Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io as io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create linear dataset\n",
    "X = np.arange(100)\n",
    "random = np.random.uniform(-10,10, size=(100,))\n",
    "y = .4 * X +3 + random\n",
    "X = np.reshape(X, (X.shape[0], 1))\n",
    "y = np.reshape(y, (y.shape[0], 1))\n",
    "linear = {\"X\": X, \"y\": y}\n",
    "\n",
    "def f(x, a, b, c, d):\n",
    "    return a / (1. + np.exp(-c * (x - d))) + b\n",
    "\n",
    "a, c = np.random.exponential(size=2)\n",
    "b, d = np.random.randn(2)\n",
    "n = 100\n",
    "X = np.linspace(-10., 10., n)\n",
    "y = f(X, a, b, c, d)\n",
    "y = y + a * .2 * np.random.randn(n)\n",
    "\n",
    "# create non-linear datasets\n",
    "nonlinear = io.loadmat(\"./ex5data1.mat\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Generating data\n",
    "# X = np.random.randn(100,1)\n",
    "# c = np.random.uniform(-10,10,(100,))\n",
    "# # adding another non-linear column\n",
    "# X = np.hstack((X, X*X))\n",
    "\n",
    "# y = (4*X[:,1] + c)\n",
    "\n",
    "# # X = np.reshape(X, (X.shape[0], 1))\n",
    "# y = np.reshape(y, (y.shape[0], 1))\n",
    "# random = np.random.uniform(-10,10, size=(100,))\n",
    "# nonlinear = {\"X\": X, \"y\": y}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of linear input (100, 1) (100, 1)\n",
      "Shape of non-linear input (12, 1) (12, 1)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of linear input\", linear[\"X\"].shape, linear[\"y\"].shape)\n",
    "print(\"Shape of non-linear input\", nonlinear[\"X\"].shape, nonlinear[\"y\"].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "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.figure(figsize=(6, 4))\n",
    "plt.scatter(linear[\"X\"], linear[\"y\"])\n",
    "plt.show()"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 4))\n",
    "plt.scatter(nonlinear[\"X\"], nonlinear[\"y\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LinearRegression:\n",
    "    def __init__(self, alpha= 0.0001, n_iters = 100, beta = 0):\n",
    "        self.n_iters_ = n_iters\n",
    "        self.alpha_ = alpha\n",
    "        self.beta_ = beta\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        m = X.shape[0]\n",
    "        \n",
    "        # Adding bias term\n",
    "        X = np.column_stack((np.ones((m, 1)), X))\n",
    "        \n",
    "        # Coeficients\n",
    "        self.coef_ = np.ones((X.shape[1], 1))\n",
    "          \n",
    "        cost = []\n",
    "        # Linear form\n",
    "        h_x = np.dot(X, self.coef_)\n",
    "            \n",
    "        for epoch in range(self.n_iters_):\n",
    "            # Linear form\n",
    "            h_x = np.dot(X, self.coef_)\n",
    "            \n",
    "            # calculating regularized cost\n",
    "            reg = (float(self.beta_) / (2 * m)) * np.sum(np.power((self.coef_[1:self.coef_.shape[0]]), 2))\n",
    "            \n",
    "            # Cost function\n",
    "            J = (1./(2 * m)) * np.sum(np.power((h_x - y), 2)) + reg\n",
    "            \n",
    "            # Gradient descent\n",
    "            self.coef_ = self.coef_ - self.alpha_ * ((1./m) *  np.dot(X.T, h_x - y)) + \\\n",
    "                        (float(self.beta_) / m) * self.coef_\n",
    "            # unregularize first gradient\n",
    "            self.coef_[0] = ((1./m) *  np.dot(X.T, h_x - y))[0]\n",
    "            cost.append(J)\n",
    "            \n",
    "        return self.coef_, cost\n",
    "    \n",
    "    def predict(self, X):\n",
    "        m = X.shape[0]\n",
    "        # Adding bias term\n",
    "        X = np.column_stack((np.ones(m), X))\n",
    "        return np.dot(X, self.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "theta, cost = lr.fit(linear[\"X\"], linear[\"y\"])\n",
    "y_pred = lr.predict(linear[\"X\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.81948526],\n",
       "       [ 0.46840313]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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(cost)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "# plotting linear residuals vs predicted\n",
    "plt.plot()\n",
    "plt.scatter(y_pred, (linear[\"y\"] - y_pred))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta, cost = lr.fit(nonlinear[\"X\"], nonlinear[\"y\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lr.predict(nonlinear[\"X\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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(cost)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "# plotting residuals vs predicted\n",
    "plt.plot()\n",
    "plt.scatter(y_pred, (nonlinear[\"y\"] - y_pred))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}