Chapter01/Activity1.01/Activity1_01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activity 1.01\n",
    "## Adding regularization to the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this activity we will utilize the same logistic regression model from the scikit-learn package. This time however we will add regularization to the model, and search for the optimum regularization parameter, a process often called tuning the hyperparameters.\n",
    "\n",
    "After training the models we will test the predictions and compare the model evaluation metrics to those produced by the baseline model and the model without regularization.\n",
    "\n",
    "First, let's load the feature data from the first exercise and the target data from the second activity, the feature data from the second activity can also be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "feats = pd.read_csv('../data/OSI_feats_e3.csv')\n",
    "target = pd.read_csv('../data/OSI_target_e2.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will again create a test and train dataset. We will train the data using the training dataset, his time however we will use part of the training dataset for validation, in order to choose the most appropriate hyperparameter.\n",
    "\n",
    "We will again use a test_size = 0.2 which means that 20% of the data will be reserved for testing. The size of our validation set will be determined by how many validation folds we have, if we do 10-fold cross validation this equates to reserving 10% of the training dataset to validate our model on, each fold will use a different 10% of the training dataset, and the average error across all folds is used to compare models with different hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "test_size = 0.2\n",
    "random_state = 13\n",
    "X_train, X_test, y_train, y_test = train_test_split(feats, target, test_size=test_size, random_state=random_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make sure our dimensions are correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of X_train: (9864, 68)\n",
      "Shape of y_train: (9864, 1)\n",
      "Shape of X_test: (2466, 68)\n",
      "Shape of y_test: (2466, 1)\n"
     ]
    }
   ],
   "source": [
    "print(f'Shape of X_train: {X_train.shape}')\n",
    "print(f'Shape of y_train: {y_train.shape}')\n",
    "print(f'Shape of X_test: {X_test.shape}')\n",
    "print(f'Shape of y_test: {y_test.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit our model first by instantiating it, then by fitting the model to the training data.\n",
    "We also add in a penalty, denoted by 'l1' and 'l2', our goal is to find the penalty type and penalty value that gives us the best results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a reminder of how to use certain functions we can always use the help function to look at the details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class LogisticRegressionCV in module sklearn.linear_model._logistic:\n",
      "\n",
      "class LogisticRegressionCV(LogisticRegression, sklearn.base.BaseEstimator, sklearn.linear_model._base.LinearClassifierMixin)\n",
      " |  LogisticRegressionCV(Cs=10, fit_intercept=True, cv=None, dual=False, penalty='l2', scoring=None, solver='lbfgs', tol=0.0001, max_iter=100, class_weight=None, n_jobs=None, verbose=0, refit=True, intercept_scaling=1.0, multi_class='auto', random_state=None, l1_ratios=None)\n",
      " |  \n",
      " |  Logistic Regression CV (aka logit, MaxEnt) classifier.\n",
      " |  \n",
      " |  See glossary entry for :term:`cross-validation estimator`.\n",
      " |  \n",
      " |  This class implements logistic regression using liblinear, newton-cg, sag\n",
      " |  of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2\n",
      " |  regularization with primal formulation. The liblinear solver supports both\n",
      " |  L1 and L2 regularization, with a dual formulation only for the L2 penalty.\n",
      " |  Elastic-Net penalty is only supported by the saga solver.\n",
      " |  \n",
      " |  For the grid of `Cs` values and `l1_ratios` values, the best hyperparameter\n",
      " |  is selected by the cross-validator\n",
      " |  :class:`~sklearn.model_selection.StratifiedKFold`, but it can be changed\n",
      " |  using the :term:`cv` parameter. The 'newton-cg', 'sag', 'saga' and 'lbfgs'\n",
      " |  solvers can warm-start the coefficients (see :term:`Glossary<warm_start>`).\n",
      " |  \n",
      " |  Read more in the :ref:`User Guide <logistic_regression>`.\n",
      " |  \n",
      " |  Parameters\n",
      " |  ----------\n",
      " |  Cs : list of floats or int, optional (default=10)\n",
      " |      Each of the values in Cs describes the inverse of regularization\n",
      " |      strength. If Cs is as an int, then a grid of Cs values are chosen\n",
      " |      in a logarithmic scale between 1e-4 and 1e4.\n",
      " |      Like in support vector machines, smaller values specify stronger\n",
      " |      regularization.\n",
      " |  \n",
      " |  fit_intercept : bool, optional (default=True)\n",
      " |      Specifies if a constant (a.k.a. bias or intercept) should be\n",
      " |      added to the decision function.\n",
      " |  \n",
      " |  cv : int or cross-validation generator, optional (default=None)\n",
      " |      The default cross-validation generator used is Stratified K-Folds.\n",
      " |      If an integer is provided, then it is the number of folds used.\n",
      " |      See the module :mod:`sklearn.model_selection` module for the\n",
      " |      list of possible cross-validation objects.\n",
      " |  \n",
      " |      .. versionchanged:: 0.22\n",
      " |          ``cv`` default value if None changed from 3-fold to 5-fold.\n",
      " |  \n",
      " |  dual : bool, optional (default=False)\n",
      " |      Dual or primal formulation. Dual formulation is only implemented for\n",
      " |      l2 penalty with liblinear solver. Prefer dual=False when\n",
      " |      n_samples > n_features.\n",
      " |  \n",
      " |  penalty : str, 'l1', 'l2', or 'elasticnet', optional (default='l2')\n",
      " |      Used to specify the norm used in the penalization. The 'newton-cg',\n",
      " |      'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is\n",
      " |      only supported by the 'saga' solver.\n",
      " |  \n",
      " |  scoring : string, callable, or None, optional (default=None)\n",
      " |      A string (see model evaluation documentation) or\n",
      " |      a scorer callable object / function with signature\n",
      " |      ``scorer(estimator, X, y)``. For a list of scoring functions\n",
      " |      that can be used, look at :mod:`sklearn.metrics`. The\n",
      " |      default scoring option used is 'accuracy'.\n",
      " |  \n",
      " |  solver : str, {'newton-cg', 'lbfgs', 'liblinear', 'sag', 'saga'},              optional (default='lbfgs')\n",
      " |  \n",
      " |      Algorithm to use in the optimization problem.\n",
      " |  \n",
      " |      - For small datasets, 'liblinear' is a good choice, whereas 'sag' and\n",
      " |        'saga' are faster for large ones.\n",
      " |      - For multiclass problems, only 'newton-cg', 'sag', 'saga' and 'lbfgs'\n",
      " |        handle multinomial loss; 'liblinear' is limited to one-versus-rest\n",
      " |        schemes.\n",
      " |      - 'newton-cg', 'lbfgs' and 'sag' only handle L2 penalty, whereas\n",
      " |        'liblinear' and 'saga' handle L1 penalty.\n",
      " |      - 'liblinear' might be slower in LogisticRegressionCV because it does\n",
      " |        not handle warm-starting.\n",
      " |  \n",
      " |      Note that 'sag' and 'saga' fast convergence is only guaranteed on\n",
      " |      features with approximately the same scale. You can preprocess the data\n",
      " |      with a scaler from sklearn.preprocessing.\n",
      " |  \n",
      " |      .. versionadded:: 0.17\n",
      " |         Stochastic Average Gradient descent solver.\n",
      " |      .. versionadded:: 0.19\n",
      " |         SAGA solver.\n",
      " |  \n",
      " |  tol : float, optional (default=1e-4)\n",
      " |      Tolerance for stopping criteria.\n",
      " |  \n",
      " |  max_iter : int, optional (default=100)\n",
      " |      Maximum number of iterations of the optimization algorithm.\n",
      " |  \n",
      " |  class_weight : dict or 'balanced', optional (default=None)\n",
      " |      Weights associated with classes in the form ``{class_label: weight}``.\n",
      " |      If not given, all classes are supposed to have weight one.\n",
      " |  \n",
      " |      The \"balanced\" mode uses the values of y to automatically adjust\n",
      " |      weights inversely proportional to class frequencies in the input data\n",
      " |      as ``n_samples / (n_classes * np.bincount(y))``.\n",
      " |  \n",
      " |      Note that these weights will be multiplied with sample_weight (passed\n",
      " |      through the fit method) if sample_weight is specified.\n",
      " |  \n",
      " |      .. versionadded:: 0.17\n",
      " |         class_weight == 'balanced'\n",
      " |  \n",
      " |  n_jobs : int or None, optional (default=None)\n",
      " |      Number of CPU cores used during the cross-validation loop.\n",
      " |      ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.\n",
      " |      ``-1`` means using all processors. See :term:`Glossary <n_jobs>`\n",
      " |      for more details.\n",
      " |  \n",
      " |  verbose : int, optional (default=0)\n",
      " |      For the 'liblinear', 'sag' and 'lbfgs' solvers set verbose to any\n",
      " |      positive number for verbosity.\n",
      " |  \n",
      " |  refit : bool, optional (default=True)\n",
      " |      If set to True, the scores are averaged across all folds, and the\n",
      " |      coefs and the C that corresponds to the best score is taken, and a\n",
      " |      final refit is done using these parameters.\n",
      " |      Otherwise the coefs, intercepts and C that correspond to the\n",
      " |      best scores across folds are averaged.\n",
      " |  \n",
      " |  intercept_scaling : float, optional (default=1)\n",
      " |      Useful only when the solver 'liblinear' is used\n",
      " |      and self.fit_intercept is set to True. In this case, x becomes\n",
      " |      [x, self.intercept_scaling],\n",
      " |      i.e. a \"synthetic\" feature with constant value equal to\n",
      " |      intercept_scaling is appended to the instance vector.\n",
      " |      The intercept becomes ``intercept_scaling * synthetic_feature_weight``.\n",
      " |  \n",
      " |      Note! the synthetic feature weight is subject to l1/l2 regularization\n",
      " |      as all other features.\n",
      " |      To lessen the effect of regularization on synthetic feature weight\n",
      " |      (and therefore on the intercept) intercept_scaling has to be increased.\n",
      " |  \n",
      " |  multi_class : {'ovr', 'multinomial', 'auto'}, default='auto'\n",
      " |      If the option chosen is 'ovr', then a binary problem is fit for each\n",
      " |      label. For 'multinomial' the loss minimised is the multinomial loss fit\n",
      " |      across the entire probability distribution, *even when the data is\n",
      " |      binary*. 'multinomial' is unavailable when solver='liblinear'.\n",
      " |      'auto' selects 'ovr' if the data is binary, or if solver='liblinear',\n",
      " |      and otherwise selects 'multinomial'.\n",
      " |  \n",
      " |      .. versionadded:: 0.18\n",
      " |         Stochastic Average Gradient descent solver for 'multinomial' case.\n",
      " |      .. versionchanged:: 0.22\n",
      " |          Default changed from 'ovr' to 'auto' in 0.22.\n",
      " |  \n",
      " |  random_state : int, RandomState instance or None, optional (default=None)\n",
      " |      If int, random_state is the seed used by the random number generator;\n",
      " |      If RandomState instance, random_state is the random number generator;\n",
      " |      If None, the random number generator is the RandomState instance used\n",
      " |      by `np.random`. Used when `solver='sag'` or `solver='liblinear'`.\n",
      " |      Note that this only applies to the solver and not the cross-validation\n",
      " |      generator.\n",
      " |  \n",
      " |  l1_ratios : list of float or None, optional (default=None)\n",
      " |      The list of Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``.\n",
      " |      Only used if ``penalty='elasticnet'``. A value of 0 is equivalent to\n",
      " |      using ``penalty='l2'``, while 1 is equivalent to using\n",
      " |      ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a combination\n",
      " |      of L1 and L2.\n",
      " |  \n",
      " |  Attributes\n",
      " |  ----------\n",
      " |  classes_ : array, shape (n_classes, )\n",
      " |      A list of class labels known to the classifier.\n",
      " |  \n",
      " |  coef_ : array, shape (1, n_features) or (n_classes, n_features)\n",
      " |      Coefficient of the features in the decision function.\n",
      " |  \n",
      " |      `coef_` is of shape (1, n_features) when the given problem\n",
      " |      is binary.\n",
      " |  \n",
      " |  intercept_ : array, shape (1,) or (n_classes,)\n",
      " |      Intercept (a.k.a. bias) added to the decision function.\n",
      " |  \n",
      " |      If `fit_intercept` is set to False, the intercept is set to zero.\n",
      " |      `intercept_` is of shape(1,) when the problem is binary.\n",
      " |  \n",
      " |  Cs_ : array, shape (n_cs)\n",
      " |      Array of C i.e. inverse of regularization parameter values used\n",
      " |      for cross-validation.\n",
      " |  \n",
      " |  l1_ratios_ : array, shape (n_l1_ratios)\n",
      " |      Array of l1_ratios used for cross-validation. If no l1_ratio is used\n",
      " |      (i.e. penalty is not 'elasticnet'), this is set to ``[None]``\n",
      " |  \n",
      " |  coefs_paths_ : array, shape (n_folds, n_cs, n_features) or                    (n_folds, n_cs, n_features + 1)\n",
      " |      dict with classes as the keys, and the path of coefficients obtained\n",
      " |      during cross-validating across each fold and then across each Cs\n",
      " |      after doing an OvR for the corresponding class as values.\n",
      " |      If the 'multi_class' option is set to 'multinomial', then\n",
      " |      the coefs_paths are the coefficients corresponding to each class.\n",
      " |      Each dict value has shape ``(n_folds, n_cs, n_features)`` or\n",
      " |      ``(n_folds, n_cs, n_features + 1)`` depending on whether the\n",
      " |      intercept is fit or not. If ``penalty='elasticnet'``, the shape is\n",
      " |      ``(n_folds, n_cs, n_l1_ratios_, n_features)`` or\n",
      " |      ``(n_folds, n_cs, n_l1_ratios_, n_features + 1)``.\n",
      " |  \n",
      " |  scores_ : dict\n",
      " |      dict with classes as the keys, and the values as the\n",
      " |      grid of scores obtained during cross-validating each fold, after doing\n",
      " |      an OvR for the corresponding class. If the 'multi_class' option\n",
      " |      given is 'multinomial' then the same scores are repeated across\n",
      " |      all classes, since this is the multinomial class. Each dict value\n",
      " |      has shape ``(n_folds, n_cs`` or ``(n_folds, n_cs, n_l1_ratios)`` if\n",
      " |      ``penalty='elasticnet'``.\n",
      " |  \n",
      " |  C_ : array, shape (n_classes,) or (n_classes - 1,)\n",
      " |      Array of C that maps to the best scores across every class. If refit is\n",
      " |      set to False, then for each class, the best C is the average of the\n",
      " |      C's that correspond to the best scores for each fold.\n",
      " |      `C_` is of shape(n_classes,) when the problem is binary.\n",
      " |  \n",
      " |  l1_ratio_ : array, shape (n_classes,) or (n_classes - 1,)\n",
      " |      Array of l1_ratio that maps to the best scores across every class. If\n",
      " |      refit is set to False, then for each class, the best l1_ratio is the\n",
      " |      average of the l1_ratio's that correspond to the best scores for each\n",
      " |      fold.  `l1_ratio_` is of shape(n_classes,) when the problem is binary.\n",
      " |  \n",
      " |  n_iter_ : array, shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs)\n",
      " |      Actual number of iterations for all classes, folds and Cs.\n",
      " |      In the binary or multinomial cases, the first dimension is equal to 1.\n",
      " |      If ``penalty='elasticnet'``, the shape is ``(n_classes, n_folds,\n",
      " |      n_cs, n_l1_ratios)`` or ``(1, n_folds, n_cs, n_l1_ratios)``.\n",
      " |  \n",
      " |  \n",
      " |  Examples\n",
      " |  --------\n",
      " |  >>> from sklearn.datasets import load_iris\n",
      " |  >>> from sklearn.linear_model import LogisticRegressionCV\n",
      " |  >>> X, y = load_iris(return_X_y=True)\n",
      " |  >>> clf = LogisticRegressionCV(cv=5, random_state=0).fit(X, y)\n",
      " |  >>> clf.predict(X[:2, :])\n",
      " |  array([0, 0])\n",
      " |  >>> clf.predict_proba(X[:2, :]).shape\n",
      " |  (2, 3)\n",
      " |  >>> clf.score(X, y)\n",
      " |  0.98...\n",
      " |  \n",
      " |  See also\n",
      " |  --------\n",
      " |  LogisticRegression\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      LogisticRegressionCV\n",
      " |      LogisticRegression\n",
      " |      sklearn.base.BaseEstimator\n",
      " |      sklearn.linear_model._base.LinearClassifierMixin\n",
      " |      sklearn.base.ClassifierMixin\n",
      " |      sklearn.linear_model._base.SparseCoefMixin\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __init__(self, Cs=10, fit_intercept=True, cv=None, dual=False, penalty='l2', scoring=None, solver='lbfgs', tol=0.0001, max_iter=100, class_weight=None, n_jobs=None, verbose=0, refit=True, intercept_scaling=1.0, multi_class='auto', random_state=None, l1_ratios=None)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  fit(self, X, y, sample_weight=None)\n",
      " |      Fit the model according to the given training data.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |          Training vector, where n_samples is the number of samples and\n",
      " |          n_features is the number of features.\n",
      " |      \n",
      " |      y : array-like, shape (n_samples,)\n",
      " |          Target vector relative to X.\n",
      " |      \n",
      " |      sample_weight : array-like, shape (n_samples,) optional\n",
      " |          Array of weights that are assigned to individual samples.\n",
      " |          If not provided, then each sample is given unit weight.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self : object\n",
      " |  \n",
      " |  score(self, X, y, sample_weight=None)\n",
      " |      Returns the score using the `scoring` option on the given\n",
      " |      test data and labels.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like of shape (n_samples, n_features)\n",
      " |          Test samples.\n",
      " |      \n",
      " |      y : array-like of shape (n_samples,)\n",
      " |          True labels for X.\n",
      " |      \n",
      " |      sample_weight : array-like of shape (n_samples,), default=None\n",
      " |          Sample weights.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      score : float\n",
      " |          Score of self.predict(X) wrt. y.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from LogisticRegression:\n",
      " |  \n",
      " |  predict_log_proba(self, X)\n",
      " |      Predict logarithm of probability estimates.\n",
      " |      \n",
      " |      The returned estimates for all classes are ordered by the\n",
      " |      label of classes.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like of shape (n_samples, n_features)\n",
      " |          Vector to be scored, where `n_samples` is the number of samples and\n",
      " |          `n_features` is the number of features.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      T : array-like of shape (n_samples, n_classes)\n",
      " |          Returns the log-probability of the sample for each class in the\n",
      " |          model, where classes are ordered as they are in ``self.classes_``.\n",
      " |  \n",
      " |  predict_proba(self, X)\n",
      " |      Probability estimates.\n",
      " |      \n",
      " |      The returned estimates for all classes are ordered by the\n",
      " |      label of classes.\n",
      " |      \n",
      " |      For a multi_class problem, if multi_class is set to be \"multinomial\"\n",
      " |      the softmax function is used to find the predicted probability of\n",
      " |      each class.\n",
      " |      Else use a one-vs-rest approach, i.e calculate the probability\n",
      " |      of each class assuming it to be positive using the logistic function.\n",
      " |      and normalize these values across all the classes.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like of shape (n_samples, n_features)\n",
      " |          Vector to be scored, where `n_samples` is the number of samples and\n",
      " |          `n_features` is the number of features.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      T : array-like of shape (n_samples, n_classes)\n",
      " |          Returns the probability of the sample for each class in the model,\n",
      " |          where classes are ordered as they are in ``self.classes_``.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __getstate__(self)\n",
      " |  \n",
      " |  __repr__(self, N_CHAR_MAX=700)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __setstate__(self, state)\n",
      " |  \n",
      " |  get_params(self, deep=True)\n",
      " |      Get parameters for this estimator.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      deep : bool, default=True\n",
      " |          If True, will return the parameters for this estimator and\n",
      " |          contained subobjects that are estimators.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      params : mapping of string to any\n",
      " |          Parameter names mapped to their values.\n",
      " |  \n",
      " |  set_params(self, **params)\n",
      " |      Set the parameters of this estimator.\n",
      " |      \n",
      " |      The method works on simple estimators as well as on nested objects\n",
      " |      (such as pipelines). The latter have parameters of the form\n",
      " |      ``<component>__<parameter>`` so that it's possible to update each\n",
      " |      component of a nested object.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      **params : dict\n",
      " |          Estimator parameters.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self : object\n",
      " |          Estimator instance.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.linear_model._base.LinearClassifierMixin:\n",
      " |  \n",
      " |  decision_function(self, X)\n",
      " |      Predict confidence scores for samples.\n",
      " |      \n",
      " |      The confidence score for a sample is the signed distance of that\n",
      " |      sample to the hyperplane.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array_like or sparse matrix, shape (n_samples, n_features)\n",
      " |          Samples.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)\n",
      " |          Confidence scores per (sample, class) combination. In the binary\n",
      " |          case, confidence score for self.classes_[1] where >0 means this\n",
      " |          class would be predicted.\n",
      " |  \n",
      " |  predict(self, X)\n",
      " |      Predict class labels for samples in X.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array_like or sparse matrix, shape (n_samples, n_features)\n",
      " |          Samples.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      C : array, shape [n_samples]\n",
      " |          Predicted class label per sample.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.linear_model._base.SparseCoefMixin:\n",
      " |  \n",
      " |  densify(self)\n",
      " |      Convert coefficient matrix to dense array format.\n",
      " |      \n",
      " |      Converts the ``coef_`` member (back) to a numpy.ndarray. This is the\n",
      " |      default format of ``coef_`` and is required for fitting, so calling\n",
      " |      this method is only required on models that have previously been\n",
      " |      sparsified; otherwise, it is a no-op.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self\n",
      " |          Fitted estimator.\n",
      " |  \n",
      " |  sparsify(self)\n",
      " |      Convert coefficient matrix to sparse format.\n",
      " |      \n",
      " |      Converts the ``coef_`` member to a scipy.sparse matrix, which for\n",
      " |      L1-regularized models can be much more memory- and storage-efficient\n",
      " |      than the usual numpy.ndarray representation.\n",
      " |      \n",
      " |      The ``intercept_`` member is not converted.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self\n",
      " |          Fitted estimator.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      For non-sparse models, i.e. when there are not many zeros in ``coef_``,\n",
      " |      this may actually *increase* memory usage, so use this method with\n",
      " |      care. A rule of thumb is that the number of zero elements, which can\n",
      " |      be computed with ``(coef_ == 0).sum()``, must be more than 50% for this\n",
      " |      to provide significant benefits.\n",
      " |      \n",
      " |      After calling this method, further fitting with the partial_fit\n",
      " |      method (if any) will not work until you call densify.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegressionCV\n",
    "help(LogisticRegressionCV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegressionCV(Cs=array([1.e-02, 1.e-01, 1.e+00, 1.e+01, 1.e+02, 1.e+03, 1.e+04, 1.e+05,\n",
       "       1.e+06]),\n",
       "                     class_weight=None, cv=10, dual=False, fit_intercept=True,\n",
       "                     intercept_scaling=1.0, l1_ratios=None, max_iter=10000,\n",
       "                     multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                     random_state=42, refit=True, scoring=None, solver='lbfgs',\n",
       "                     tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.linear_model import LogisticRegressionCV\n",
    "Cs = np.logspace(-2, 6, 9)\n",
    "model_l1 = LogisticRegressionCV(Cs=Cs, penalty='l1', cv=10, solver='liblinear', random_state=42, max_iter=10000)\n",
    "model_l2 = LogisticRegressionCV(Cs=Cs, penalty='l2', cv=10, random_state=42, max_iter=10000)\n",
    "\n",
    "model_l1.fit(X_train, y_train['Revenue'])\n",
    "model_l2.fit(X_train, y_train['Revenue'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the model performance we will predict the outcome on the test features (X_test), and compare those outcomes to real values (y_test) for each of the models.\n",
    "\n",
    "With the 'LogisiticRegressionCV' model when the is fit the hyperparameter wthat resulted in the lowest error is automatically chosen for any subsequent predictions.\n",
    "\n",
    "We can also look at what the hyperparameters are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best hyperparameter for l1 regularization model: 1000000.0\n",
      "Best hyperparameter for l2 regularization model: 1.0\n"
     ]
    }
   ],
   "source": [
    "print(f'Best hyperparameter for l1 regularization model: {model_l1.C_[0]}')\n",
    "print(f'Best hyperparameter for l2 regularization model: {model_l2.C_[0]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred_l1 = model_l1.predict(X_test)\n",
    "y_pred_l2 = model_l2.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can again compare the accuracy against the true values. Remember that our baseline model (predicting 'no' or False for all) gave us an accuracy of 70.27972%, so we want to try and beat that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the model with l1 regularization is 89.2133%\n",
      "Accuracy of the model with l2 regularization is 89.2944%\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "accuracy_l1 = metrics.accuracy_score(y_pred=y_pred_l1, y_true=y_test)\n",
    "accuracy_l2 = metrics.accuracy_score(y_pred=y_pred_l2, y_true=y_test)\n",
    "print(f'Accuracy of the model with l1 regularization is {accuracy_l1*100:.4f}%')\n",
    "print(f'Accuracy of the model with l2 regularization is {accuracy_l2*100:.4f}%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They both performed slightly worse than the baseline model and the model with l1 regularization performed about as well as the model without regularization.\n",
    "\n",
    "It's worth noting that due to the small amount of data it may be difficult to get an accurate model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other evaluation metrics\n",
    "\n",
    "Let's test again with the other evaluation metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "l1\n",
      "Precision: 0.7300\n",
      "Recall: 0.4078\n",
      "fscore: 0.5233\n",
      "\n",
      "\n",
      "l2\n",
      "Precision: 0.7350\n",
      "Recall: 0.4106\n",
      "fscore: 0.5269\n"
     ]
    }
   ],
   "source": [
    "precision_l1, recall_l1, fscore_l1, _ = metrics.precision_recall_fscore_support(y_pred=y_pred_l1, y_true=y_test, average='binary')\n",
    "precision_l2, recall_l2, fscore_l2, _ = metrics.precision_recall_fscore_support(y_pred=y_pred_l2, y_true=y_test, average='binary')\n",
    "print(f'l1\\nPrecision: {precision_l1:.4f}\\nRecall: {recall_l1:.4f}\\nfscore: {fscore_l1:.4f}\\n\\n')\n",
    "print(f'l2\\nPrecision: {precision_l2:.4f}\\nRecall: {recall_l2:.4f}\\nfscore: {fscore_l2:.4f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall the model with l2 performs slightly better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature importances\n",
    "   \n",
    "Examining the feature importances can show us how the regularization affected the values of the coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ExitRates: -15.883224778812533\n",
      "TrafficType_15: -14.795568293882813\n",
      "TrafficType_19: -14.572417554129022\n",
      "Browser_11: -14.194513734001333\n",
      "TrafficType_18: -13.580838983781868\n",
      "TrafficType_12: -10.887010740988496\n",
      "Browser_3: -1.591759861518971\n",
      "OperatingSystems_6: -1.3061883214341672\n",
      "Browser_13: -1.1580420838412984\n",
      "TrafficType_13: -1.1370525347807676\n",
      "TrafficType_14: -1.0975546272442658\n",
      "Browser_6: -1.0010333108800196\n",
      "BounceRates: -0.9141131252024657\n",
      "Browser_7: -0.8502023615800486\n",
      "TrafficType_3: -0.811958144680347\n",
      "TrafficType_6: -0.610088799226249\n",
      "OperatingSystems_3: -0.608450446552214\n",
      "TrafficType_1: -0.6050916722027272\n",
      "OperatingSystems_1: -0.5365902656959869\n",
      "OperatingSystems_4: -0.5111451125487375\n",
      "TrafficType_4: -0.5062856279182754\n",
      "Browser_2: -0.5059966973246434\n",
      "TrafficType_2: -0.46430066907789846\n",
      "TrafficType_9: -0.4466955982654509\n",
      "Browser_4: -0.4214541023779841\n",
      "Browser_5: -0.41616336572267953\n",
      "TrafficType_5: -0.415441717179765\n",
      "TrafficType_7: -0.3955699524561608\n",
      "Browser_1: -0.3880867021005534\n",
      "Browser_8: -0.3829361496965676\n",
      "OperatingSystems_2: -0.3452133463717456\n",
      "TrafficType_10: -0.26699389912184146\n",
      "TrafficType_11: -0.20084569889820056\n",
      "SpecialDay: -0.16993604135246643\n",
      "VisitorType_Returning_Visitor: -0.1585189488537066\n",
      "Region_9: -0.1357553937048372\n",
      "Browser_10: -0.11275136307019001\n",
      "Region_4: -0.07146513811457653\n",
      "TrafficType_20: -0.027994440964808312\n",
      "TrafficType_8: -0.01080321579230938\n",
      "Administrative: -0.008848764565436021\n",
      "ProductRelated_Duration: 7.884230862995893e-05\n",
      "Administrative_Duration: 0.00010234279673558182\n",
      "Informational_Duration: 0.0003083388371428332\n",
      "ProductRelated: 0.0011034989322559698\n",
      "Informational: 0.00462053503124074\n",
      "OperatingSystems_8: 0.014922953675113934\n",
      "VisitorType_New_Visitor: 0.015142798459659391\n",
      "Region_7: 0.035576200252320694\n",
      "Region_1: 0.03654049619361953\n",
      "Region_3: 0.06097956829573871\n",
      "PageValues: 0.08295642466041496\n",
      "is_weekend: 0.12026927900778797\n",
      "Region_8: 0.15007889661364254\n",
      "Region_6: 0.1946605704463812\n",
      "Region_2: 0.2409191030186223\n",
      "OperatingSystems_7: 0.6430414471829574\n",
      "Month_Dec: 0.9259040930136528\n",
      "Month_Mar: 0.9329536574050367\n",
      "Month_May: 1.0175770611658324\n",
      "TrafficType_16: 1.219454600596873\n",
      "Month_June: 1.3396248804059154\n",
      "Month_Aug: 1.383936112795327\n",
      "Month_Oct: 1.4462669163574475\n",
      "Browser_12: 1.521383337562806\n",
      "Month_Sep: 1.527112925006471\n",
      "Month_Jul: 1.7056603829598316\n",
      "Month_Nov: 2.0227013012240787\n"
     ]
    }
   ],
   "source": [
    "coef_list = [f'{feature}: {coef}' for coef, feature in sorted(zip(model_l1.coef_[0], X_train.columns.values.tolist()))]\n",
    "for item in coef_list:\n",
    "    print(item)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "l1 regularization tends to send coefficients all the way down to zero, and is useful for reducing the total number of features in a training dataset. Here we can see some columns are very close to zero. \n",
    "\n",
    "Let's take a look at the the model coefficients for the model with l2 reglarization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TrafficType_13: -0.34009141528704256\n",
      "Month_May: -0.2996216354738292\n",
      "TrafficType_3: -0.26886567044331466\n",
      "Month_Dec: -0.2600371384272894\n",
      "Month_Mar: -0.234528066357572\n",
      "VisitorType_Returning_Visitor: -0.2092729117037135\n",
      "ExitRates: -0.20125071612863224\n",
      "OperatingSystems_3: -0.17171727353008637\n",
      "BounceRates: -0.15860752704242273\n",
      "SpecialDay: -0.15806189654702138\n",
      "TrafficType_1: -0.14304912321990237\n",
      "Browser_6: -0.10194914517637654\n",
      "Region_4: -0.09904631488404457\n",
      "Region_9: -0.09873197637696395\n",
      "Browser_3: -0.08914198358022751\n",
      "Month_June: -0.042681926326746056\n",
      "TrafficType_15: -0.04024689666293222\n",
      "Browser_7: -0.03327911496921953\n",
      "TrafficType_6: -0.031102643479272572\n",
      "Region_1: -0.027052218462517107\n",
      "OperatingSystems_6: -0.02574568309220721\n",
      "TrafficType_19: -0.02203436126130139\n",
      "Browser_13: -0.021797739222369092\n",
      "Browser_2: -0.017512124173199008\n",
      "Region_7: -0.010600896457621618\n",
      "TrafficType_14: -0.009414755781185648\n",
      "TrafficType_18: -0.008565351627323418\n",
      "Browser_11: -0.007825344595778813\n",
      "Region_3: -0.00722706571136333\n",
      "Informational: -0.0028431294868954964\n",
      "OperatingSystems_1: -0.0027540039503951706\n",
      "TrafficType_9: -0.00239566032775648\n",
      "OperatingSystems_8: -0.0016314917865704064\n",
      "TrafficType_12: -0.0010615530198468937\n",
      "OperatingSystems_4: 1.6377699949524623e-05\n",
      "ProductRelated_Duration: 6.203896052153687e-05\n",
      "Administrative_Duration: 0.0001498531976570715\n",
      "Informational_Duration: 0.0002646491833362014\n",
      "ProductRelated: 0.003308445071856749\n",
      "Browser_8: 0.0054882974452588875\n",
      "Month_Aug: 0.009417525299432315\n",
      "TrafficType_7: 0.009865390498040204\n",
      "OperatingSystems_7: 0.01068588800764906\n",
      "Administrative: 0.011818428072388093\n",
      "Browser_5: 0.011917760976019723\n",
      "TrafficType_16: 0.016810452784330476\n",
      "Browser_1: 0.022909998435860734\n",
      "Region_8: 0.023998792506279735\n",
      "Browser_4: 0.03535665081078685\n",
      "Browser_12: 0.042525537053214074\n",
      "TrafficType_5: 0.050267199536111515\n",
      "TrafficType_4: 0.06057990490809306\n",
      "Month_Oct: 0.07064830444129157\n",
      "Region_6: 0.0736506138448771\n",
      "Browser_10: 0.0810882098129662\n",
      "TrafficType_20: 0.08608941436142269\n",
      "Month_Sep: 0.0878149242855243\n",
      "PageValues: 0.08801299639787297\n",
      "TrafficType_11: 0.0991850902887261\n",
      "Region_2: 0.11817125757973408\n",
      "TrafficType_2: 0.1195593468057169\n",
      "OperatingSystems_2: 0.12562135700649213\n",
      "TrafficType_10: 0.12594481607945368\n",
      "Month_Jul: 0.13420860404449297\n",
      "is_weekend: 0.15588521706821454\n",
      "VisitorType_New_Visitor: 0.18484311217638447\n",
      "TrafficType_8: 0.22599108047373068\n",
      "Month_Nov: 0.6282700212046415\n"
     ]
    }
   ],
   "source": [
    "coef_list = [f'{feature}: {coef}' for coef, feature in sorted(zip(model_l2.coef_[0], X_train.columns.values.tolist()))]\n",
    "for item in coef_list:\n",
    "    print(item)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see that none of the coefficients go right down to zero, which is rare when applying l2 regularization, this is because the feature coefficients get penalized less when they small, and much greater when the coefficients are larger."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this activity we have seen how to create models that include regularization. While the regularization added little to model performance in this dataset, regularization is an important technique with which to prevent your models from overfitting to the training dataset.\n",
    "\n",
    "In the following lesson we will apply many of the same techniques learned in the this lesson, namely creating test and training datasets, performaing cross-validation, and using model evaluation metrics to score our models, however we we apply them to deep learning models in using the Keras library."
   ]
  }
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