polynomial_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = make_regression(n_features=1, noise=14, bias=1, random_state=42)\n",
    "y = y**2\n",
    "\n",
    "plt.scatter(X, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(X, y, W):\n",
    "    return 1 / (2 * m) * np.sum((np.dot(X, W) - y) ** 2)\n",
    "\n",
    "def normal_equation(X, y):\n",
    "    A = np.linalg.pinv(np.dot(X.T, X))\n",
    "    return np.dot(A, np.dot(X.T, y))\n",
    "\n",
    "class PolynomialRegression:\n",
    "    \n",
    "    def __init__(self, norm_eq=True, lr=0.01, num_iters=1500):\n",
    "        \n",
    "        self.lr = lr\n",
    "        self.num_iters = num_iters\n",
    "        self.norm_eq = norm_eq\n",
    "        \n",
    "    def fit(self, X, y):\n",
    "        if self.norm_eq:\n",
    "            self.W = normal_equation(X, y)\n",
    "        else:\n",
    "            self.W = np.zeros((X.shape[1], 1))\n",
    "            for _ in range(self.num_iters):\n",
    "                cost = compute_cost(X, y, self.W)\n",
    "                grad = np.dot(X.T, np.dot(X, self.W) - y)\n",
    "                self.W -= self.lr * (1 / m) * grad\n",
    "    \n",
    "    def predict(self, X):\n",
    "        return np.dot(X, self.W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polynomial_features(X, degree):\n",
    "    return np.hstack([X ** i for i in range(degree+1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_new = polynomial_features(X, degree=2)\n",
    "\n",
    "poly = PolynomialRegression()\n",
    "poly.fit(X_new, y)\n",
    "preds = poly.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_X, plt_y = zip(*sorted(zip(X, preds)))\n",
    "\n",
    "plt.scatter(X, y, c='b', s=25)\n",
    "plt.plot(plt_X, plt_y, c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sklearn way\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "poly_features = PolynomialFeatures()\n",
    "X_new = poly_features.fit_transform(X)\n",
    "\n",
    "poly_reg = LinearRegression()\n",
    "poly_reg.fit(X_new, y)\n",
    "preds = poly_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_X, plt_y = zip(*sorted(zip(X, preds)))\n",
    "\n",
    "plt.scatter(X, y, c='b', s=25)\n",
    "plt.plot(plt_X, plt_y, c='r')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}