lwlr.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "Muskan Pandey\n",
    "Linear Regression and Locally Weighted Linear Regression\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(84, 2)\n",
      "Index(['SAT', 'GPA'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('slr.csv')\n",
    "print(data.shape)\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "msk = np.random.rand(len(data)) < 0.8\n",
    "train = data[msk]\n",
    "test = data[~msk]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1670</td>\n",
       "      <td>2.91</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "4  1693  2.83\n",
       "5  1670  2.91"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "67 17\n"
     ]
    }
   ],
   "source": [
    "print(len(train), len(test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = train['SAT']\n",
    "Y_train = train['GPA']\n",
    "X_test = test['SAT']\n",
    "Y_test = test['GPA']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1848.0298507462687 3.3402985074626868\n"
     ]
    }
   ],
   "source": [
    "x_mean = sum(X_train)/len(X_train)\n",
    "y_mean = sum(Y_train)/len(Y_train)\n",
    "print(x_mean, y_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1 = sum((X_train - x_mean)*(Y_train - y_mean)) / sum((X_train - x_mean)**2)\n",
    "b0 = y_mean - b1*x_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight = -(X_test - X_train)**2\n",
    "weight = weight/(2*t**2)\n",
    "weight.to_numpy(dtype ='float32')\n",
    "weight = np.exp(weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "h_theta = (b0 + b1*X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5     3.020232\n",
       "8     3.237846\n",
       "9     3.341303\n",
       "10    3.136174\n",
       "20    3.182551\n",
       "Name: SAT, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_theta.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5     0.000000\n",
       "8     0.000000\n",
       "9     0.980747\n",
       "10    0.000000\n",
       "20    0.000000\n",
       "Name: SAT, dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_pred = b0 + b1*X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train, Y_train, color = \"b\")\n",
    "plt.plot()\n",
    "plt.plot(X_train, Y_pred, color=\"r\")\n",
    "plt.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from math import ceil\n",
    "from scipy import linalg\n",
    "\n",
    "\n",
    "def lowess(x, y, f=2. / 3., iter=3):\n",
    "    n = len(x)\n",
    "    r = int(ceil(f * n))\n",
    "    h = [np.sort(np.abs(x - x[i]))[r] for i in range(n)]\n",
    "    w = np.clip(np.abs((x[:, None] - x[None, :]) / h), 0.0, 1.0)\n",
    "    w = (1 - w ** 3) ** 3\n",
    "    yest = np.zeros(n)\n",
    "    delta = np.ones(n)\n",
    "    for iteration in range(iter):\n",
    "        for i in range(n):\n",
    "            weights = delta * w[:, i]\n",
    "            b = np.array([np.sum(weights * y), np.sum(weights * y * x)])\n",
    "            A = np.array([[np.sum(weights), np.sum(weights * x)],\n",
    "                          [np.sum(weights * x), np.sum(weights * x * x)]])\n",
    "            beta = linalg.solve(A, b)\n",
    "            yest[i] = beta[0] + beta[1] * x[i]\n",
    "\n",
    "        residuals = y - yest\n",
    "        s = np.median(np.abs(residuals))\n",
    "        delta = np.clip(residuals / (6.0 * s), -1, 1)\n",
    "        delta = (1 - delta ** 2) ** 2\n",
    "\n",
    "    return yest\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    x = data['SAT']\n",
    "    y = data['GPA']\n",
    "\n",
    "    f = 0.2\n",
    "    yest = lowess(x, y, f=f, iter=5)\n",
    "\n",
    "    plt.plot(x, y, color=\"r\")\n",
    "    plt.plot()\n",
    "    plt.plot(x, yest, color=\"g\")\n",
    "    plt.plot()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}