1.48353759e+00,\n",
       "       -0.00000000e+00,  3.89367421e+00, -1.96048179e-02, -1.10561397e+00,\n",
       "        2.16673479e-01, -1.05844004e-02, -7.44014516e-01,  1.23959059e-02,\n",
       "       -6.02281637e-01])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "lasso = Lasso(alpha=0.1)#, normalize=True)\n",
    "lasso.fit(X_train, y_train)\n",
    "lasso_pred = lasso.predict(X_test)\n",
    "#Returns the coefficient of determination R^2 of the prediction.\n",
    "lasso.score(X_test, y_test)\n",
    "lasso.coef_"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Feature Selection Property of the LASSO**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names = boston.drop('medv', axis=1).columns\n",
    "lasso_coef = lasso.fit(X, y).coef_\n",
    "_ = plt.plot(range(len(names)), lasso_coef)\n",
    "_ = plt.xticks(range(len(names)), names, rotation=60)\n",
    "_ = plt.ylabel('Coefficients')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tuning the shrinkage parameter with CV**\n",
    "\n",
    "(It seems that $\\lambda$ is often referred to as $\\alpha$)\n",
    "\n",
    "From sklearn.linear_model:\n",
    "\n",
    "* LassoCV\n",
    "* RidgeCV\n",
    "* GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 37.30292142,  37.34720525,  37.76559526,  40.43439122],\n",
       "       [ 11.99700574,  11.97375126,  11.75676579,  10.50095584],\n",
       "       [ 17.48829647,  17.4924878 ,  17.53207192,  17.7864549 ],\n",
       "       ...,\n",
       "       [ 14.6418552 ,  14.67645052,  15.00346175,  17.07274067],\n",
       "       [ 17.86227108,  17.90234473,  18.28115447,  20.68282383],\n",
       "       [113.70883594, 113.81266571, 114.7926396 , 120.99657642]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import RidgeCV\n",
    "\n",
    "reg = RidgeCV(alphas=[1e-3, 1e-2, 1e-1, 1],store_cv_values = True)\n",
    "reg.fit(X, y)\n",
    "reg.score(X, y)\n",
    "\n",
    "reg.cv_values_\n",
    "#Open Questions: \n",
    "#1. how to extract all scores, possibly even the individual folds?\n",
    "#2. What is the optimal alpha ??\n",
    "#reg.cv_values_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.702"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "\n",
    "reg = LassoCV(cv=5, random_state=0).fit(X, y)\n",
    "reg.score(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GridSearchCV(cv=5, estimator=Lasso(max_iter=2000, random_state=0),\n",
       "             param_grid=[{&#x27;alpha&#x27;: array([1.00000000e-04, 1.52830673e-04, 2.33572147e-04, 3.56969885e-04,\n",
       "       5.45559478e-04, 8.33782223e-04, 1.27427499e-03, 1.94748304e-03,\n",
       "       2.97635144e-03, 4.54877795e-03, 6.95192796e-03, 1.06246783e-02,\n",
       "       1.62377674e-02, 2.48162892e-02, 3.79269019e-02, 5.79639395e-02,\n",
       "       8.85866790e-02, 1.35387618e-01, 2.06913808e-01, 3.16227766e-01])}],\n",
       "             refit=False)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GridSearchCV</label><div class=\"sk-toggleable__content\"><pre>GridSearchCV(cv=5, estimator=Lasso(max_iter=2000, random_state=0),\n",
       "             param_grid=[{&#x27;alpha&#x27;: array([1.00000000e-04, 1.52830673e-04, 2.33572147e-04, 3.56969885e-04,\n",
       "       5.45559478e-04, 8.33782223e-04, 1.27427499e-03, 1.94748304e-03,\n",
       "       2.97635144e-03, 4.54877795e-03, 6.95192796e-03, 1.06246783e-02,\n",
       "       1.62377674e-02, 2.48162892e-02, 3.79269019e-02, 5.79639395e-02,\n",
       "       8.85866790e-02, 1.35387618e-01, 2.06913808e-01, 3.16227766e-01])}],\n",
       "             refit=False)</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">estimator: Lasso</label><div class=\"sk-toggleable__content\"><pre>Lasso(max_iter=2000, random_state=0)</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">Lasso</label><div class=\"sk-toggleable__content\"><pre>Lasso(max_iter=2000, random_state=0)</pre></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "GridSearchCV(cv=5, estimator=Lasso(max_iter=2000, random_state=0),\n",
       "             param_grid=[{'alpha': array([1.00000000e-04, 1.52830673e-04, 2.33572147e-04, 3.56969885e-04,\n",
       "       5.45559478e-04, 8.33782223e-04, 1.27427499e-03, 1.94748304e-03,\n",
       "       2.97635144e-03, 4.54877795e-03, 6.95192796e-03, 1.06246783e-02,\n",
       "       1.62377674e-02, 2.48162892e-02, 3.79269019e-02, 5.79639395e-02,\n",
       "       8.85866790e-02, 1.35387618e-01, 2.06913808e-01, 3.16227766e-01])}],\n",
       "             refit=False)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "diabetes = datasets.load_diabetes()\n",
    "X = diabetes.data[:150]\n",
    "y = diabetes.target[:150]\n",
    "\n",
    "\n",
    "lasso = Lasso(random_state=0,max_iter=2000)\n",
    "#logarithmically spaced sequence\n",
    "alphas = np.logspace(-4, -0.5, 20)\n",
    "\n",
    "tuned_parameters = [{'alpha': alphas}]\n",
    "n_folds = 5\n",
    "\n",
    "reg = GridSearchCV(lasso, tuned_parameters, cv=n_folds, refit=False)\n",
    "reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.000, 0.316)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scores = reg.cv_results_['mean_test_score']\n",
    "scores_std = reg.cv_results_['std_test_score']\n",
    "plt.figure().set_size_inches(8, 6)\n",
    "plt.semilogx(alphas, scores)\n",
    "\n",
    "# plot error lines showing +/- std. errors of the scores\n",
    "std_error = scores_std / np.sqrt(n_folds)\n",
    "\n",
    "plt.semilogx(alphas, scores + std_error, 'b--')\n",
    "plt.semilogx(alphas, scores - std_error, 'b--')\n",
    "\n",
    "# alpha=0.2 controls the translucency of the fill color\n",
    "plt.fill_between(alphas, scores + std_error, scores - std_error, alpha=0.2)\n",
    "\n",
    "plt.ylabel('CV score +/- std error')\n",
    "plt.xlabel('alpha')\n",
    "plt.axhline(np.max(scores), linestyle='--', color='.5')\n",
    "plt.xlim([alphas[0], alphas[-1]])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How much can you trust the selection of alpha?**\n",
    "\n",
    "Task: Find the opimal Alpha parameters (maximising the generalization score) on different subsets of the data"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ElasticNet\n",
    "\n",
    "**The mystery of the additional $\\alpha$ paramater**\n",
    "\n",
    "* The elastic net for correlated variables, which uses a penalty that is part L1, part L2.\n",
    "* Compromise between the ridge regression penalty $(\\alpha = 0)$ and the lasso penalty $(\\alpha = 1)$. \n",
    "* This penalty is particularly useful in the $p >> N$ situation, or any situation where there are many correlated predictor variables.\n",
    "\n",
    "\n",
    "$RSS + \\lambda \\sum_{j=1}^p{ \\left( \\frac{1}{2} (1-\\alpha) \\beta_j^2 + \\alpha | \\beta_j | \\right)}$\n",
    "\n",
    "The right hand side can be written as\n",
    "\n",
    "$\\sum_{j=1}^p{ \\frac{1}{2} \\lambda (1-\\alpha) \\beta_j^2 + \\alpha \\lambda | \\beta_j |} = \\sum_{j=1}^p{  \\lambda_R \\beta_j^2 +  \\lambda_L | \\beta_j |}$\n",
    "\n",
    "with the Ridge penalty parameter $\\lambda_R \\equiv \\frac{1}{2} \\lambda (1-\\alpha)$ and the lasso penalty parameter $\\lambda_L \\equiv \\alpha \\lambda$.\n",
    "\n",
    "So we see that with\n",
    "\n",
    "$\\alpha = \\frac{\\lambda_L}{\\lambda_L+ 2 \\lambda_R}, \\text{ and } \\lambda= \\lambda_L+ 2 \\lambda_R$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Further Reading:\n",
    "- this [notebook](plot_lasso_coordinate_descent_path.ipynb) shows how to plot the entire \"path\" of coefficients."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kaggle\n",
    "\n",
    "####  [Housing Data](https://www.kaggle.com/c/house-prices-advanced-regression-techniques)\n",
    "\n",
    "    "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This [notebook](../data/kaggle/HousePrices/EDA.ipynb) (despite its annoying \"humor\") is a good start. \n",
    "(Get it [directly](https://www.kaggle.com/pmarcelino/comprehensive-data-exploration-with-python) from kaggle)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Your first submission\n",
    "\n",
    "<img src=\"./figures/kaggle_HousePrices1.jpg\" width=600>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = pd.read_csv('data/kaggle/HousePrices/train.csv')\n",
    "df_test = pd.read_csv('data/kaggle/HousePrices/test.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>MSSubClass</th>\n",
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       "      <td>WD</td>\n",
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       "      <td>208500</td>\n",
       "    </tr>\n",
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       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>20</td>\n",
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       "      <td>68.0</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>2008</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>223500</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>70</td>\n",
       "      <td>RL</td>\n",
       "      <td>60.0</td>\n",
       "      <td>9550</td>\n",
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       "      <td>140000</td>\n",
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       "      <td>NaN</td>\n",
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       "      <td>2008</td>\n",
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       "      <td>2</td>\n",
       "      <td>2010</td>\n",
       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>210000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1457</th>\n",
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       "      <td>70</td>\n",
       "      <td>RL</td>\n",
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       "      <td>WD</td>\n",
       "      <td>Normal</td>\n",
       "      <td>142125</td>\n",
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       "    <tr>\n",
       "      <th>1459</th>\n",
       "      <td>1460</td>\n",
       "      <td>20</td>\n",
       "      <td>RL</td>\n",
       "      <td>75.0</td>\n",
       "      <td>9937</td>\n",
       "      <td>Pave</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Reg</td>\n",
       "      <td>Lvl</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>6</td>\n",
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       "      <td>WD</td>\n",
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       "      <td>147500</td>\n",
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      "text/plain": [
       "        Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
       "0        1          60       RL         65.0     8450   Pave   NaN      Reg   \n",
       "1        2          20       RL         80.0     9600   Pave   NaN      Reg   \n",
       "2        3          60       RL         68.0    11250   Pave   NaN      IR1   \n",
       "3        4          70       RL         60.0     9550   Pave   NaN      IR1   \n",
       "4        5          60       RL         84.0    14260   Pave   NaN      IR1   \n",
       "...    ...         ...      ...          ...      ...    ...   ...      ...   \n",
       "1455  1456          60       RL         62.0     7917   Pave   NaN      Reg   \n",
       "1456  1457          20       RL         85.0    13175   Pave   NaN      Reg   \n",
       "1457  1458          70       RL         66.0     9042   Pave   NaN      Reg   \n",
       "1458  1459          20       RL         68.0     9717   Pave   NaN      Reg   \n",
       "1459  1460          20       RL         75.0     9937   Pave   NaN      Reg   \n",
       "\n",
       "     LandContour Utilities  ... PoolArea PoolQC  Fence MiscFeature MiscVal  \\\n",
       "0            Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "1            Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "2            Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "3            Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "4            Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "...          ...       ...  ...      ...    ...    ...         ...     ...   \n",
       "1455         Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "1456         Lvl    AllPub  ...        0    NaN  MnPrv         NaN       0   \n",
       "1457         Lvl    AllPub  ...        0    NaN  GdPrv        Shed    2500   \n",
       "1458         Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "1459         Lvl    AllPub  ...        0    NaN    NaN         NaN       0   \n",
       "\n",
       "     MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
       "0         2   2008        WD         Normal     208500  \n",
       "1         5   2007        WD         Normal     181500  \n",
       "2         9   2008        WD         Normal     223500  \n",
       "3         2   2006        WD        Abnorml     140000  \n",
       "4        12   2008        WD         Normal     250000  \n",
       "...     ...    ...       ...            ...        ...  \n",
       "1455      8   2007        WD         Normal     175000  \n",
       "1456      2   2010        WD         Normal     210000  \n",
       "1457      5   2010        WD         Normal     266500  \n",
       "1458      4   2010        WD         Normal     142125  \n",
       "1459      6   2008        WD         Normal     147500  \n",
       "\n",
       "[1460 rows x 81 columns]"
      ]
     },
     "execution_count": 62,
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    }
   ],
   "source": [
    "df_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Submission:\n",
    "# pred_df = pd.DataFrame(y_pred, index=df_test.index, columns=[\"SalePrice\"])\n",
    "# pred_df.to_csv('../data/kaggle/HousePrices/submissions/en1.csv', header=True, index_label='Id')"
   ]
  }
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