Chapter_06_Linear_Model_Selection_and_Regularization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 6 Linear Model Selection and Regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Recall the linear model\n",
    "\\begin{equation}Y=\\beta_{0}+\\beta_{1} X_{1}+\\cdots+\\beta_{p} X_{p}+\\epsilon\\end{equation}\n",
    "- In the lectures that follow, we consider some approaches for extending the linear model framework. In the lectures covering Chapter 7 of the text, we generalize the linear model in order to accommodate non-linear, but still additive, relationships.\n",
    "- In the lectures covering Chapter 8 we consider even more general non-linear models.\n",
    "- Despite its simplicity, the linear model has distinct advantages in terms of its interpretability and often shows good predictive performance.\n",
    "- Hence we discuss in this lecture some ways in which the simple linear model can be improved, by replacing ordinary least squares fitting with some alternative fitting procedures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why consider alternatives to least squares?\n",
    "\n",
    "- Prediction Accuracy: especially when p > n, to control the variance.\n",
    "- Model Interpretability: By removing irrelevant features, that is, by setting the corresponding coefficient estimates to zero we can obtain a model that is more easily interpreted. We will present some approaches for automatically performing feature selection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Three classes of methods\n",
    "\n",
    "- Subset Selection. We identify a subset of the p predictors\n",
    "that we believe to be related to the response. We then fit a\n",
    "model using least squares on the reduced set of variables.\n",
    "- Shrinkage. We fit a model involving all p predictors, but\n",
    "the estimated coefficients are shrunken towards zero\n",
    "relative to the least squares estimates. This shrinkage (also\n",
    "known as regularization) has the effect of reducing variance\n",
    "and can also perform variable selection.\n",
    "- Dimension Reduction. We project the p predictors into a\n",
    "M-dimensional subspace, where M < p. This is achieved by\n",
    "computing M different linear combinations, or projections,\n",
    "of the variables. Then these M projections are used as\n",
    "predictors to fit a linear regression model by least squares."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Subset selection\n",
    "\n",
    "#### Best Subset Selection\n",
    "1. Let $\\mathcal{M}_{0}$ denote the null model, which contains no predictors. This model simply predicts the sample mean for each observation.\n",
    "2. For $k=1,2, \\ldots p:$\n",
    "(a) Fit all $\\left(\\begin{array}{l}p \\\\ k\\end{array}\\right)$ models that contain exactly $k$ predictors.\n",
    "(b) Pick the best among these $\\left(\\begin{array}{l}p \\\\ k\\end{array}\\right)$ models, and call it $\\mathcal{M}_{k} .$ Here best is defined as having the smallest RSS, or equivalently largest $R^{2}$.\n",
    "3. Select a single best model from among $\\mathcal{M}_{0}, \\ldots, \\mathcal{M}_{p}$ using cross-validated prediction error, $C_{p}(\\mathrm{AIC}), \\mathrm{BIC},$ or adjusted $R^{2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example - Credit data set\n",
    "#load modules\n",
    "import pandas as pd\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from mlxtend.feature_selection import ExhaustiveFeatureSelector as EFS\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mlxtend.feature_selection import SequentialFeatureSelector as sfs\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Limit         int64\n",
       "Rating        int64\n",
       "Cards         int64\n",
       "Age           int64\n",
       "Education     int64\n",
       "Gender       object\n",
       "Student      object\n",
       "Married      object\n",
       "Ethnicity    object\n",
       "Balance       int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#load credit card dataset\n",
    "credit = pd.read_csv('data/Credit.csv', index_col =0)\n",
    "credit.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mark the predictors and respond variables\n",
    "X= credit.iloc[:, :-1]\n",
    "y= credit.Balance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method DataFrame.info of          Limit  Rating  Cards  Age  Education  Balance  Gender_ Male  \\\n",
       "Income                                                                 \n",
       "14.891    3606     283      2   34         11      333             1   \n",
       "106.025   6645     483      3   82         15      903             0   \n",
       "104.593   7075     514      4   71         11      580             1   \n",
       "148.924   9504     681      3   36         11      964             0   \n",
       "55.882    4897     357      2   68         16      331             1   \n",
       "...        ...     ...    ...  ...        ...      ...           ...   \n",
       "12.096    4100     307      3   32         13      560             1   \n",
       "13.364    3838     296      5   65         17      480             1   \n",
       "57.872    4171     321      5   67         12      138             0   \n",
       "37.728    2525     192      1   44         13        0             1   \n",
       "18.701    5524     415      5   64          7      966             0   \n",
       "\n",
       "         Student_Yes  Married_Yes  Ethnicity_Asian  Ethnicity_Caucasian  \n",
       "Income                                                                   \n",
       "14.891             0            1                0                    1  \n",
       "106.025            1            1                1                    0  \n",
       "104.593            0            0                1                    0  \n",
       "148.924            0            0                1                    0  \n",
       "55.882             0            1                0                    1  \n",
       "...              ...          ...              ...                  ...  \n",
       "12.096             0            1                0                    1  \n",
       "13.364             0            0                0                    0  \n",
       "57.872             0            1                0                    1  \n",
       "37.728             0            1                0                    1  \n",
       "18.701             0            0                1                    0  \n",
       "\n",
       "[400 rows x 11 columns]>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#convert the categorical variables\n",
    "credit_dummies = pd.get_dummies(credit[['Gender', 'Student', 'Married', 'Ethnicity']])\n",
    "credit =credit.drop(credit[['Gender', 'Student', 'Married', 'Ethnicity']],axis=1)\n",
    "credit_dummies =credit_dummies.drop(['Gender_Female', 'Student_No', 'Married_No', 'Ethnicity_African American'],axis=1)\n",
    "credit_df= pd.concat([credit, credit_dummies], axis=1)\n",
    "credit_df.info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mark the predictors and respond variables\n",
    "X= credit_df.loc[:, credit_df.columns != 'Balance']\n",
    "y= credit_df.Balance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "def fit_ols(X,y):\n",
    "    ols = LinearRegression()\n",
    "    ols_model =ols.fit(X,y)\n",
    "    RSS= round(mean_squared_error(y,ols_model.predict(X)) * len(y),2)\n",
    "    R_square = round(ols_model.score(X,y),2)\n",
    "    return RSS, R_square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14617892.35, 0.83)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_ols(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "\n",
    "k = 11\n",
    "RSS_list, R_squared_list, feature_list = [],[], []\n",
    "numb_features = []\n",
    "\n",
    "#Looping over k = 1 to k = 11 features in X\n",
    "for k in range(1,len(X.columns) + 1):\n",
    "    #Looping over all possible combinations: from 11 choose k\n",
    "    for combo in itertools.combinations(X.columns,k):\n",
    "        tmp_result = fit_ols(X[list(combo)],y)   #Store temp result b\n",
    "        RSS_list.append(tmp_result[0])                  #Append lists\n",
    "        R_squared_list.append(tmp_result[1])\n",
    "        feature_list.append(combo)\n",
    "        numb_features.append(len(combo))   \n",
    "\n",
    "#Store in DataFrame\n",
    "df = pd.DataFrame({'numb_features': numb_features,'RSS': RSS_list, 'R_squared':R_squared_list,'features':feature_list})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['min_RSS'] = df.groupby('numb_features')['RSS'].transform(min)\n",
    "df['max_R_squared'] = df.groupby('numb_features')['R_squared'].transform(max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (16,6))\n",
    "ax = fig.add_subplot(1, 2, 1)\n",
    "\n",
    "ax.scatter(df.numb_features,df.RSS, alpha = .2, color = 'darkblue' )\n",
    "ax.set_xlabel('# Features')\n",
    "ax.set_ylabel('RSS')\n",
    "ax.set_title('RSS - Best subset selection')\n",
    "ax.plot(df.numb_features,df.min_RSS,color = 'r', label = 'Best subset')\n",
    "ax.legend()\n",
    "\n",
    "ax = fig.add_subplot(1, 2, 2)\n",
    "ax.scatter(df.numb_features,df.R_squared, alpha = .2, color = 'darkblue' )\n",
    "ax.plot(df.numb_features,df.max_R_squared,color = 'r', label = 'Best subset')\n",
    "ax.set_xlabel('# Features')\n",
    "ax.set_ylabel('R squared')\n",
    "ax.set_title('R_squared - Best subset selection')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each possible model containing a subset of the ten predictors in the Credit data set, the RSS and R2 are displayed. The red frontier tracks the best model for a given number of predictors, according to RSS and R2. Though the data set contains only ten predictors, the x-axis ranges from 1 to 11, since one of the variables is categorical and takes on three values, leading to the creation of two dummy variables.\n",
    "Although we have presented best subset selection here for least squares regression, the same ideas apply to other types of models, such as logistic regression. The deviance, negative two times the maximized log-likelihood, plays the role of RSS for a broader class of models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stepwise Selection\n",
    "\n",
    "- For computational reasons, best subset selection cannot be\n",
    "applied with very large p. Why not?\n",
    "- Best subset selection may also suffer from statistical\n",
    "problems when p is large: larger the search space, the\n",
    "higher the chance of finding models that look good on the\n",
    "training data, even though they might not have any\n",
    "predictive power on future data.\n",
    "- Thus an enormous search space can lead to overfitting and\n",
    "high variance of the coefficient estimates.\n",
    "- For both of these reasons, stepwise methods, which explore\n",
    "a far more restricted set of models, are attractive\n",
    "alternatives to best subset selection."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Stepwise Selection\n",
    "- Forward stepwise selection begins with a model containing\n",
    "no predictors, and then adds predictors to the model,\n",
    "one-at-a-time, until all of the predictors are in the model.\n",
    "- In particular, at each step the variable that gives the\n",
    "greatest additional improvement to the fit is added to the\n",
    "model.\n",
    "1. Let $\\mathcal{M}_{0}$ denote the null model, which contains no predictors.\n",
    "2. For $k=0, \\ldots, p-1:$\n",
    "2.1 Consider all $p-k$ models that augment the predictors in $\\mathcal{M}_{k}$ with one additional predictor.\n",
    "2.2 Choose the best among these $p-k$ models, and call it $\\mathcal{M}_{k+1} .$ Here best is defined as having smallest RSS or highest $R^{2}$\n",
    "3. Select a single best model from among $\\mathcal{M}_{0}, \\ldots, \\mathcal{M}_{p}$ using cross-validated prediction error, $C_{p}(\\mathrm{AIC}), \\mathrm{BIC},$ or adjusted $R^{2}$.\n",
    "\n",
    "- Computational advantage over best subset selection is\n",
    "clear.\n",
    "- It is not guaranteed to find the best possible model out of\n",
    "all $2^{p}$ models containing subsets of the p predictors. Why\n",
    "not? Give an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    2.5s finished\n",
      "\n",
      "[2020-04-22 16:39:18] Features: 1/1 -- score: -54293.176584293506"
     ]
    },
    {
     "data": {
      "text/plain": [
       "SequentialFeatureSelector(clone_estimator=True, cv=5,\n",
       "                          estimator=LinearRegression(copy_X=True,\n",
       "                                                     fit_intercept=True,\n",
       "                                                     n_jobs=None,\n",
       "                                                     normalize=False),\n",
       "                          fixed_features=None, floating=False, forward=True,\n",
       "                          k_features=1, n_jobs=-1, pre_dispatch='2*n_jobs',\n",
       "                          scoring='neg_mean_squared_error', verbose=2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# one variable\n",
    "ols = LinearRegression()\n",
    "sfs1 = sfs(ols,\n",
    "           k_features=1,\n",
    "           forward=True,\n",
    "           floating=False,\n",
    "           verbose=2,\n",
    "           scoring='neg_mean_squared_error',\n",
    "           cv=5,\n",
    "           n_jobs=-1)\n",
    "sfs1.fit(X, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:20] Features: 1/2 -- score: -54293.176584293506[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   7 out of   9 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:20] Features: 2/2 -- score: -40104.361174004574"
     ]
    },
    {
     "data": {
      "text/plain": [
       "SequentialFeatureSelector(clone_estimator=True, cv=5,\n",
       "                          estimator=LinearRegression(copy_X=True,\n",
       "                                                     fit_intercept=True,\n",
       "                                                     n_jobs=None,\n",
       "                                                     normalize=False),\n",
       "                          fixed_features=None, floating=False, forward=True,\n",
       "                          k_features=2, n_jobs=-1, pre_dispatch='2*n_jobs',\n",
       "                          scoring='neg_mean_squared_error', verbose=2)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# two variables\n",
    "sfs2 = sfs(ols,\n",
    "           k_features=2,\n",
    "           forward=True,\n",
    "           floating=False,\n",
    "           verbose=2,\n",
    "           scoring='neg_mean_squared_error',\n",
    "           cv=5,\n",
    "           n_jobs=-1)\n",
    "sfs2.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:21] Features: 1/3 -- score: -54293.176584293506[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   7 out of   9 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:21] Features: 2/3 -- score: -40104.361174004574[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   6 out of   8 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:21] Features: 3/3 -- score: -38706.395570382505"
     ]
    },
    {
     "data": {
      "text/plain": [
       "SequentialFeatureSelector(clone_estimator=True, cv=5,\n",
       "                          estimator=LinearRegression(copy_X=True,\n",
       "                                                     fit_intercept=True,\n",
       "                                                     n_jobs=None,\n",
       "                                                     normalize=False),\n",
       "                          fixed_features=None, floating=False, forward=True,\n",
       "                          k_features=3, n_jobs=-1, pre_dispatch='2*n_jobs',\n",
       "                          scoring='neg_mean_squared_error', verbose=2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# three variable\n",
    "sfs3 = sfs(ols, k_features =3, forward =True, floating =False, verbose= 2, scoring = 'neg_mean_squared_error', cv=5, n_jobs=-1)\n",
    "sfs3.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:21] Features: 1/4 -- score: -54293.176584293506[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   7 out of   9 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:21] Features: 2/4 -- score: -40104.361174004574[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   6 out of   8 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:22] Features: 3/4 -- score: -38706.395570382505[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done   4 out of   7 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=-1)]: Done   7 out of   7 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-04-22 16:39:22] Features: 4/4 -- score: -38285.92694490571"
     ]
    },
    {
     "data": {
      "text/plain": [
       "SequentialFeatureSelector(clone_estimator=True, cv=5,\n",
       "                          estimator=LinearRegression(copy_X=True,\n",
       "                                                     fit_intercept=True,\n",
       "                                                     n_jobs=None,\n",
       "                                                     normalize=False),\n",
       "                          fixed_features=None, floating=False, forward=True,\n",
       "                          k_features=4, n_jobs=-1, pre_dispatch='2*n_jobs',\n",
       "                          scoring='neg_mean_squared_error', verbose=2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# four variables\n",
    "sfs4 = sfs(ols, k_features =4, forward =True, floating =False, verbose= 2, scoring = 'neg_mean_squared_error', cv=5, n_jobs=-1)\n",
    "sfs4.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Number of Variables         Forward stepwise Selection\n",
      "0        one variable                          (Rating,)\n",
      "1       two variables              (Rating, Student_Yes)\n",
      "2     three variables         (Rating, Age, Student_Yes)\n",
      "3      four variables  (Rating, Cards, Age, Student_Yes)\n"
     ]
    }
   ],
   "source": [
    "dat= [['one variable', sfs1.k_feature_names_],['two variables', sfs2.k_feature_names_], ['three variables', sfs3.k_feature_names_], ['four variables', sfs4.k_feature_names_]]\n",
    "\n",
    "dat_df = pd.DataFrame(dat, columns=['Number of Variables','Forward stepwise Selection'])\n",
    "\n",
    "print(dat_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first four selected models for best subset selection and\n",
    "forward stepwise selection on the Credit data set. The first\n",
    "three models are identical but the fourth models differ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backward Subset Selection\n",
    "\n",
    "- Like forward stepwise selection, backward stepwise selection\n",
    "provides an efficient alternative to best subset selection.\n",
    "- However, unlike forward stepwise selection, it begins with\n",
    "the full least squares model containing all p predictors, and\n",
    "then iteratively removes the least useful predictor,\n",
    "one-at-a-time.\n",
    "\n",
    "1. Let $\\mathcal{M}_{p}$ denote the full model, which contains all $p$ predictors.\n",
    "2. For $k=p, p-1, \\ldots, 1:$\n",
    "2.1 Consider all $k$ models that contain all but one of the predictors in $\\mathcal{M}_{k},$ for a total of $k-1$ predictors.\n",
    "2.2 Choose the best among these $k$ models, and call it $\\mathcal{M}_{k-1}$ Here best is defined as having smallest RSS or highest $R^{2}$.\n",
    "3. Select a single best model from among $\\mathcal{M}_{0}, \\ldots, \\mathcal{M}_{p}$ using cross-validated prediction error, $C_{p}(\\mathrm{AIC}), \\mathrm{BIC},$ or adjusted $R^{2}$\n",
    "\n",
    "- Like forward stepwise selection, the backward selection\n",
    "approach searches through only 1 + p(p + 1)=2 models, and\n",
    "so can be applied in settings where p is too large to apply\n",
    "best subset selection\n",
    "- Like forward stepwise selection, backward stepwise\n",
    "selection is not guaranteed to yield the best model\n",
    "containing a subset of the p predictors.\n",
    "- Backward selection requires that the number of samples n\n",
    "is larger than the number of variables p (so that the full\n",
    "model can be fit). In contrast, forward stepwise can be\n",
    "used even when n < p, and so is the only viable subset\n",
    "method when p is very large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Choosing the optimal model\n",
    "\n",
    "- The model containing all of the predictors will always have\n",
    "the smallest RSS and the largest R2, since these quantities\n",
    "are related to the training error.\n",
    "- We wish to choose a model with low test error, not a model\n",
    "with low training error. Recall that training error is usually\n",
    "a poor estimate of test error.\n",
    "- Therefore, RSS and R2 are not suitable for selecting the\n",
    "best model among a collection of models with di\u000b",
    "erent\n",
    "numbers of predictors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating test error: two approaches\n",
    "\n",
    "- We can indirectly estimate test error by making an\n",
    "adjustment to the training error to account for the bias due\n",
    "to overfitting.\n",
    "- We can directly estimate the test error, using either a\n",
    "validation set approach or a cross-validation approach, as\n",
    "discussed in previous lectures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adjusting training error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- These techniques adjust the training error for the model\n",
    "size, and can be used to select among a set of models with\n",
    "different numbers of variables.\n",
    "- The next figures displays Cp, BIC, and adjusted R2 for the\n",
    "best model of each size produced by best subset selection\n",
    "on the Credit data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mallow's $C_{p}$ :\n",
    "$$\n",
    "C_{p}=\\frac{1}{n}\\left(\\mathrm{RSS}+2 d \\hat{\\sigma}^{2}\\right)\n",
    "$$\n",
    "where $d$ is the total # of parameters used and $\\hat{\\sigma}^{2}$ is an estimate of the variance of the error $\\epsilon$ associated with each response measurement.\n",
    "- The $A I C$ criterion is defined for a large class of models fit by maximum likelihood:\n",
    "$$\n",
    "\\mathrm{AIC}=-2 \\log L+2 \\cdot d\n",
    "$$\n",
    "where $L$ is the maximized value of the likelihood function for the estimated model.\n",
    ": In the case of the linear model with Gaussian errors, maximum likelihood and least squares are the same thing, and $C_{p}$ and AIC are equivalent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BIC\n",
    "$$\n",
    "\\mathrm{BIC}=\\frac{1}{n}\\left(\\mathrm{RSS}+\\log (n) d \\hat{\\sigma}^{2}\\right)\n",
    "$$\n",
    "- Like $C_{p},$ the BIC will tend to take on a small value for a model with a low test error, and so generally we select the model that has the lowest BIC value.\n",
    "\" Notice that BIC replaces the $2 d \\hat{\\sigma}^{2}$ used by $C_{p}$ with a $\\log (n) d \\hat{\\sigma}^{2}$ term, where $n$ is the number of observations.\n",
    "- since $\\log n>2$ for any $n>7,$ the BIC statistic generally places a heavier penalty on models with many variables, and hence results in the selection of smaller models than $C_{p} .$ See Figure on slide 19"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adjusted $R^{2}$\n",
    "- For a least squares model with $d$ variables, the adjusted $R^{2}$ statistic is calculated as\n",
    "$$\n",
    "\\text { Adjusted } R^{2}=1-\\frac{\\mathrm{RSS} /(n-d-1)}{\\operatorname{TSS} /(n-1)}\n",
    "$$\n",
    "where TSS is the total sum of squares.\n",
    "\\bullet Unlike $C_{p}, \\mathrm{AIC},$ and $\\mathrm{BIC},$ for which a small value indicates a model with a low test error, a large value of adjusted $R^{2}$ indicates a model with a small test error.\n",
    "- Maximizing the adjusted $R^{2}$ is equivalent to minimizing $\\frac{\\mathrm{RSS}}{n-d-1} \\cdot$ While RSS always decreases as the number of variables in the model increases, $\\frac{\\mathrm{RSS}}{n-d-1}$ may increase or decrease, due to the presence of $d$ in the denominator.\n",
    "- Unlike the $R^{2}$ statistic, the adjusted $R^{2}$ statistic pays $a$ price for the inclusion of unnecessary variables in the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Validation and Cross-Validation\n",
    "。 Each of the procedures returns a sequence of models $\\mathcal{M}_{k}$ indexed by model size $k=0,1,2, \\ldots . .$ Our job here is to select $\\hat{k} .$ Once selected, we will return model $\\mathcal{M}_{\\hat{k}}$\n",
    "・ We compute the validation set error or the cross-validation error for each model $\\mathcal{M}_{k}$ under consideration, and then select the $k$ for which the resulting estimated test error is smallest.\n",
    "- This procedure has an advantage relative to AIC, BIC, $C_{p}$ and adjusted $R^{2},$ in that it provides a direct estimate of the test error, and doesn't require an estimate of the error variance $\\sigma^{2}$\n",
    "It can also be used in a wider range of model selection tasks, even in cases where it is hard to pinpoint the model degrees of freedom (e.g. the number of predictors in the model) or hard to estimate the error variance $\\sigma^{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ridge regression and Lasso\n",
    "- The subset selection methods use least squares to fit a\n",
    "linear model that contains a subset of the predictors.\n",
    "- As an alternative, we can fit a model containing all p\n",
    "predictors using a technique that constrains or regularizes\n",
    "the coefficient estimates, or equivalently, that shrinks the\n",
    "coefficient estimates towards zero.\n",
    "- It may not be immediately obvious why such a constraint\n",
    "should improve the fit, but it turns out that shrinking the\n",
    "coefficient estimates can significantly reduce their variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ridge Regression\n",
    "。 Recall that the least squares fitting procedure estimates $\\beta_{0}, \\beta_{1}, \\ldots, \\beta_{p}$ using the values that minimize\n",
    "$$\n",
    "\\mathrm{RSS}=\\sum_{i=1}^{n}\\left(y_{i}-\\beta_{0}-\\sum_{j=1}^{p} \\beta_{j} x_{i j}\\right)^{2}\n",
    "$$\n",
    "In contrast, the ridge regression coefficient estimates $\\hat{\\beta}^{R}$ are the values that minimize\n",
    "$\\sum_{i=1}^{n}\\left(y_{i}-\\beta_{0}-\\sum_{j=1}^{p} \\beta_{j} x_{i j}\\right)^{2}+\\lambda \\sum_{j=1}^{p} \\beta_{j}^{2}=\\mathrm{RSS}+\\lambda \\sum_{j=1}^{p} \\beta_{j}^{2}$\n",
    "where $\\lambda \\geq 0$ is a tuning parameter, to be determined separately.\n",
    "- As with least squares, ridge regression seeks coefficient\n",
    "estimates that fit the data well, by making the RSS small.\n",
    "- However, the second term, $\\lambda \\sum_{j=1}^{p}$, called a shrinkage\n",
    "penalty, is small when $\\beta_{0}, \\beta_{1}, \\ldots, \\beta_{p}$ are close to zero, and so it\n",
    "has the effect of shrinking the estimates of $\\beta_{j}$ towards zero.\n",
    "- The tuning parameter $\\lambda$ serves to control the relative\n",
    "impact of these two terms on the regression coefficient\n",
    "estimates.\n",
    "- Selecting a good value for $\\lambda$ is critical; cross-validation is\n",
    "used for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Credit Card Example\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy import linalg\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.preprocessing import scale, StandardScaler\n",
    "from sklearn import model_selection\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.model_selection import KFold, cross_val_score\n",
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "import itertools\n",
    "from itertools import combinations\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-white') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Float64Index: 400 entries, 14.890999999999998 to 18.701\n",
      "Data columns (total 10 columns):\n",
      " #   Column     Non-Null Count  Dtype   \n",
      "---  ------     --------------  -----   \n",
      " 0   Limit      400 non-null    int64   \n",
      " 1   Rating     400 non-null    int64   \n",
      " 2   Cards      400 non-null    int64   \n",
      " 3   Age        400 non-null    int64   \n",
      " 4   Education  400 non-null    int64   \n",
      " 5   Gender     400 non-null    category\n",
      " 6   Student    400 non-null    category\n",
      " 7   Married    400 non-null    category\n",
      " 8   Ethnicity  400 non-null    category\n",
      " 9   Balance    400 non-null    int64   \n",
      "dtypes: category(4), int64(6)\n",
      "memory usage: 23.8 KB\n"
     ]
    }
   ],
   "source": [
    "df_credit = pd.read_csv('Data/Credit.csv', index_col=0)\n",
    "df_credit[\"Gender\"] = df_credit[\"Gender\"].astype('category')\n",
    "df_credit[\"Student\"] = df_credit[\"Student\"].astype('category')\n",
    "df_credit[\"Married\"] = df_credit[\"Married\"].astype('category')\n",
    "df_credit[\"Ethnicity\"] = df_credit[\"Ethnicity\"].astype('category')\n",
    "df_credit.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Education</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Ethnicity_Asian</th>\n",
       "      <th>Ethnicity_Caucasian</th>\n",
       "      <th>Gender_Female</th>\n",
       "      <th>Married_Yes</th>\n",
       "      <th>Student_Yes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Income</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>14.891</th>\n",
       "      <td>34</td>\n",
       "      <td>2</td>\n",
       "      <td>11</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106.025</th>\n",
       "      <td>82</td>\n",
       "      <td>3</td>\n",
       "      <td>15</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104.593</th>\n",
       "      <td>71</td>\n",
       "      <td>4</td>\n",
       "      <td>11</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Age  Cards  Education  Limit  Rating  Ethnicity_Asian  \\\n",
       "Income                                                           \n",
       "14.891    34      2         11   3606     283                0   \n",
       "106.025   82      3         15   6645     483                1   \n",
       "104.593   71      4         11   7075     514                1   \n",
       "\n",
       "         Ethnicity_Caucasian  Gender_Female  Married_Yes  Student_Yes  \n",
       "Income                                                                 \n",
       "14.891                     1              0            1            0  \n",
       "106.025                    0              1            1            1  \n",
       "104.593                    0              0            0            0  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = df_credit.Balance\n",
    "\n",
    "X = df_credit[df_credit.columns.difference(['Balance'])]\n",
    "# Use K-1 columns for K categories so Yes/No uses only one column 0/1\n",
    "X = pd.get_dummies(X, drop_first=True)\n",
    "X_scaled = scale(X)\n",
    "X.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_lambdas = 200\n",
    "lambdas = np.logspace(5, -2, n_lambdas)\n",
    "\n",
    "coefs = []\n",
    "scores = []\n",
    "for lam in lambdas:\n",
    "    ridge = Ridge(alpha=lam)\n",
    "    # it's very important to scale the data for Ridge regression\n",
    "    ridge.fit(X_scaled, y)\n",
    "    coefs.append(ridge.coef_)\n",
    "    scores.append(ridge.score(X_scaled, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15,4))\n",
    "\n",
    "# get the four largest (in abs value) coefficient positions\n",
    "ind = np.argpartition(np.abs(coefs[-1]), -4)[-4:]\n",
    "\n",
    "# firt plot\n",
    "ax1.plot(lambdas, coefs)\n",
    "ax1.set_xscale('log')\n",
    "ax1.set_xlabel('lambda')\n",
    "ax1.set_ylabel('Standardized Coefficients')\n",
    "ax1.legend(np.array(ax1.get_lines())[ind], X.columns[ind]);\n",
    "\n",
    "# second plot\n",
    "no_ridge_norm = linalg.norm(coefs[-1])\n",
    "norm_coefs = linalg.norm(coefs/no_ridge_norm, axis=1)\n",
    "ax2.plot(norm_coefs, coefs)\n",
    "ax2.set_xlabel('Normalized Ridge coefficients')\n",
    "ax2.set_ylabel('Standardized Coefficients')\n",
    "ax2.legend(np.array(ax2.get_lines())[ind], X.columns[ind]); #delimiter\n",
    "\n",
    "# third\n",
    "ax3.plot(lambdas, scores)\n",
    "ax3.set_xscale('log')\n",
    "ax3.set_xlabel('lambda')\n",
    "ax3.set_ylabel('R^2')\n",
    "ax3.set_title('R^2 as a function of regularization');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- In the left-hand panel, each curve corresponds to the ridge regression coefficient estimate for one of the ten variables, plotted as a function of $\\lambda$\n",
    "- The right-hand panel displays the same ridge coefficient estimates as the left-hand panel, but instead of displaying $\\lambda$ on the $x$ -axis, we now display $\\left\\|\\hat{\\beta}_{\\lambda}^{R}\\right\\|_{2} /\\|\\hat{\\beta}\\|_{2},$ where $\\hat{\\beta}$ denotes the vector of least squares coefficient estimates.\n",
    "- The notation $\\|\\beta\\|_{2}$ denotes the $\\ell_{2}$ norm (pronounced \"ell $\\left.2^{\\prime \\prime}\\right)$ of a vector, and is defined as $\\|\\beta\\|_{2}=\\sqrt{\\sum_{j=1}^{p} \\beta_{j}^{2}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scaling of predictors\n",
    "\n",
    "- The standard least squares coefficient estimates are scale equivariant: multiplying $X_{j}$ by a constant $c$ simply leads to a scaling of the least squares coefficient estimates by a factor of $1 / c .$ In other words, regardless of how the $j$ th predictor is scaled, $X_{j} \\hat{\\beta}_{j}$ will remain the same.\n",
    "In contrast, the ridge regression coefficient estimates can change substantially when multiplying a given predictor by a constant, due to the sum of squared coefficients term in the penalty part of the ridge regression objective function.\n",
    "- Therefore, it is best to apply ridge regression after standardizing the predictors, using the formula\n",
    "$$\n",
    "\\tilde{x}_{i j}=\\frac{x_{i j}}{\\sqrt{\\frac{1}{n} \\sum_{i=1}^{n}\\left(x_{i j}-\\bar{x}_{j}\\right)^{2}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lasso\n",
    "- Ridge regression does have one obvious disadvantage:\n",
    "unlike subset selection, which will generally select models that involve just a subset of the variables, ridge regression will include all $p$ predictors in the final model\n",
    "- The Lasso is a relatively recent alternative to ridge regression that overcomes this disadvantage. The lasso coefficients, $\\hat{\\beta}_{\\lambda}^{L},$ minimize the quantity\n",
    "$\\sum_{i=1}^{n}\\left(y_{i}-\\beta_{0}-\\sum_{j=1}^{p} \\beta_{j} x_{i j}\\right)^{2}+\\lambda \\sum_{j=1}^{p}\\left|\\beta_{j}\\right|=\\mathrm{RSS}+\\lambda \\sum_{j=1}^{p}\\left|\\beta_{j}\\right|$\n",
    "- In statistical parlance, the lasso uses an $\\ell_{1}$ (pronounced\n",
    "\"ell 1\") penalty instead of an $\\ell_{2}$ penalty. The $\\ell_{1}$ norm of a coefficient vector $\\beta$ is given by $\\|\\beta\\|_{1}=\\sum\\left|\\beta_{j}\\right|$\n",
    "- As with ridge regression, the lasso shrinks the coefficient\n",
    "estimates towards zero.\n",
    "- However, in the case of the lasso, the $l_{1}$ penalty has the\n",
    "efect of forcing some of the coefficient estimates to be\n",
    "exactly equal to zero when the tuning parameter $\\lambda$ is\n",
    "sufficiently large.\n",
    "- Hence, much like best subset selection, the lasso performs\n",
    "variable selection.\n",
    "- We say that the lasso yields sparse models | that is,\n",
    "models that involve only a subset of the variables.\n",
    "- As in ridge regression, selecting a good value of $\\lambda$ for the\n",
    "lasso is critical; cross-validation is again the method of\n",
    "choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_lambdas = 200\n",
    "lambdas = np.logspace(3, 0.5, n_lambdas)\n",
    "\n",
    "coefs = []\n",
    "scores = []\n",
    "for lam in lambdas:\n",
    "    lasso = Lasso(alpha=lam)\n",
    "    lasso.fit(X_scaled, y)\n",
    "    coefs.append(lasso.coef_)\n",
    "    scores.append(lasso.score(X_scaled, y));\n",
    "    \n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15,4))\n",
    "\n",
    "# get the four largest (in abs value) coefficient positions\n",
    "ind = np.argpartition(np.abs(coefs[-1]), -4)[-4:]\n",
    "\n",
    "# firt plot\n",
    "ax1.plot(lambdas, coefs)\n",
    "ax1.set_xscale('log')\n",
    "ax1.set_xlabel('lambda')\n",
    "ax1.set_ylabel('Standardized Coefficients')\n",
    "ax1.legend(np.array(ax1.get_lines())[ind], X.columns[ind]);\n",
    "\n",
    "# second plot\n",
    "no_lasso_norm = linalg.norm(coefs[-1], ord=1)\n",
    "norm_coefs = linalg.norm(coefs/no_lasso_norm, axis=1, ord=1)\n",
    "ax2.plot(norm_coefs, coefs)\n",
    "ax2.set_xlabel('Normalized Lasso coefficients')\n",
    "ax2.set_ylabel('Standardized Coefficients')\n",
    "ax2.legend(np.array(ax2.get_lines())[ind], X.columns[ind]);\n",
    "\n",
    "# third\n",
    "ax3.plot(lambdas, scores)\n",
    "ax3.set_xscale('log')\n",
    "ax3.set_xlabel('lambda')\n",
    "ax3.set_ylabel('R^2')\n",
    "ax3.set_title('R^2 as a function of regularization');\n",
    "\n",
    "# the values for lambda are different here than in the text\n",
    "# most likely the function that is minimized is a bit different in scikit-learn and R\n",
    "# there's probably a factor of N or 2N (N=len(y)) difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why is it that the lasso, unlike ridge regression, results in coefficient estimates that are exactly equal to zero?\n",
    "\n",
    "One can show that the lasso and ridge regression coefficient estimates solve the problems\n",
    "$$\n",
    "\\underset{\\beta}{\\operatorname{minimize}} \\sum_{i=1}^{n}\\left(y_{i}-\\beta_{0}-\\sum_{j=1}^{p} \\beta_{j} x_{i j}\\right)^{2} \\quad \\text { subject to } \\quad \\sum_{j=1}^{p}\\left|\\beta_{j}\\right| \\leq s\n",
    "$$\n",
    "and\n",
    "$$\n",
    "\\underset{\\beta}{\\operatorname{minimize}} \\sum_{i=1}^{n}\\left(y_{i}-\\beta_{0}-\\sum_{j=1}^{p} \\beta_{j} x_{i j}\\right)^{2} \\quad \\text { subject to } \\quad \\sum_{j=1}^{p} \\beta_{j}^{2} \\leq s\n",
    "$$\n",
    "respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![ridge and lasso](images/ridge.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Conclusions\n",
    "- These two examples illustrate that neither ridge regression\n",
    "nor the lasso will universally dominate the other.\n",
    "- In general, one might expect the lasso to perform better\n",
    "when the response is a function of only a relatively small\n",
    "number of predictors.\n",
    "- However, the number of predictors that is related to the\n",
    "response is never known a priori for real data sets.\n",
    "- A technique such as cross-validation can be used in order\n",
    "to determine which approach is better on a particular data\n",
    "set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Selecting the Tuning Parameter for Ridge Regression and Lasso\n",
    "- As for subset selection, for ridge regression and lasso we\n",
    "require a method to determine which of the models under\n",
    "consideration is best.\n",
    "- That is, we require a method selecting a value for the\n",
    "tuning parameter $\\lambda$ or equivalently, the value of the\n",
    "constraint s.\n",
    "- Cross-validation provides a simple way to tackle this\n",
    "problem. We choose a grid of $\\lambda$ values, and compute the\n",
    "cross-validation error rate for each value of $\\lambda$.\n",
    "- We then select the tuning parameter value for which the\n",
    "cross-validation error is smallest.\n",
    "- Finally, the model is re-fit using all of the available\n",
    "observations and the selected value of the tuning\n",
    "parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lambdas = np.logspace(0.5, -4, 100)\n",
    "ridgeCV = RidgeCV(alphas=lambdas, store_cv_values=True)\n",
    "ridgeCV.fit(X_scaled, y)\n",
    "MSE_alphas = np.mean(ridgeCV.cv_values_, axis=0)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(5,4))\n",
    "ax.plot(lambdas, MSE_alphas)\n",
    "ax.axvline(ridgeCV.alpha_, color='k', linestyle='--')\n",
    "ax.set_xscale('log')\n",
    "ax.set_xlabel('lambda')\n",
    "ax.set_ylabel('CV MSE');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dimension Reduction Methods\n",
    "- The methods that we have discussed so far in this chapter\n",
    "have involved fitting linear regression models, via least\n",
    "squares or a shrunken approach, using the original\n",
    "predictors, $X_{0}, X_{1}, \\ldots, X_{p}$.\n",
    "- We now explore a class of approaches that transform the\n",
    "predictors and then fit a least squares model using the\n",
    "transformed variables. We will refer to these techniques as\n",
    "dimension reduction methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dimension Reduction Methods: details\n",
    "- Let $Z_{1}, Z_{2}, \\ldots, Z_{M}$ represent $M<p$ linear combinations of our original $p$ predictors. That is,\n",
    "$Z_{m}=\\sum_{j=1}^{p} \\phi_{m j} X_{j}$\n",
    "for some constants $\\phi_{m 1}, \\ldots, \\phi_{m p}$\n",
    "- We can then fit the linear regression model,\n",
    "$$\n",
    "y_{i}=\\theta_{0}+\\sum_{m=1}^{M} \\theta_{m} z_{i m}+\\epsilon_{i}, \\quad i=1, \\ldots, n\n",
    "$$\n",
    "using ordinary least squares.\n",
    "- Note that in model (2), the regression coefficients are given by $\\theta_{0}, \\theta_{1}, \\ldots, \\theta_{M} .$ If the constants $\\phi_{m 1}, \\ldots, \\phi_{m p}$ are chosen wisely, then such dimension reduction approaches can often outperform OLS regression\n",
    "\n",
    "- Notice that from definition (1),\n",
    "$\\sum_{m=1}^{M} \\theta_{m} z_{i m}=\\sum_{m=1}^{M} \\theta_{m} \\sum_{j=1}^{p} \\phi_{m j} x_{i j}=\\sum_{j=1}^{p} \\sum_{m=1}^{M} \\theta_{m} \\phi_{m j} x_{i j}=\\sum_{j=1}^{p} \\beta_{j} x_{i j}$\n",
    "where $\\beta_{j}=\\sum_{m=1}^{M} \\theta_{m} \\phi_{m j}$\n",
    "- Hence model (2) can be thought of as a special case of the original linear regression model.\n",
    "- Dimension reduction serves to constrain the estimated $\\beta_{j}$ coefficients, since now they must take the form (3)\n",
    "- Can win in the bias-variance tradeoff."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Principal Components Regression\n",
    "- Here we apply principal components analysis (PCA)\n",
    "(discussed in Chapter 10 of the text) to define the linear\n",
    "combinations of the predictors, for use in our regression.\n",
    "- The first principal component is that (normalized) linear\n",
    "combination of the variables with the largest variance.\n",
    "- The second principal component has largest variance,\n",
    "subject to being uncorrelated with the first.\n",
    "- Hence with many correlated original variables, we replace\n",
    "them with a small set of principal components that capture\n",
    "their joint variation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "components = list(range(1, X_scaled.shape[1]+1))\n",
    "coefs = []\n",
    "scores = []\n",
    "for comp in components:\n",
    "    pca = PCA(n_components=comp)\n",
    "    X_pca_comp = pca.fit_transform(X_scaled)\n",
    "    # use the first comp components\n",
    "    #X_pca_comp = X_pca[:, 0:comp+1]\n",
    "    linear = LinearRegression(fit_intercept=False)\n",
    "    linear.fit(X_pca_comp, y)\n",
    "    coefs.append(linear.coef_)\n",
    "    scores.append(linear.score(X_pca_comp, y));\n",
    "    \n",
    "coefs = np.array(list(itertools.zip_longest(*coefs, fillvalue=0))).T\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10,4))\n",
    "\n",
    "# get the four largest (in abs value) coefficient positions\n",
    "ind = np.argpartition(np.abs(coefs[-1]), -4)[-4:]\n",
    "\n",
    "# firt plot\n",
    "ax1.plot(components, coefs)\n",
    "ax1.set_xlabel('Number of PCA components')\n",
    "ax1.set_ylabel('Standardized Coefficients')\n",
    "ax1.legend(np.array(ax1.get_lines())[ind], X.columns[ind])\n",
    "\n",
    "# third\n",
    "ax2.plot(components, scores)\n",
    "ax2.set_xlabel('Number of PCA components')\n",
    "ax2.set_ylabel('R^2')\n",
    "ax2.set_title('R^2 as a function of regularization');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Partial Least Squares\n",
    "- PCR identifies linear combinations, or directions, that best\n",
    "represent the predictors $X_{0}, X_{1}, \\ldots, X_{p}$.\n",
    "- These directions are identified in an unsupervised way, since\n",
    "the response Y is not used to help determine the principal\n",
    "component directions.\n",
    "- That is, the response does not supervise the identification\n",
    "of the principal components.\n",
    "- Consequently, PCR suffers from a potentially serious\n",
    "drawback: there is no guarantee that the directions that\n",
    "best explain the predictors will also be the best directions\n",
    "to use for predicting the response. \n",
    "- Like PCR, PLS is a dimension reduction method, which\n",
    "first identifies a new set of features $Z_{0}, Z_{1}, \\ldots, Z_{p}$ that are\n",
    "linear combinations of the original features, and then fits a\n",
    "linear model via OLS using these M new features.\n",
    "- But unlike PCR, PLS identifies these new features in a\n",
    "supervised way - that is, it makes use of the response Y in\n",
    "order to identify new features that not only approximate\n",
    "the old features well, but also that are related to the\n",
    "response.\n",
    "- Roughly speaking, the PLS approach attempts to find\n",
    "directions that help explain both the response and the\n",
    "predictors.\n",
    "- After standardizing the $p$ predictors, PLS computes the first direction $Z_{1}$ by setting each $\\phi_{1 j}$ in (1) equal to the coefficient from the simple linear regression of $Y$ onto $X_{j}$\n",
    "one can show that this coefficient is proportional to the correlation between $Y$ and $X_{j}$\n",
    "- Hence, in computing $Z_{1}=\\sum_{j=1}^{p} \\phi_{1 j} X_{j},$ PLS places the highest weight on the variables that are most strongly related to the response.\n",
    "- Subsequent directions are found by taking residuals and then repeating the above prescription."
   ]
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    "### Summary\n",
    "- Model selection methods are an essential tool for data\n",
    "analysis, especially for big datasets involving many\n",
    "predictors.\n",
    "- Research into methods that give sparsity, such as the lasso\n",
    "is an especially hot area.\n",
    "- Later, we will return to sparsity in more detail, and will\n",
    "describe related approaches such as the elastic net."
   ]
  },
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   "source": [
    "### End of Chapter 6"
   ]
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   "source": [
    "# Exercise Problems"
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