Gradient Descent LR.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "from builtins import range\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [[1. 1. 0.]\n",
      " [1. 1. 0.]\n",
      " [1. 1. 0.]\n",
      " [1. 1. 0.]\n",
      " [1. 1. 0.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "N = 10\n",
    "D = 3\n",
    "X = np.zeros((N, D))\n",
    "X[:,0] = 1 # bias term\n",
    "X[:5,1] = 1\n",
    "X[5:,2] = 1\n",
    "Y = np.array([0]*5 + [1]*5)\n",
    "\n",
    "# print X so you know what it looks like\n",
    "print(\"X:\", X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.,  5.,  5.],\n",
       "       [ 5.,  5.,  0.],\n",
       "       [ 5.,  0.,  5.]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T.dot(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5., 0., 5.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.T.dot(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Singular matrix",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-87dc64944cd9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36msolve\u001b[0;34m(a, b)\u001b[0m\n\u001b[1;32m    388\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'DD->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'dd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    389\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 390\u001b[0;31m     \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgufunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    391\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    392\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m     87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     88\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 89\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     90\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     91\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix"
     ]
    }
   ],
   "source": [
    "w = np.linalg.solve(X.T.dot(X), X.T.dot(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.73132963, 0.02384178, 0.08038328])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Gradient descent\n",
    "costs = [] # keep track of squared error cost\n",
    "w = np.random.randn(D) / np.sqrt(D) # randomly initialize w\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "learning_rate = 0.001\n",
    "for t in range(1000):\n",
    "    Yhat = X.dot(w)\n",
    "    delta = Yhat - Y\n",
    "    w = w - learning_rate*X.T.dot(delta)\n",
    "    #print(w.shape)\n",
    "    #\n",
    "\n",
    "  # find and store the cost\n",
    "    mse = delta.dot(delta) / N\n",
    "    print(mse)\n",
    "    costs.append(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.40618204222905e-10"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "final w: [ 0.54236819 -0.54236819  0.45763181]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " #plot the costs\n",
    "plt.plot(costs)\n",
    "plt.show()\n",
    "\n",
    "print(\"final w:\", w)\n",
    "\n",
    "# plot prediction vs target\n",
    "plt.plot(Yhat, label='prediction')\n",
    "plt.plot(Y, label='target')\n",
    "plt.legend()\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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}