Homework 2 - Regularization with Lasso .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "\n",
    "In this homework, you'll be required to load in a dataset which has about 500 features. By using\n",
    "Lasso ($L^1$) regression, we'll find the optimal constraint on the $L^1$ norm which gives us the best\n",
    "$R^2$. Then we'll plot the results.\n",
    "\n",
    "Recall we minimize the following on ** training data: $(x_i,y_i)$**\n",
    "\n",
    "$$\\min_{\\beta} \\frac{1}{N} \\sum_{i=1}^N (y_i - \\beta \\cdot x_i)^2 + \\lambda \\|\\beta \\|_{L^1}.$$\n",
    "\n",
    "\n",
    "Denoting $\\beta_{\\lambda}$ as the minimum of the above, we then choose $\\lambda$ to maximize $R^2$ on **testing data: $(x_j,y_j)$**\n",
    "\n",
    "$$ \\max_{\\lambda} 1 - \\frac{\\sum_{j} (y_j - \\beta_{\\lambda} \\cdot x_j)^2}{\\sum_j (y_j - \\bar y)^2}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lasso Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Load in hw2data.csv from ../data into a pandas dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>...</th>\n",
       "      <th>491</th>\n",
       "      <th>492</th>\n",
       "      <th>493</th>\n",
       "      <th>494</th>\n",
       "      <th>495</th>\n",
       "      <th>496</th>\n",
       "      <th>497</th>\n",
       "      <th>498</th>\n",
       "      <th>499</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.382732</th>\n",
       "      <td>-0.034242</td>\n",
       "      <td>1.096347</td>\n",
       "      <td>-0.234216</td>\n",
       "      <td>-0.347451</td>\n",
       "      <td>-0.581268</td>\n",
       "      <td>-1.632635</td>\n",
       "      <td>-1.567768</td>\n",
       "      <td>-1.179158</td>\n",
       "      <td>1.301428</td>\n",
       "      <td>0.895260</td>\n",
       "      <td>...</td>\n",
       "      <td>0.178793</td>\n",
       "      <td>-0.799422</td>\n",
       "      <td>0.240788</td>\n",
       "      <td>0.289121</td>\n",
       "      <td>0.412871</td>\n",
       "      <td>-0.198399</td>\n",
       "      <td>0.094192</td>\n",
       "      <td>-1.147611</td>\n",
       "      <td>-0.358114</td>\n",
       "      <td>-2.663126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.555963</th>\n",
       "      <td>0.892474</td>\n",
       "      <td>-0.422315</td>\n",
       "      <td>0.104714</td>\n",
       "      <td>0.228053</td>\n",
       "      <td>0.201480</td>\n",
       "      <td>0.540774</td>\n",
       "      <td>-1.818078</td>\n",
       "      <td>-0.049324</td>\n",
       "      <td>0.239034</td>\n",
       "      <td>-1.000330</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.740137</td>\n",
       "      <td>-0.565498</td>\n",
       "      <td>0.476031</td>\n",
       "      <td>-2.158069</td>\n",
       "      <td>1.318551</td>\n",
       "      <td>-0.239297</td>\n",
       "      <td>-0.246794</td>\n",
       "      <td>-1.079343</td>\n",
       "      <td>-0.114226</td>\n",
       "      <td>10.399650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.013240</th>\n",
       "      <td>-0.121945</td>\n",
       "      <td>0.339059</td>\n",
       "      <td>-0.589632</td>\n",
       "      <td>-0.895816</td>\n",
       "      <td>0.548328</td>\n",
       "      <td>0.098667</td>\n",
       "      <td>0.197181</td>\n",
       "      <td>1.059027</td>\n",
       "      <td>-1.022564</td>\n",
       "      <td>-0.855240</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.739936</td>\n",
       "      <td>1.315138</td>\n",
       "      <td>-0.323457</td>\n",
       "      <td>0.197828</td>\n",
       "      <td>0.097751</td>\n",
       "      <td>1.401523</td>\n",
       "      <td>0.158434</td>\n",
       "      <td>-1.141901</td>\n",
       "      <td>-1.310970</td>\n",
       "      <td>-21.762801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.532921</th>\n",
       "      <td>-1.711970</td>\n",
       "      <td>0.046135</td>\n",
       "      <td>-0.958374</td>\n",
       "      <td>-0.080812</td>\n",
       "      <td>-0.703859</td>\n",
       "      <td>-0.770784</td>\n",
       "      <td>-0.480845</td>\n",
       "      <td>0.703586</td>\n",
       "      <td>0.929145</td>\n",
       "      <td>0.371173</td>\n",
       "      <td>...</td>\n",
       "      <td>0.473488</td>\n",
       "      <td>1.855246</td>\n",
       "      <td>1.415656</td>\n",
       "      <td>-0.302746</td>\n",
       "      <td>0.989679</td>\n",
       "      <td>0.585851</td>\n",
       "      <td>1.136388</td>\n",
       "      <td>0.671617</td>\n",
       "      <td>-0.974167</td>\n",
       "      <td>2.139453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.619685</th>\n",
       "      <td>0.572627</td>\n",
       "      <td>1.902618</td>\n",
       "      <td>-0.775664</td>\n",
       "      <td>-0.188090</td>\n",
       "      <td>-1.035748</td>\n",
       "      <td>1.177830</td>\n",
       "      <td>-2.305167</td>\n",
       "      <td>-2.263660</td>\n",
       "      <td>0.375020</td>\n",
       "      <td>-0.082344</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.303220</td>\n",
       "      <td>0.466751</td>\n",
       "      <td>0.161106</td>\n",
       "      <td>0.320032</td>\n",
       "      <td>2.079177</td>\n",
       "      <td>-0.907466</td>\n",
       "      <td>-0.192404</td>\n",
       "      <td>-1.212516</td>\n",
       "      <td>-0.080599</td>\n",
       "      <td>0.194017</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 500 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  1         2         3         4         5         6  \\\n",
       "0                                                                       \n",
       " 0.382732 -0.034242  1.096347 -0.234216 -0.347451 -0.581268 -1.632635   \n",
       " 0.555963  0.892474 -0.422315  0.104714  0.228053  0.201480  0.540774   \n",
       " 0.013240 -0.121945  0.339059 -0.589632 -0.895816  0.548328  0.098667   \n",
       "-1.532921 -1.711970  0.046135 -0.958374 -0.080812 -0.703859 -0.770784   \n",
       "-1.619685  0.572627  1.902618 -0.775664 -0.188090 -1.035748  1.177830   \n",
       "\n",
       "                  7         8         9        10    ...           491  \\\n",
       "0                                                    ...                 \n",
       " 0.382732 -1.567768 -1.179158  1.301428  0.895260    ...      0.178793   \n",
       " 0.555963 -1.818078 -0.049324  0.239034 -1.000330    ...     -0.740137   \n",
       " 0.013240  0.197181  1.059027 -1.022564 -0.855240    ...     -0.739936   \n",
       "-1.532921 -0.480845  0.703586  0.929145  0.371173    ...      0.473488   \n",
       "-1.619685 -2.305167 -2.263660  0.375020 -0.082344    ...     -1.303220   \n",
       "\n",
       "                492       493       494       495       496       497  \\\n",
       "0                                                                       \n",
       " 0.382732 -0.799422  0.240788  0.289121  0.412871 -0.198399  0.094192   \n",
       " 0.555963 -0.565498  0.476031 -2.158069  1.318551 -0.239297 -0.246794   \n",
       " 0.013240  1.315138 -0.323457  0.197828  0.097751  1.401523  0.158434   \n",
       "-1.532921  1.855246  1.415656 -0.302746  0.989679  0.585851  1.136388   \n",
       "-1.619685  0.466751  0.161106  0.320032  2.079177 -0.907466 -0.192404   \n",
       "\n",
       "                498       499          y  \n",
       "0                                         \n",
       " 0.382732 -1.147611 -0.358114  -2.663126  \n",
       " 0.555963 -1.079343 -0.114226  10.399650  \n",
       " 0.013240 -1.141901 -1.310970 -21.762801  \n",
       "-1.532921  0.671617 -0.974167   2.139453  \n",
       "-1.619685 -1.212516 -0.080599   0.194017  \n",
       "\n",
       "[5 rows x 500 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "from sklearn import preprocessing\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv('/Users/hanzehu/Downloads/APMAE4990--master/data/hw2data.csv',index_col=0)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Set y to be the y variable in the dataframe from a and X to be the remaining features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = df.y\n",
    "X = df.drop(labels='y', axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) As shown in the Booking.com example, using Lasso regression, find the regularization strength\n",
    "which optimizes the $R^2$. \n",
    "\n",
    "**Hint:** Take a range of alpha from `np.logspace(-8,-3,1000)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/cross_validation.py:41: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000298177229002\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD8CAYAAACb4nSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfLlEqcGT9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a0c5b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "X = X.as_matrix().astype(np.float)\n",
    "X = scaler.fit_transform(X)\n",
    "\n",
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "\n",
    "# Take the range of alpha\n",
    "alphas = np.logspace(-8,-3,1000)\n",
    "scores = []\n",
    "\n",
    "for alpha in alphas:\n",
    "    regr = Lasso(alpha=alpha)\n",
    "    # Train the model using the training sets\n",
    "    regr.fit(X_train, y_train)\n",
    "    scores.append(regr.score(X_test,y_test))\n",
    "plt.plot(alphas,scores)\n",
    "\n",
    "best_alpha=alphas[np.argmax(scores)]\n",
    "print (best_alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d) Plot the training perforamnce versus the testing performance, and observe whree the test performance is\n",
    "maximized. I've written an outline of the code you need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAACXCAYAAAD6SkdsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQUREEv4/6Oui3e1eMtAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a0fb922b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a187cd5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "\n",
    "# Fill these in\n",
    "\n",
    "train_errors=[]\n",
    "test_errors=[]\n",
    "\n",
    "for alpha in alphas:\n",
    "    regr = Lasso(alpha=alpha)\n",
    "    regr.fit(X_train, y_train)\n",
    "    train_errors.append(regr.score(X_train, y_train))\n",
    "    test_errors.append(regr.score(X_test, y_test))\n",
    "\n",
    "plt.semilogx(alphas, train_errors, label='Train')\n",
    "plt.semilogx(alphas, test_errors, label='Test')\n",
    "plt.vlines(best_alpha, plt.ylim()[0], np.max(test_errors), color='k',\n",
    "           linewidth=3, label='Optimum on test')\n",
    "plt.legend(loc='lower left')\n",
    "plt.ylim([0, 1.2])\n",
    "plt.xlabel('Regularization parameter')\n",
    "plt.ylabel('Performance')\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "regr = Lasso(alpha = best_alpha)\n",
    "regr.fit(X_train,y_train)\n",
    "\n",
    "R2_train = regr.score(X_train,y_train)\n",
    "R2_test = regr.score(X_test,y_test)\n",
    "coef = regr.coef_\n",
    "\n",
    "plt.plot(coef, label='Optimal Parameter')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "e) Plot the top coefficients based on this optimal paramter. Why do you think so many are zero? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngSBJAgwESVJjIEiSAPh/9EvOvhTgkDgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a18d0b630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "regr = Lasso(alpha=best_alpha)\n",
    "regr.fit(X_train,y_train)\n",
    "coefficient = np.sort(np.array(regr.coef_))\n",
    "plt.xlabel('Parameters')\n",
    "plt.ylabel('Performance')\n",
    "plt.bar(range(499), coefficient)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "f) Compute the $R^2$ with the optimal coefficient found above on 5 folds using cross_val_score and plot the\n",
    "results. Does the model work well on all random subsets?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEWCAYAAACXGLsWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmZkVOSzMzKzIYWFmZkUOCzMzK/o/4u7YwB9dMkgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a192c8550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAE4tJREFUeJzt3H+0XWV95/H3hwSEQtRpc7VAosES\nqKn9wTQFW2xLFdqIEGzHttDWyipTVmuxdXS02DoMRWZKa9fIrFVsS1sXIwpIrZ1maTQ4AmO1oAQR\nWhJYjfwwacCEX0rqWAp+54+9Y08P98e54eYe73Pfr7XOyt77ec4+37137uc+99nnnFQVkqS2HDDu\nAiRJc89wl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuAJKclGTHuOtYSJJUkqP75T9O8l9G6bsPr/Pz\nSa7b1zq1OC0ddwGaWpL7gOcDTwF7gI8B51XVnnHWpaerql+Zi/0kWQXcCxxYVU/2+34/8P652L8W\nD0fu3/xOr6rDgO8DjgPeNuZ65k0SBx8LmNdvvAz3BaKqHgQ20YU8AEleleS2JF9Jsj3JhQNtq/qp\ngNcl+WKSh5L89kD7IUmuSPJoki3ADwy+XpIXJ7kxyWNJ7kyyfqDtiiTvTvLRJHuSfDrJtye5tN/f\nXUmOm+pYknxXko8neSTJl5L8Vr/9wiQfTPK+JF8Bzk7yrH6/O/vHpUme1fdfnuTDfY2PJPmbJAf0\nbb+Z5B+TPJ7k7iSvmKSOlyZ5MMmSgW0/meSOfvn4JDf1+38gyR8mOWiKY7oiycUD62/pn7MzyS8N\n9Z3yugGf7P99rD+3P5jk7CSfGnj+DyW5JcmX+39/aKDtxiTv6K/J40muS7J8ipqnO38rk3woye4k\nDyf5w377AUnenuT+JLuSvDfJc/q2vf/nzknyReD6gfP8t/3r3J7kpIEazk5yT1/rvUl+frJatQ+q\nysc36QO4Dzi5X14B/B3wPwfaTwK+m+6X9PcAXwJe3betAgr4U+AQ4HuBfwZe3LdfAvwN8K3ASuDv\ngR1924HANuC3gIOAlwOPA8f27VcADwHfDxxM90N8L/CLwBLgYuCGKY5pGfAA8Ob+ucuAE/q2C4F/\nAV7dH9MhwEXAzcDzgAngb4F39P1/F/jjvt4DgR8GAhwLbAeOGDgX3zFFPV8AThlY/wvg/H75+4GX\n0k1frgK2Am8c6FvA0QPn5OJ+eV1/LV4CHApcNdR3lOu2dOB1zgY+1S9/K/Ao8Nq+rrP69W/r22/s\nj+mY/vzdCFwyxbFPdf6WALcD7+rrPxh4Wf+cX6L7v/Ei4DDgQ8CVQ7W/t3/eIcCRwMPAqf3xntKv\nT/R9vsK//r86HPiucf/ctfIYewE+prk4XbjvoQvWAj4BPHea/pcC7+qX9/6grRho/yxwZr98D7Bu\noO1c/jXcfxh4EDhgoP1q4MJ++QrgTwfa3gBsHVj/buCxKWo8C7htirYLgU8ObfsCcOrA+k8A9/XL\nFwF/TR+aA32OBnYBJ9PNXU93ji8G3tMvLwP+CXjhFH3fCPzVwPpU4f6ewUClC9oarnOG6zZVuL8W\n+OzQ828Czu6XbwTePtD2euBjU7zuVOfvB4HdgzUMtH0CeP3A+rF0v5D3/gIs4EUD7b9JH/4D2zYB\nr6ML98eA/wAcMu6ft9YeTst883t1VS2jG+19J/CNP7GTnJDkhv5P5y8DvzLY3ntwYPmrdKMtgCPo\nRrd73T+wfASwvaq+PtR+5MD6lwaW/98k64cxuZV0gT2V7UPrRwzVdn+/DeCddKPI6/o/7c8HqKpt\ndEF8IbAryTVJjmByVwE/1U/1/BTwuaq6HyDJMf20xYP9NNF/5+nndzLTndtRr9t0+75/aNvwtZnq\nmg+b9PzRXaP7q7+hO8Pr308X7M8f2DZ47C8EfrqfknksyWPAy4DDq+qfgJ+lO/4HknwkyXdOUatm\nyXBfIKrq/9KNDv9gYPNVwAZgZVU9h+5P7Iy4ywfofoj3esHA8k5g5d7514H2f5xl2ZPZDnzHNO3D\nX1O6ky4gBuvYCVBVj1fVm6vqRcDpwJv2zq1X1VVV9bL+uQX83qQvVrWFLqBeCfwc3Tnd64+Au4DV\nVfVsummqUc7vdOcWpr9uM31N6/D52Lv/WV+bac7fduAFmfyG6GTX40n+7S/3wWPYTjdyf+7A49Cq\nuqSvYVNVnUI3JXMX3TSi5oDhvrBcCpySZO9N1WXAI1X1tSTH04XTqK4F3pbk3yVZQTe1stdn6KYn\n3prkwP4G2OnANc/4CODDwLcneWN/s3RZkhOm6X818PYkE/2NwQuA9wEkOS3J0UlCN3f7FPBUkmOT\nvLwfjX+N7i+Jp6Z5jauAXwd+hG7Ofa9l/X739CPKXx3xGK+luxm8Jsm3AP91qH2667Yb+DrdnPZk\nNgLHJPm5JEuT/Cywhu68zspU549u+u4B4JIkhyY5OMmJ/dOuBv5TkqOSHEb318wHphjlQ3etTk/y\nE0mW9Ps6KcmKJM9Psj7JoXT3g/Yw/XXSLBjuC0hV7aa7WbX3wzKvBy5K8jhd6F07i939Dt2I9V7g\nOuDKgdd5AlhPN5p9CHg38ItVddccHMPjdDfVTqebPvgH4MemecrFwGbgDrobyp/rtwGsBv4PXSjc\nBLy7qm4EnkV3w/ih/jWeRzfqnsrVdNNe11fVQwPb/zNd8D5ON6L8wIjH+FG6X8TX0017XD/UZcrr\nVlVfBf4b8Ol+GuOlQ/t+GDiN7ob0w8BbgdOG6h7VpOevqp6iuz5HA18EdtBNn0B3P+FKunf13Ev3\ny/MNTKGqtgNn0J3/3XQj+bfQZc8B/XHsBB4BfrQ/N5oD6W9wSJIa4shdkhpkuEtSgwx3SWqQ4S5J\nDRrbF/ssX768Vq1aNa6Xl6QF6dZbb32oqiZm6je2cF+1ahWbN28e18tL0oKUZPgTypNyWkaSGmS4\nS1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkho0tk+oStJsrDr/I+MuYc7cd8mr9vtr\nOHKXpAYtyJG7v8ElaXqO3CWpQYa7JDVoQU7LLHatTEs5JSXtP47cJalBhrskNchwl6QGGe6S1CDD\nXZIaZLhLUoN8K6QWlFbeBgq+FVT7lyN3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1KCRwj3JuiR3\nJ9mW5PxJ2l+Q5IYktyW5I8mpc1+qJGlUM77PPckS4DLgFGAHcEuSDVW1ZaDb24Frq+qPkqwBNgKr\n9kO90qLWyvv8fY///jfKyP14YFtV3VNVTwDXAGcM9Sng2f3yc4Cdc1eiJGm2RvmE6pHA9oH1HcAJ\nQ30uBK5L8gbgUODkOalOkrRPRhm5Z5JtNbR+FnBFVa0ATgWuTPK0fSc5N8nmJJt37949+2olSSMZ\nJdx3ACsH1lfw9GmXc4BrAarqJuBgYPnwjqrq8qpaW1VrJyYm9q1iSdKMRgn3W4DVSY5KchBwJrBh\nqM8XgVcAJHkxXbg7NJekMZkx3KvqSeA8YBOwle5dMXcmuSjJ+r7bm4FfTnI7cDVwdlUNT91IkubJ\nSF/5W1Ub6d7eOLjtgoHlLcCJc1uaJGlf+QlVSWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIa\nZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGG\nuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhL\nUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktSgkcI9ybokdyfZluT8Kfr8TJItSe5MctXclilJ\nmo2lM3VIsgS4DDgF2AHckmRDVW0Z6LMaeBtwYlU9muR5+6tgSdLMRhm5Hw9sq6p7quoJ4BrgjKE+\nvwxcVlWPAlTVrrktU5I0G6OE+5HA9oH1Hf22QccAxyT5dJKbk6ybbEdJzk2yOcnm3bt371vFkqQZ\njRLumWRbDa0vBVYDJwFnAX+W5LlPe1LV5VW1tqrWTkxMzLZWSdKIRgn3HcDKgfUVwM5J+vx1Vf1L\nVd0L3E0X9pKkMRgl3G8BVic5KslBwJnAhqE+/xv4MYAky+mmae6Zy0IlSaObMdyr6kngPGATsBW4\ntqruTHJRkvV9t03Aw0m2ADcAb6mqh/dX0ZKk6c34VkiAqtoIbBzadsHAcgFv6h+SpDHzE6qS1CDD\nXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwl\nqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIa\nZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNGinck6xL\ncneSbUnOn6bfa5JUkrVzV6IkabZmDPckS4DLgFcCa4CzkqyZpN8y4NeBz8x1kZKk2Rll5H48sK2q\n7qmqJ4BrgDMm6fcO4PeBr81hfZKkfTBKuB8JbB9Y39Fv+4YkxwErq+rD0+0oyblJNifZvHv37lkX\nK0kazSjhnkm21TcakwOAdwFvnmlHVXV5Va2tqrUTExOjVylJmpVRwn0HsHJgfQWwc2B9GfAS4MYk\n9wEvBTZ4U1WSxmeUcL8FWJ3kqCQHAWcCG/Y2VtWXq2p5Va2qqlXAzcD6qtq8XyqWJM1oxnCvqieB\n84BNwFbg2qq6M8lFSdbv7wIlSbO3dJROVbUR2Di07YIp+p70zMuSJD0TfkJVkhpkuEtSgwx3SWqQ\n4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnu\nktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5J\nDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ0y3CWpQSOFe5J1Se5Osi3J+ZO0\nvynJliR3JPlEkhfOfamSpFHNGO5JlgCXAa8E1gBnJVkz1O02YG1VfQ/wQeD357pQSdLoRhm5Hw9s\nq6p7quoJ4BrgjMEOVXVDVX21X70ZWDG3ZUqSZmOUcD8S2D6wvqPfNpVzgI9O1pDk3CSbk2zevXv3\n6FVKkmZllHDPJNtq0o7JLwBrgXdO1l5Vl1fV2qpaOzExMXqVkqRZWTpCnx3AyoH1FcDO4U5JTgZ+\nG/jRqvrnuSlPkrQvRhm53wKsTnJUkoOAM4ENgx2SHAf8CbC+qnbNfZmSpNmYMdyr6kngPGATsBW4\ntqruTHJRkvV9t3cChwF/keTzSTZMsTtJ0jwYZVqGqtoIbBzadsHA8slzXJck6RnwE6qS1CDDXZIa\nZLhLUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNMtwlqUGG\nuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDTLcJalBhrskNchwl6QGGe6S1CDDXZIaZLhL\nUoMMd0lqkOEuSQ0y3CWpQYa7JDXIcJekBhnuktQgw12SGmS4S1KDDHdJapDhLkkNGinck6xLcneS\nbUnOn6T9WUk+0Ld/JsmquS5UkjS6GcM9yRLgMuCVwBrgrCRrhrqdAzxaVUcD7wJ+b64LlSSNbpSR\n+/HAtqq6p6qeAK4Bzhjqcwbwv/rlDwKvSJK5K1OSNBupquk7JK8B1lXVf+zXXwucUFXnDfT5+77P\njn79C32fh4b2dS5wbr96LHD3XB3IfrIceGjGXm3y2BevxXz8C+HYX1hVEzN1WjrCjiYbgQ//Rhil\nD1V1OXD5CK/5TSHJ5qpaO+46xsFjX5zHDov7+Fs69lGmZXYAKwfWVwA7p+qTZCnwHOCRuShQkjR7\no4T7LcDqJEclOQg4E9gw1GcD8Lp++TXA9TXTfI8kab+ZcVqmqp5Mch6wCVgCvKeq7kxyEbC5qjYA\nfw5cmWQb3Yj9zP1Z9DxaMFNI+4HHvngt5uNv5thnvKEqSVp4/ISqJDXIcJekBhnuk0jyniS7+vfv\nLypJVia5IcnWJHcm+Y1x1zRfkhyc5LNJbu+P/XfGXdN8S7IkyW1JPjzuWuZbkvuS/F2SzyfZPO56\nninn3CeR5EeAPcB7q+ol465nPiU5HDi8qj6XZBlwK/Dqqtoy5tL2u/5T1YdW1Z4kBwKfAn6jqm4e\nc2nzJsmbgLXAs6vqtHHXM5+S3AesHf7w5ULlyH0SVfVJFun79Kvqgar6XL/8OLAVOHK8Vc2P6uzp\nVw/sH4tm9JNkBfAq4M/GXYueOcNdU+q/3fM44DPjrWT+9NMSnwd2AR+vqkVz7MClwFuBr4+7kDEp\n4Lokt/ZflbKgGe6aVJLDgL8E3lhVXxl3PfOlqp6qqu+j+yT28UkWxbRcktOAXVV167hrGaMTq+rf\n030D7q/107MLluGup+nnm/8SeH9VfWjc9YxDVT0G3AisG3Mp8+VEYH0/73wN8PIk7xtvSfOrqnb2\n/+4C/oruG3EXLMNd/0Z/U/HPga1V9T/GXc98SjKR5Ln98iHAycBd461qflTV26pqRVWtovuE+fVV\n9QtjLmveJDm0fwMBSQ4FfhxY0O+WM9wnkeRq4Cbg2CQ7kpwz7prm0YnAa+lGbp/vH6eOu6h5cjhw\nQ5I76L5T6eNVtejeErhIPR/4VJLbgc8CH6mqj425pmfEt0JKUoMcuUtSgwx3SWqQ4S5JDTLcJalB\nhrskNchwl6QGGe6S1KD/DzbF2tpKNA2hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a193d5518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.90348127  0.78805702  0.89698882  0.87333405  0.85299781]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "regr = Lasso(alpha=best_alpha)\n",
    "scores = cross_val_score(regr, X, y, cv=5)\n",
    "plt.xlabel('lambda')\n",
    "plt.ylabel('R^2')\n",
    "plt.title('Performance on 5 folds with lambda=' + str(best_alpha))\n",
    "plt.bar(range(1,6),scores)\n",
    "plt.show()\n",
    "\n",
    "from sklearn.model_selection import ShuffleSplit\n",
    "cv = ShuffleSplit(n_splits=5, test_size=0.2)\n",
    "scorecv = cross_val_score(regr, X, y, cv=cv)\n",
    "plt.bar(range(1, 6), scorecv)\n",
    "plt.title('Random cross validation scores')\n",
    "plt.show()\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "f) Repeat e) but using cross validation. Use error bars on the features which are the standard deviation of the \n",
    "coefficiens obtained above. For this problem I\"ll walk you through the code. You just need to apply your optimal\n",
    "$\\alpha$ found above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hanzehu/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cross_validation import KFold\n",
    "from sklearn import preprocessing\n",
    "def run_cv_coeffs(X,y,clf_class,**kwargs):\n",
    "    # Construct a kfolds object\n",
    "    kf = KFold(len(y),n_folds=5,shuffle=True)\n",
    "    y_pred = y.copy()\n",
    "    coeffs=[]\n",
    "    # Iterate through folds\n",
    "    for train_index, test_index in kf:\n",
    "        \n",
    "        X_train, X_test = X[train_index], X[test_index]\n",
    "        y_train = y[train_index]\n",
    "        # Initialize a classifier with key word arguments\n",
    "        clf = clf_class(**kwargs)\n",
    "        clf.fit(X_train,y_train)\n",
    "        y_pred[test_index] = clf.predict(X_test)\n",
    "        coeffs.append(clf.coef_)\n",
    "    return coeffs\n",
    "\n",
    "\n",
    "\n",
    "scaler = preprocessing.StandardScaler()\n",
    "\n",
    "X_scaled = scaler.fit_transform(X)\n",
    "\n",
    "coeffs=run_cv_coeffs(X_scaled,np.array(y),Lasso,alpha=best_alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def get_coeffs(coeffs):\n",
    "    coeffs_avgd = [(coeffs[0][i] + coeffs[1][i] + coeffs[2][i] + coeffs[3][i] + coeffs[4][i])/5 for i in range(0,len(X))]\n",
    "    coeffs_std = [np.std([coeffs[0][i],coeffs[1][i],coeffs[2][i],coeffs[3][i],coeffs[4][i]]) for i in range(0,len(X))]\n",
    "    X_columns_values = [np.std([coeffs[0][i],coeffs[1][i],coeffs[2][i],coeffs[3][i],coeffs[4][i]]) for i in range(0,len(X))]\n",
    "    return coeffs_avgd, coeffs_std, X_columns_values\n",
    "coeffs_avg,coeffs_std,X_columns_values=get_coeffs(coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a19462358>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a193f4128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2wAAAOxCAYAAACJzCSgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1944c588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfCoeffs = pd.DataFrame({'type':X_columns_values, 'coef':coeffs_avg, 'std':coeffs_std})\n",
    "dfCoeffs = dfCoeffs[(dfCoeffs['coef']>1) |(dfCoeffs['coef']<-1) ]\n",
    "plt.figure(figsize=(15,15))\n",
    "dfCoeffs_sorted = dfCoeffs.sort_values(['coef'])[::-1]\n",
    "yerr_vals = dfCoeffs_sorted['std'].values\n",
    "dfCoeffs_sorted.plot(x='type',y='coef',kind='bar',yerr=yerr_vals,figsize=(15,15))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}