# Authors: Alexandre Gramfort # Vincent Michel # Gilles Louppe # # License: BSD 3 clause """Recursive feature elimination for feature ranking""" import numpy as np from joblib import Parallel, delayed, effective_n_jobs from ..utils import safe_sqr from ..utils.metaestimators import if_delegate_has_method from ..utils.metaestimators import _safe_split from ..utils.validation import check_is_fitted from ..utils.validation import _deprecate_positional_args from ..base import BaseEstimator from ..base import MetaEstimatorMixin from ..base import clone from ..base import is_classifier from ..model_selection import check_cv from ..model_selection._validation import _score from ..metrics import check_scoring from ._base import SelectorMixin def _rfe_single_fit(rfe, estimator, X, y, train, test, scorer): """ Return the score for a fit across one fold. """ X_train, y_train = _safe_split(estimator, X, y, train) X_test, y_test = _safe_split(estimator, X, y, test, train) return rfe._fit( X_train, y_train, lambda estimator, features: _score(estimator, X_test[:, features], y_test, scorer)).scores_ class RFE(SelectorMixin, MetaEstimatorMixin, BaseEstimator): """Feature ranking with recursive feature elimination. Given an external estimator that assigns weights to features (e.g., the coefficients of a linear model), the goal of recursive feature elimination (RFE) is to select features by recursively considering smaller and smaller sets of features. First, the estimator is trained on the initial set of features and the importance of each feature is obtained either through a ``coef_`` attribute or through a ``feature_importances_`` attribute. Then, the least important features are pruned from current set of features. That procedure is recursively repeated on the pruned set until the desired number of features to select is eventually reached. Read more in the :ref:`User Guide `. Parameters ---------- estimator : object A supervised learning estimator with a ``fit`` method that provides information about feature importance either through a ``coef_`` attribute or through a ``feature_importances_`` attribute. n_features_to_select : int or None (default=None) The number of features to select. If `None`, half of the features are selected. step : int or float, optional (default=1) If greater than or equal to 1, then ``step`` corresponds to the (integer) number of features to remove at each iteration. If within (0.0, 1.0), then ``step`` corresponds to the percentage (rounded down) of features to remove at each iteration. verbose : int, (default=0) Controls verbosity of output. Attributes ---------- n_features_ : int The number of selected features. support_ : array of shape [n_features] The mask of selected features. ranking_ : array of shape [n_features] The feature ranking, such that ``ranking_[i]`` corresponds to the ranking position of the i-th feature. Selected (i.e., estimated best) features are assigned rank 1. estimator_ : object The external estimator fit on the reduced dataset. Examples -------- The following example shows how to retrieve the 5 most informative features in the Friedman #1 dataset. >>> from sklearn.datasets import make_friedman1 >>> from sklearn.feature_selection import RFE >>> from sklearn.svm import SVR >>> X, y = make_friedman1(n_samples=50, n_features=10, random_state=0) >>> estimator = SVR(kernel="linear") >>> selector = RFE(estimator, n_features_to_select=5, step=1) >>> selector = selector.fit(X, y) >>> selector.support_ array([ True, True, True, True, True, False, False, False, False, False]) >>> selector.ranking_ array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5]) Notes ----- Allows NaN/Inf in the input if the underlying estimator does as well. See also -------- RFECV : Recursive feature elimination with built-in cross-validated selection of the best number of features References ---------- .. [1] Guyon, I., Weston, J., Barnhill, S., & Vapnik, V., "Gene selection for cancer classification using support vector machines", Mach. Learn., 46(1-3), 389--422, 2002. """ @_deprecate_positional_args def __init__(self, estimator, *, n_features_to_select=None, step=1, verbose=0): self.estimator = estimator self.n_features_to_select = n_features_to_select self.step = step self.verbose = verbose @property def _estimator_type(self): return self.estimator._estimator_type @property def classes_(self): return self.estimator_.classes_ def fit(self, X, y): """Fit the RFE model and then the underlying estimator on the selected features. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) The training input samples. y : array-like of shape (n_samples,) The target values. """ return self._fit(X, y) def _fit(self, X, y, step_score=None): # Parameter step_score controls the calculation of self.scores_ # step_score is not exposed to users # and is used when implementing RFECV # self.scores_ will not be calculated when calling _fit through fit tags = self._get_tags() X, y = self._validate_data( X, y, accept_sparse="csc", ensure_min_features=2, force_all_finite=not tags.get('allow_nan', True), multi_output=True ) # Initialization n_features = X.shape[1] if self.n_features_to_select is None: n_features_to_select = n_features // 2 else: n_features_to_select = self.n_features_to_select if 0.0 < self.step < 1.0: step = int(max(1, self.step * n_features)) else: step = int(self.step) if step <= 0: raise ValueError("Step must be >0") support_ = np.ones(n_features, dtype=np.bool) ranking_ = np.ones(n_features, dtype=np.int) if step_score: self.scores_ = [] # Elimination while np.sum(support_) > n_features_to_select: # Remaining features features = np.arange(n_features)[support_] # Rank the remaining features estimator = clone(self.estimator) if self.verbose > 0: print("Fitting estimator with %d features." % np.sum(support_)) estimator.fit(X[:, features], y) # Get coefs if hasattr(estimator, 'coef_'): coefs = estimator.coef_ else: coefs = getattr(estimator, 'feature_importances_', None) if coefs is None: raise RuntimeError('The classifier does not expose ' '"coef_" or "feature_importances_" ' 'attributes') # Get ranks if coefs.ndim > 1: ranks = np.argsort(safe_sqr(coefs).sum(axis=0)) else: ranks = np.argsort(safe_sqr(coefs)) # for sparse case ranks is matrix ranks = np.ravel(ranks) # Eliminate the worse features threshold = min(step, np.sum(support_) - n_features_to_select) # Compute step score on the previous selection iteration # because 'estimator' must use features # that have not been eliminated yet if step_score: self.scores_.append(step_score(estimator, features)) support_[features[ranks][:threshold]] = False ranking_[np.logical_not(support_)] += 1 # Set final attributes features = np.arange(n_features)[support_] self.estimator_ = clone(self.estimator) self.estimator_.fit(X[:, features], y) # Compute step score when only n_features_to_select features left if step_score: self.scores_.append(step_score(self.estimator_, features)) self.n_features_ = support_.sum() self.support_ = support_ self.ranking_ = ranking_ return self @if_delegate_has_method(delegate='estimator') def predict(self, X): """Reduce X to the selected features and then predict using the underlying estimator. Parameters ---------- X : array of shape [n_samples, n_features] The input samples. Returns ------- y : array of shape [n_samples] The predicted target values. """ check_is_fitted(self) return self.estimator_.predict(self.transform(X)) @if_delegate_has_method(delegate='estimator') def score(self, X, y): """Reduce X to the selected features and then return the score of the underlying estimator. Parameters ---------- X : array of shape [n_samples, n_features] The input samples. y : array of shape [n_samples] The target values. """ check_is_fitted(self) return self.estimator_.score(self.transform(X), y) def _get_support_mask(self): check_is_fitted(self) return self.support_ @if_delegate_has_method(delegate='estimator') def decision_function(self, X): """Compute the decision function of ``X``. Parameters ---------- X : {array-like or sparse matrix} of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``. Returns ------- score : array, shape = [n_samples, n_classes] or [n_samples] The decision function of the input samples. The order of the classes corresponds to that in the attribute :term:`classes_`. Regression and binary classification produce an array of shape [n_samples]. """ check_is_fitted(self) return self.estimator_.decision_function(self.transform(X)) @if_delegate_has_method(delegate='estimator') def predict_proba(self, X): """Predict class probabilities for X. Parameters ---------- X : {array-like or sparse matrix} of shape (n_samples, n_features) The input samples. Internally, it will be converted to ``dtype=np.float32`` and if a sparse matrix is provided to a sparse ``csr_matrix``. Returns ------- p : array of shape (n_samples, n_classes) The class probabilities of the input samples. The order of the classes corresponds to that in the attribute :term:`classes_`. """ check_is_fitted(self) return self.estimator_.predict_proba(self.transform(X)) @if_delegate_has_method(delegate='estimator') def predict_log_proba(self, X): """Predict class log-probabilities for X. Parameters ---------- X : array of shape [n_samples, n_features] The input samples. Returns ------- p : array of shape (n_samples, n_classes) The class log-probabilities of the input samples. The order of the classes corresponds to that in the attribute :term:`classes_`. """ check_is_fitted(self) return self.estimator_.predict_log_proba(self.transform(X)) def _more_tags(self): estimator_tags = self.estimator._get_tags() return {'poor_score': True, 'allow_nan': estimator_tags.get('allow_nan', True), 'requires_y': True, } class RFECV(RFE): """Feature ranking with recursive feature elimination and cross-validated selection of the best number of features. See glossary entry for :term:`cross-validation estimator`. Read more in the :ref:`User Guide `. Parameters ---------- estimator : object A supervised learning estimator with a ``fit`` method that provides information about feature importance either through a ``coef_`` attribute or through a ``feature_importances_`` attribute. step : int or float, optional (default=1) If greater than or equal to 1, then ``step`` corresponds to the (integer) number of features to remove at each iteration. If within (0.0, 1.0), then ``step`` corresponds to the percentage (rounded down) of features to remove at each iteration. Note that the last iteration may remove fewer than ``step`` features in order to reach ``min_features_to_select``. min_features_to_select : int, (default=1) The minimum number of features to be selected. This number of features will always be scored, even if the difference between the original feature count and ``min_features_to_select`` isn't divisible by ``step``. .. versionadded:: 0.20 cv : int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 5-fold cross-validation, - integer, to specify the number of folds. - :term:`CV splitter`, - An iterable yielding (train, test) splits as arrays of indices. For integer/None inputs, if ``y`` is binary or multiclass, :class:`sklearn.model_selection.StratifiedKFold` is used. If the estimator is a classifier or if ``y`` is neither binary nor multiclass, :class:`sklearn.model_selection.KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. .. versionchanged:: 0.22 ``cv`` default value of None changed from 3-fold to 5-fold. scoring : string, callable or None, optional, (default=None) A string (see model evaluation documentation) or a scorer callable object / function with signature ``scorer(estimator, X, y)``. verbose : int, (default=0) Controls verbosity of output. n_jobs : int or None, optional (default=None) Number of cores to run in parallel while fitting across folds. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. .. versionadded:: 0.18 Attributes ---------- n_features_ : int The number of selected features with cross-validation. support_ : array of shape [n_features] The mask of selected features. ranking_ : array of shape [n_features] The feature ranking, such that `ranking_[i]` corresponds to the ranking position of the i-th feature. Selected (i.e., estimated best) features are assigned rank 1. grid_scores_ : array of shape [n_subsets_of_features] The cross-validation scores such that ``grid_scores_[i]`` corresponds to the CV score of the i-th subset of features. estimator_ : object The external estimator fit on the reduced dataset. Notes ----- The size of ``grid_scores_`` is equal to ``ceil((n_features - min_features_to_select) / step) + 1``, where step is the number of features removed at each iteration. Allows NaN/Inf in the input if the underlying estimator does as well. Examples -------- The following example shows how to retrieve the a-priori not known 5 informative features in the Friedman #1 dataset. >>> from sklearn.datasets import make_friedman1 >>> from sklearn.feature_selection import RFECV >>> from sklearn.svm import SVR >>> X, y = make_friedman1(n_samples=50, n_features=10, random_state=0) >>> estimator = SVR(kernel="linear") >>> selector = RFECV(estimator, step=1, cv=5) >>> selector = selector.fit(X, y) >>> selector.support_ array([ True, True, True, True, True, False, False, False, False, False]) >>> selector.ranking_ array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5]) See also -------- RFE : Recursive feature elimination References ---------- .. [1] Guyon, I., Weston, J., Barnhill, S., & Vapnik, V., "Gene selection for cancer classification using support vector machines", Mach. Learn., 46(1-3), 389--422, 2002. """ @_deprecate_positional_args def __init__(self, estimator, *, step=1, min_features_to_select=1, cv=None, scoring=None, verbose=0, n_jobs=None): self.estimator = estimator self.step = step self.cv = cv self.scoring = scoring self.verbose = verbose self.n_jobs = n_jobs self.min_features_to_select = min_features_to_select def fit(self, X, y, groups=None): """Fit the RFE model and automatically tune the number of selected features. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Training vector, where `n_samples` is the number of samples and `n_features` is the total number of features. y : array-like of shape (n_samples,) Target values (integers for classification, real numbers for regression). groups : array-like of shape (n_samples,) or None Group labels for the samples used while splitting the dataset into train/test set. Only used in conjunction with a "Group" :term:`cv` instance (e.g., :class:`~sklearn.model_selection.GroupKFold`). .. versionadded:: 0.20 """ tags = self._get_tags() X, y = self._validate_data( X, y, accept_sparse="csr", ensure_min_features=2, force_all_finite=not tags.get('allow_nan', True), multi_output=True ) # Initialization cv = check_cv(self.cv, y, classifier=is_classifier(self.estimator)) scorer = check_scoring(self.estimator, scoring=self.scoring) n_features = X.shape[1] if 0.0 < self.step < 1.0: step = int(max(1, self.step * n_features)) else: step = int(self.step) if step <= 0: raise ValueError("Step must be >0") # Build an RFE object, which will evaluate and score each possible # feature count, down to self.min_features_to_select rfe = RFE(estimator=self.estimator, n_features_to_select=self.min_features_to_select, step=self.step, verbose=self.verbose) # Determine the number of subsets of features by fitting across # the train folds and choosing the "features_to_select" parameter # that gives the least averaged error across all folds. # Note that joblib raises a non-picklable error for bound methods # even if n_jobs is set to 1 with the default multiprocessing # backend. # This branching is done so that to # make sure that user code that sets n_jobs to 1 # and provides bound methods as scorers is not broken with the # addition of n_jobs parameter in version 0.18. if effective_n_jobs(self.n_jobs) == 1: parallel, func = list, _rfe_single_fit else: parallel = Parallel(n_jobs=self.n_jobs) func = delayed(_rfe_single_fit) scores = parallel( func(rfe, self.estimator, X, y, train, test, scorer) for train, test in cv.split(X, y, groups)) scores = np.sum(scores, axis=0) scores_rev = scores[::-1] argmax_idx = len(scores) - np.argmax(scores_rev) - 1 n_features_to_select = max( n_features - (argmax_idx * step), self.min_features_to_select) # Re-execute an elimination with best_k over the whole set rfe = RFE(estimator=self.estimator, n_features_to_select=n_features_to_select, step=self.step, verbose=self.verbose) rfe.fit(X, y) # Set final attributes self.support_ = rfe.support_ self.n_features_ = rfe.n_features_ self.ranking_ = rfe.ranking_ self.estimator_ = clone(self.estimator) self.estimator_.fit(self.transform(X), y) # Fixing a normalization error, n is equal to get_n_splits(X, y) - 1 # here, the scores are normalized by get_n_splits(X, y) self.grid_scores_ = scores[::-1] / cv.get_n_splits(X, y, groups) return self