Chapter 6 Lab.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Lab 2: Ridge Regression](#6.6.1-Ridge-Regression)\n",
    "- [Lab 2: The Lasso](#6.6.2-The-Lasso)\n",
    "- [Lab 3: Principal Components Regression](#6.7.1-Principal-Components-Regression)\n",
    "- [Lab 3: Partial Least Squares](#6.7.2-Partial-Least-Squares)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6 - Linear Model Selection and Regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# %load ../standard_import.txt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.preprocessing import scale \n",
    "from sklearn import cross_validation\n",
    "from sklearn.linear_model import LinearRegression, Ridge, RidgeCV, Lasso, LassoCV\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cross_decomposition import PLSRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "pd.set_option('display.notebook_repr_html', False)\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 263 entries, 1 to 321\n",
      "Data columns (total 20 columns):\n",
      "AtBat        263 non-null int64\n",
      "Hits         263 non-null int64\n",
      "HmRun        263 non-null int64\n",
      "Runs         263 non-null int64\n",
      "RBI          263 non-null int64\n",
      "Walks        263 non-null int64\n",
      "Years        263 non-null int64\n",
      "CAtBat       263 non-null int64\n",
      "CHits        263 non-null int64\n",
      "CHmRun       263 non-null int64\n",
      "CRuns        263 non-null int64\n",
      "CRBI         263 non-null int64\n",
      "CWalks       263 non-null int64\n",
      "League       263 non-null object\n",
      "Division     263 non-null object\n",
      "PutOuts      263 non-null int64\n",
      "Assists      263 non-null int64\n",
      "Errors       263 non-null int64\n",
      "Salary       263 non-null float64\n",
      "NewLeague    263 non-null object\n",
      "dtypes: float64(1), int64(16), object(3)\n",
      "memory usage: 43.1+ KB\n"
     ]
    }
   ],
   "source": [
    "# In R, I exported the dataset from package 'ISLR' to a csv file.\n",
    "df = pd.read_csv('Data/Hitters.csv').dropna().drop('Unnamed: 0', axis=1)\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   AtBat  Hits  HmRun  Runs  RBI  Walks  Years  CAtBat  CHits  CHmRun  CRuns  \\\n",
       "1    315    81      7    24   38     39     14    3449    835      69    321   \n",
       "2    479   130     18    66   72     76      3    1624    457      63    224   \n",
       "3    496   141     20    65   78     37     11    5628   1575     225    828   \n",
       "4    321    87     10    39   42     30      2     396    101      12     48   \n",
       "5    594   169      4    74   51     35     11    4408   1133      19    501   \n",
       "\n",
       "   CRBI  CWalks League Division  PutOuts  Assists  Errors  Salary NewLeague  \n",
       "1   414     375      N        W      632       43      10   475.0         N  \n",
       "2   266     263      A        W      880       82      14   480.0         A  \n",
       "3   838     354      N        E      200       11       3   500.0         N  \n",
       "4    46      33      N        E      805       40       4    91.5         N  \n",
       "5   336     194      A        W      282      421      25   750.0         A  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 263 entries, 1 to 321\n",
      "Data columns (total 6 columns):\n",
      "League_A       263 non-null float64\n",
      "League_N       263 non-null float64\n",
      "Division_E     263 non-null float64\n",
      "Division_W     263 non-null float64\n",
      "NewLeague_A    263 non-null float64\n",
      "NewLeague_N    263 non-null float64\n",
      "dtypes: float64(6)\n",
      "memory usage: 14.4 KB\n",
      "   League_A  League_N  Division_E  Division_W  NewLeague_A  NewLeague_N\n",
      "1         0         1           0           1            0            1\n",
      "2         1         0           0           1            1            0\n",
      "3         0         1           1           0            0            1\n",
      "4         0         1           1           0            0            1\n",
      "5         1         0           0           1            1            0\n"
     ]
    }
   ],
   "source": [
    "dummies = pd.get_dummies(df[['League', 'Division', 'NewLeague']])\n",
    "dummies.info()\n",
    "print(dummies.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 263 entries, 1 to 321\n",
      "Data columns (total 19 columns):\n",
      "AtBat          263 non-null float64\n",
      "Hits           263 non-null float64\n",
      "HmRun          263 non-null float64\n",
      "Runs           263 non-null float64\n",
      "RBI            263 non-null float64\n",
      "Walks          263 non-null float64\n",
      "Years          263 non-null float64\n",
      "CAtBat         263 non-null float64\n",
      "CHits          263 non-null float64\n",
      "CHmRun         263 non-null float64\n",
      "CRuns          263 non-null float64\n",
      "CRBI           263 non-null float64\n",
      "CWalks         263 non-null float64\n",
      "PutOuts        263 non-null float64\n",
      "Assists        263 non-null float64\n",
      "Errors         263 non-null float64\n",
      "League_N       263 non-null float64\n",
      "Division_W     263 non-null float64\n",
      "NewLeague_N    263 non-null float64\n",
      "dtypes: float64(19)\n",
      "memory usage: 41.1 KB\n"
     ]
    }
   ],
   "source": [
    "y = df.Salary\n",
    "\n",
    "# Drop the column with the independent variable (Salary), and columns for which we created dummy variables\n",
    "X_ = df.drop(['Salary', 'League', 'Division', 'NewLeague'], axis=1).astype('float64')\n",
    "# Define the feature set X.\n",
    "X = pd.concat([X_, dummies[['League_N', 'Division_W', 'NewLeague_N']]], axis=1)\n",
    "\n",
    "X_train, X_test , y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.5, random_state=1)\n",
    "\n",
    "X.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6.1 Ridge Regression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The __glmnet__ algorithms in R optimize the objective function using cyclical coordinate descent, while scikit-learn Ridge regression uses linear least squares with L2 regularization. They are rather different implementations, but the general principles are the same.\n",
    "\n",
    "For the __glmnet() function in R__ the penalty is defined as:\n",
    "### $$ \\lambda\\bigg(\\frac{1}{2}(1−\\alpha)|\\beta|^2_2 \\ +\\ \\alpha|\\beta|_1\\bigg) $$\n",
    "(See R documentation and https://cran.r-project.org/web/packages/glmnet/vignettes/glmnet_beta.html)<BR>\n",
    "The function supports L1 and L2 regularization. For just Ridge regression we need to use $\\alpha = 0 $. This reduces the above penalty to\n",
    "### $$ \\frac{1}{2}\\lambda |\\beta|^2_2 $$\n",
    "The __sklearn Ridge()__ function has the standard L2 penalty:\n",
    "### $$ \\lambda |\\beta|^2_2 $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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GL3z5Ol+Xb2Jwl3785OzrURSFSKiBnV+9QjTsJafPJNJyzqN6+Rfs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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118c60390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alphas = 10**np.linspace(10,-2,100)*0.5\n",
    "\n",
    "ridge = Ridge()\n",
    "coefs = []\n",
    "\n",
    "for a in alphas:\n",
    "    ridge.set_params(alpha=a)\n",
    "    ridge.fit(scale(X), y)\n",
    "    coefs.append(ridge.coef_)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Ridge coefficients as a function of the regularization');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot shows that the Ridge coefficients get larger when we decrease alpha."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Alpha = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104835.06228323365"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2 = Ridge(alpha=4)\n",
    "ridge2.fit(scale(X_train), y_train)\n",
    "pred = ridge2.predict(scale(X_test))\n",
    "mean_squared_error(y_test, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Alpha = $10^{10}$ \n",
    "This big penalty shrinks the coefficients to a very large degree and makes the model more biased, resulting in a higher MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "172862.2200557664"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2.set_params(alpha=10**10)\n",
    "ridge2.fit(scale(X_train), y_train)\n",
    "pred = ridge2.predict(scale(X_test))\n",
    "mean_squared_error(y_test, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute the regularization path using RidgeCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RidgeCV(alphas=array([  5.00000e+09,   3.78232e+09, ...,   6.60971e-03,   5.00000e-03]),\n",
       "    cv=None, fit_intercept=True, gcv_mode=None, normalize=False,\n",
       "    scoring='mean_squared_error', store_cv_values=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgecv = RidgeCV(alphas=alphas, scoring='mean_squared_error')\n",
    "ridgecv.fit(scale(X_train), y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "66.097057423301436"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgecv.alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101437.87891789111"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge2.set_params(alpha=ridgecv.alpha_)\n",
    "ridge2.fit(scale(X_train), y_train)\n",
    "mean_squared_error(y_test, ridge2.predict(scale(X_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat          -5.266903\n",
       "Hits           42.293974\n",
       "HmRun          -4.414799\n",
       "Runs           18.300973\n",
       "RBI            35.122753\n",
       "Walks          50.045214\n",
       "Years           4.266424\n",
       "CAtBat         13.869952\n",
       "CHits          34.924052\n",
       "CHmRun         47.437613\n",
       "CRuns          35.565533\n",
       "CRBI           47.132307\n",
       "CWalks         23.839983\n",
       "PutOuts        87.503814\n",
       "Assists        -2.311463\n",
       "Errors         -2.639522\n",
       "League_N       10.060616\n",
       "Division_W    -47.990988\n",
       "NewLeague_N     4.726928\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(ridge2.coef_, index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.6.2 The Lasso"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For both __glmnet__ in R and sklearn __Lasso()__ function the standard L1 penalty is:\n",
    "### $$ \\lambda |\\beta|_1 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Z0ua8O2u9PL18Gz2cNm4/uR+iccwyxwGMWeaw2HFY7PSITz2o+IQQ1Abq2d1Q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\nIiLBsGSIiEgwLBkiIhLM/wGY9Ihaq+bKBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11add3f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lasso = Lasso(max_iter=10000)\n",
    "coefs = []\n",
    "\n",
    "for a in alphas*2:\n",
    "    lasso.set_params(alpha=a)\n",
    "    lasso.fit(scale(X_train), y_train)\n",
    "    coefs.append(lasso.coef_)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.plot(alphas*2, coefs)\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlim(ax.get_xlim()[::-1])  # reverse axis\n",
    "plt.axis('tight')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('weights')\n",
    "plt.title('Lasso coefficients as a function of the regularization');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LassoCV(alphas=None, copy_X=True, cv=10, eps=0.001, fit_intercept=True,\n",
       "    max_iter=10000, n_alphas=100, n_jobs=1, normalize=False,\n",
       "    positive=False, precompute='auto', random_state=None,\n",
       "    selection='cyclic', tol=0.0001, verbose=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lassocv = LassoCV(alphas=None, cv=10, max_iter=10000)\n",
    "lassocv.fit(scale(X_train), y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27.503283261878408"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lassocv.alpha_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "106183.71692611946"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lasso.set_params(alpha=lassocv.alpha_)\n",
    "lasso.fit(scale(X_train), y_train)\n",
    "mean_squared_error(y_test, lasso.predict(scale(X_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AtBat            0.000000\n",
       "Hits            50.246197\n",
       "HmRun            0.000000\n",
       "Runs             0.000000\n",
       "RBI              0.000000\n",
       "Walks           66.794424\n",
       "Years            0.000000\n",
       "CAtBat           0.000000\n",
       "CHits            0.000000\n",
       "CHmRun          19.441152\n",
       "CRuns            0.000000\n",
       "CRBI           181.336557\n",
       "CWalks           0.000000\n",
       "PutOuts        110.307327\n",
       "Assists         -0.000000\n",
       "Errors          -0.000000\n",
       "League_N         0.000000\n",
       "Division_W     -44.530872\n",
       "NewLeague_N      0.000000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Some of the coefficients are now reduced to exactly zero.\n",
    "pd.Series(lasso.coef_, index=X.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.7.1 Principal Components Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-klearn does not have an implementation of PCA and regression combined like the 'pls' package in R.\n",
    "https://cran.r-project.org/web/packages/pls/vignettes/pls-manual.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(19, 19)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "          0         1         2         3         4         5\n",
       "0  0.198290  0.383784 -0.088626  0.031967 -0.028117  0.070646\n",
       "1  0.195861  0.377271 -0.074032  0.017982  0.004652  0.082240\n",
       "2  0.204369  0.237136  0.216186 -0.235831 -0.077660  0.149646\n",
       "3  0.198337  0.377721  0.017166 -0.049942  0.038536  0.136660\n",
       "4  0.235174  0.314531  0.073085 -0.138985 -0.024299  0.111675"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "X_reduced = pca.fit_transform(scale(X))\n",
    "\n",
    "print(pca.components_.shape)\n",
    "pd.DataFrame(pca.components_.T).loc[:4,:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above loadings are the same as in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(263, 19)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "          0         1         2         3         4         5\n",
       "0 -0.009649 -1.870522 -1.265145 -0.935481 -1.109636 -1.211972\n",
       "1  0.411434  2.429422  0.909193 -0.264212 -1.232031 -1.826617\n",
       "2  3.466822 -0.825947 -0.555469 -1.616726  0.857488  1.028712\n",
       "3 -2.558317  0.230984 -0.519642 -2.176251  0.820301 -1.491696\n",
       "4  1.027702  1.573537 -1.331382  3.494004 -0.983427 -0.513675"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(X_reduced.shape)\n",
    "pd.DataFrame(X_reduced).loc[:4,:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above principal components are the same as in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 38.31,  60.15,  70.84,  79.03,  84.29,  88.63,  92.26,  94.96,\n",
       "        96.28,  97.25,  97.97,  98.64,  99.14,  99.46,  99.73,  99.88,\n",
       "        99.95,  99.98,  99.99])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Variance explained by the principal components\n",
    "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AIYQoS4KmmslYGiGEKEuCpprJNDRCCFGWBE01s09DIzUaIYQAJGiqXUmNJl1qNEIIAUjQ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\nee25njSuYMbq8lTUNVuIayk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0NKB4Ju4vv/yyzDo5OTls374dgI8//pi7776bY8eOodPp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\nDiVBI4QQwqH+P/xUoL+NcjNxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad2e780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 10-fold CV, with shuffle\n",
    "n = len(X_reduced)\n",
    "kf_10 = cross_validation.KFold(n, n_folds=10, shuffle=True, random_state=1)\n",
    "\n",
    "regr = LinearRegression()\n",
    "mse = []\n",
    "\n",
    "# Calculate MSE with only the intercept (no principal components in regression)\n",
    "score = -1*cross_validation.cross_val_score(regr, np.ones((n,1)), y.ravel(), cv=kf_10, scoring='mean_squared_error').mean()    \n",
    "mse.append(score)\n",
    "\n",
    "# Calculate MSE using CV for the 19 principle components, adding one component at the time.\n",
    "for i in np.arange(1, 20):\n",
    "    score = -1*cross_validation.cross_val_score(regr, X_reduced[:,:i], y.ravel(), cv=kf_10, scoring='mean_squared_error').mean()\n",
    "    mse.append(score)\n",
    "    \n",
    "plt.plot(mse, '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot indicates that the lowest training MSE is reached when doing regression on 18 components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 106.36859204,   21.60350456,  -24.2942534 ,  -36.9858579 ,\n",
       "         58.41402748,  -62.20632652,  -24.63862038,   15.82817701,\n",
       "         29.57680773,   99.64801199,  -30.11209105,  -20.99269291,\n",
       "        -72.40210574, -276.68551696,   74.17098665, -422.72580227,\n",
       "        347.05662353,  561.59691587,  -83.25441536])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regr_test = LinearRegression()\n",
    "regr_test.fit(X_reduced, y)\n",
    "regr_test.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting PCA with training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YnXkvdOOpsP+RmZVL9w6N8TK5cDHZYvvvt8SMm45z0EA9jzo0rOuK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\nKGk0QgghDCWNRgghhKH+AD98r9cTHMRHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ad2ed68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca2 = PCA()\n",
    "X_reduced_train = pca2.fit_transform(scale(X_train))\n",
    "n = len(X_reduced_train)\n",
    "\n",
    "# 10-fold CV, with shuffle\n",
    "kf_10 = cross_validation.KFold(n, n_folds=10, shuffle=True, random_state=1)\n",
    "\n",
    "mse = []\n",
    "\n",
    "# Calculate MSE with only the intercept (no principal components in regression)\n",
    "score = -1*cross_validation.cross_val_score(regr, np.ones((n,1)), y_train.ravel(), cv=kf_10, scoring='mean_squared_error').mean()    \n",
    "mse.append(score)\n",
    "\n",
    "# Calculate MSE using CV for the 19 principle components, adding one component at the time.\n",
    "for i in np.arange(1, 20):\n",
    "    score = -1*cross_validation.cross_val_score(regr, X_reduced_train[:,:i], y_train.ravel(), cv=kf_10, scoring='mean_squared_error').mean()\n",
    "    mse.append(score)\n",
    "\n",
    "plt.plot(np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above plot indicates that the lowest training MSE is reached when doing regression on 6 components."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Transform test data with PCA loadings and fit regression on 6 principal components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "111994.42273636986"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_reduced_test = pca2.transform(scale(X_test))[:,:7]\n",
    "\n",
    "# Train regression model on training data \n",
    "regr = LinearRegression()\n",
    "regr.fit(X_reduced_train[:,:7], y_train)\n",
    "\n",
    "# Prediction with test data\n",
    "pred = regr.predict(X_reduced_test)\n",
    "mean_squared_error(y_test, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.7.2 Partial Least Squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-learn PLSRegression gives same results as the pls package in R when using 'method='oscorespls'. In the LAB excercise, the standard method is used which is 'kernelpls'. \n",
    "\n",
    "When doing a slightly different fitting in R, the result is close to the one obtained using scikit-learn.\n",
    "\n",
    "    pls.fit=plsr(Salary~., data=Hitters, subset=train, scale=TRUE, validation=\"CV\", method='oscorespls')\n",
    "    validationplot(pls.fit,val.type=\"MSEP\", intercept = FALSE)\n",
    "   \n",
    "See documentation:\n",
    "http://scikit-learn.org/dev/modules/generated/sklearn.cross_decomposition.PLSRegression.html#sklearn.cross_decomposition.PLSRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1, 20.0)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RDpvVCJMOAULctOvWoSqKwubNm/n+++/56aef6NKlCwkJCfTv398R8QkXcKGR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\nKdJGIyEhISExp0gbjYSEhITEnPI/7IrhtWUCR38AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a4a1048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = len(X_train)\n",
    "\n",
    "# 10-fold CV, with shuffle\n",
    "kf_10 = cross_validation.KFold(n, n_folds=10, shuffle=True, random_state=1)\n",
    "\n",
    "mse = []\n",
    "\n",
    "for i in np.arange(1, 20):\n",
    "    pls = PLSRegression(n_components=i)\n",
    "    score = cross_validation.cross_val_score(pls, scale(X_train), y_train, cv=kf_10, scoring='mean_squared_error').mean()\n",
    "    mse.append(-score)\n",
    "\n",
    "plt.plot(np.arange(1, 20), np.array(mse), '-v')\n",
    "plt.xlabel('Number of principal components in regression')\n",
    "plt.ylabel('MSE')\n",
    "plt.title('Salary')\n",
    "plt.xlim(xmin=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "104711.20627773693"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pls = PLSRegression(n_components=2)\n",
    "pls.fit(scale(X_train), y_train)\n",
    "\n",
    "mean_squared_error(y_test, pls.predict(scale(X_test)))"
   ]
  }
 ],
 "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}