LinearRegressionLasso.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import scipy as sp\n",
      "from scipy import optimize"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['clf']\n",
        "`%matplotlib` prevents importing * from pylab and numpy\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class LinearRegression:\n",
      "    \"\"\"\n",
      "    define the basic linear regresion problem\n",
      "    \"\"\"\n",
      "    def __init__(self,penalty='L2',W_initial=None,alpha=0.1,numIteration=10,penalty_para=0):\n",
      "        self.penalty=penalty\n",
      "        self.penalty_para=penalty_para\n",
      "        self.W=W_initial\n",
      "        self.alpha=alpha\n",
      "        self.numIteration=numIteration\n",
      "        return None\n",
      "    def gradient_descent(self,X,y):\n",
      "        \"\"\"\n",
      "        calculate  gradient descent\n",
      "        \"\"\"\n",
      "        number=len(X)\n",
      "        X_new=np.hstack((np.reshape(np.ones(number),(number,1)),X))\n",
      "        for i in np.arange(self.numIteration):\n",
      "            for vec_i in np.arange(number):\n",
      "                for t in np.arange(len(self.W)):\n",
      "                    y_p=np.dot(self.W,X_new[vec_i])\n",
      "                    delta=(y[vec_i]-y_p)*X_new[vec_i,t]\n",
      "                    self.W[t]=self.W[t]+self.alpha*delta\n",
      "        return self.W\n",
      "    \"\"\"\n",
      "    another write\n",
      "    for iter in range(maxIterations):\n",
      "      cost = 0\n",
      "      deltaw = np.zeros(len(vectors[0])+1)\n",
      "      for i in range(len(vectors)):\n",
      "         temp = np.append(vectors[i], -1)\n",
      "         prediction_error = np.dot(w, temp) - labels[i]\n",
      "         deltaw += prediction_error * temp\n",
      "         cost += prediction_error**2\n",
      "      w = w -  stepSize * deltaw\n",
      "    \"\"\"\n",
      "    def gradient_descent_improve(self,X,y):\n",
      "        \"\"\"\n",
      "        using the function of scipy.optimize\n",
      "        \"\"\"\n",
      "        number=len(X)\n",
      "        X_new=np.hstack((np.reshape(np.ones(number),(number,1)),X))\n",
      "       \n",
      "        for i in np.arange(len(X_new)):\n",
      "            def loss(w):\n",
      "                sum_error=0\n",
      "                penalty=0\n",
      "                for t in np.arange(i+1):\n",
      "                    sum_error+=np.square(y[t]-np.dot(w,X_new[t]))\n",
      "                if self.penalty=='L1':\n",
      "                    penalty=np.sum(np.abs(w))*self.penalty_para\n",
      "                elif self.penalty=='L2':\n",
      "                    penalty=np.sum(w**2)*self.penalty_para\n",
      "                return sum_error/(i+1)+penalty\n",
      "            self.W=optimize.fmin_powell(loss,self.W,maxiter=self.numIteration)\n",
      "        return self.W\n",
      "    def fit(self,X,y):\n",
      "        \"\"\"\n",
      "        fit the data\n",
      "        \"\"\"\n",
      "        if self.W is None:\n",
      "            self.W=np.zeros(X.shape[1]+1)\n",
      "        self.gradient_descent_improve(X,y)\n",
      "        return self\n",
      "    def predict(self,X_test):\n",
      "        \"\"\"\n",
      "            predict the test \n",
      "        \"\"\"\n",
      "        predictions=[]\n",
      "        number=len(X_test)\n",
      "        X_test_new=np.hstack((np.reshape(np.ones(number),(number,1)),X_test))\n",
      "        for vec_test in X_test_new:\n",
      "            predictions.append(np.dot(self.W,vec_test))\n",
      "        return predictions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "X_train = np.c_[.5, 1].T\n",
      "y_train = [.5, 1]\n",
      "X_test = np.c_[0, 2].T\n",
      "\n",
      "np.random.seed(0)\n",
      "\n",
      "classifiers = dict(ols=LinearRegression(),\n",
      "                   ridge=LinearRegression(penalty_para=.1),\n",
      "                   lasso=LinearRegression(penalty='L1',penalty_para=.1))\n",
      "\n",
      "fignum = 1\n",
      "for name, clf in classifiers.items():\n",
      "    fig = plt.figure(fignum, figsize=(4, 3))\n",
      "    plt.clf()\n",
      "    plt.title(name)\n",
      "    ax = plt.axes([.12, .12, .8, .8])\n",
      "\n",
      "    for _ in range(6):\n",
      "        this_X = .1 * np.random.normal(size=(2, 1)) + X_train\n",
      "        clf.fit(this_X, y_train)\n",
      "\n",
      "        ax.plot(X_test, clf.predict(X_test), color='.5')\n",
      "        ax.scatter(this_X, y_train, s=3, c='.5', marker='o', zorder=10)\n",
      "\n",
      "    clf.fit(X_train, y_train)\n",
      "    ax.plot(X_test, clf.predict(X_test), linewidth=2, color='blue')\n",
      "    ax.scatter(X_train, y_train, s=30, c='r', marker='+', zorder=10)\n",
      "\n",
      "    ax.set_xticks(())\n",
      "    ax.set_yticks(())\n",
      "    ax.set_ylim((0, 1.6))\n",
      "    ax.set_xlabel('X')\n",
      "    ax.set_ylabel('y')\n",
      "    ax.set_xlim(0, 2)\n",
      "    fignum += 1\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 47\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 35\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 35\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 35\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 35\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 47\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 2\n",
        "         Function evaluations: 35\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 65\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.017459\n",
        "         Iterations: 3\n",
        "         Function evaluations: 83\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.056011\n",
        "         Iterations: 3\n",
        "         Function evaluations: 84\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.017904\n",
        "         Iterations: 3\n",
        "         Function evaluations: 112\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.052605\n",
        "         Iterations: 3\n",
        "         Function evaluations: 63\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.016429\n",
        "         Iterations: 3\n",
        "         Function evaluations: 109\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.063683\n",
        "         Iterations: 3\n",
        "         Function evaluations: 101\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.018086\n",
        "         Iterations: 3\n",
        "         Function evaluations: 85\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.062354\n",
        "         Iterations: 3\n",
        "         Function evaluations: 96\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.021554\n",
        "         Iterations: 3\n",
        "         Function evaluations: 76\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.043102\n",
        "         Iterations: 3\n",
        "         Function evaluations: 112\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.017314\n",
        "         Iterations: 3\n",
        "         Function evaluations: 79\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.064785\n",
        "         Iterations: 3\n",
        "         Function evaluations: 114\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.018519\n",
        "         Iterations: 3\n",
        "         Function evaluations: 112\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.053191\n",
        "         Iterations: 3\n",
        "         Function evaluations: 80\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.047500\n",
        "         Iterations: 2\n",
        "         Function evaluations: 174\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.128469\n",
        "         Iterations: 3\n",
        "         Function evaluations: 117\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.047500\n",
        "         Iterations: 6\n",
        "         Function evaluations: 241\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.096555\n",
        "         Iterations: 3\n",
        "         Function evaluations: 70\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.048197\n",
        "         Iterations: 4\n",
        "         Function evaluations: 230\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.083538\n",
        "         Iterations: 4\n",
        "         Function evaluations: 171\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.047500\n",
        "         Iterations: 3\n",
        "         Function evaluations: 120\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.092052\n",
        "         Iterations: 3\n",
        "         Function evaluations: 69\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.047500\n",
        "         Iterations: 4\n",
        "         Function evaluations: 146\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.112709\n",
        "         Iterations: 3\n",
        "         Function evaluations: 99\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.050804\n",
        "         Iterations: 4\n",
        "         Function evaluations: 149\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.093856\n",
        "         Iterations: 3\n",
        "         Function evaluations: 104\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.050000\n",
        "         Iterations: 4\n",
        "         Function evaluations: 178\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.095000\n",
        "         Iterations: 3\n",
        "         Function evaluations: 107\n"
       ]
      },
      {
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2O+Lj4+vMvrxy5Qp79+6tM39C0XpRQVCvCMXFxXz66ad897vfpUOHDpw8CQsX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\nnl31sdLVePDgAcHBwTx//pz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CAwMZM2YMkyZNQgjBw4c6Jk8u4tYtR3r00HD0qC2WWM97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\namhQjQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x13d56198>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x13e77cc0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RewgIOEa3bk8RGhpKnz59zF5HGbJ0fJQ4dELKy8tJSEigtLQUjUZD376WzWiv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\nacTTT1fz4x8fo0eP/YSEhBi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xOAl8v6P/jtH3yBINf8MngSWPON5v0M9irkHfE3uptc+d\nmgSlMIuhbvEt8Asp5Q7DrNnpUspljzg0RTuiLJgUlvAKcEVKucPw+gNgtBDC/RHGpGhnVM9BoVA0\niuo5KBSKRlHioFAoGkWJg0KhaBQlDgqFolGUOCgUikZR4qBQKBpFiYNCoWiU/w9nKTM+LIqzeQAA\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1419a898>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}