# Authors: Alexandre Gramfort # Vincent Michel # Gilles Louppe # # License: BSD 3 clause """Recursive feature elimination for feature ranking""" import warnings from numbers import Integral import numpy as np from joblib import effective_n_jobs from ..base import BaseEstimator, MetaEstimatorMixin, _fit_context, clone, is_classifier from ..metrics import check_scoring from ..model_selection import check_cv from ..model_selection._validation import _score from ..utils._param_validation import HasMethods, Interval, RealNotInt from ..utils.metadata_routing import ( _raise_for_unsupported_routing, _RoutingNotSupportedMixin, ) from ..utils.metaestimators import _safe_split, available_if from ..utils.parallel import Parallel, delayed from ..utils.validation import check_is_fitted from ._base import SelectorMixin, _get_feature_importances def _rfe_single_fit(rfe, estimator, X, y, train, test, scorer): """ Return the score and n_features per step 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) rfe._fit( X_train, y_train, lambda estimator, features: _score( # TODO(SLEP6): pass score_params here estimator, X_test[:, features], y_test, scorer, score_params=None, ), ) return rfe.step_scores_, rfe.step_n_features_ def _estimator_has(attr): """Check if we can delegate a method to the underlying estimator. First, we check the fitted `estimator_` if available, otherwise we check the unfitted `estimator`. We raise the original `AttributeError` if `attr` does not exist. This function is used together with `available_if`. """ def check(self): if hasattr(self, "estimator_"): getattr(self.estimator_, attr) else: getattr(self.estimator, attr) return True return check class RFE(_RoutingNotSupportedMixin, 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 any specific attribute or callable. 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 : ``Estimator`` instance A supervised learning estimator with a ``fit`` method that provides information about feature importance (e.g. `coef_`, `feature_importances_`). n_features_to_select : int or float, default=None The number of features to select. If `None`, half of the features are selected. If integer, the parameter is the absolute number of features to select. If float between 0 and 1, it is the fraction of features to select. .. versionchanged:: 0.24 Added float values for fractions. step : int or float, 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. importance_getter : str or callable, default='auto' If 'auto', uses the feature importance either through a `coef_` or `feature_importances_` attributes of estimator. Also accepts a string that specifies an attribute name/path for extracting feature importance (implemented with `attrgetter`). For example, give `regressor_.coef_` in case of :class:`~sklearn.compose.TransformedTargetRegressor` or `named_steps.clf.feature_importances_` in case of class:`~sklearn.pipeline.Pipeline` with its last step named `clf`. If `callable`, overrides the default feature importance getter. The callable is passed with the fitted estimator and it should return importance for each feature. .. versionadded:: 0.24 Attributes ---------- classes_ : ndarray of shape (n_classes,) The classes labels. Only available when `estimator` is a classifier. estimator_ : ``Estimator`` instance The fitted estimator used to select features. n_features_ : int The number of selected features. n_features_in_ : int Number of features seen during :term:`fit`. Only defined if the underlying estimator exposes such an attribute when fit. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 ranking_ : ndarray 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. support_ : ndarray of shape (n_features,) The mask of selected features. See Also -------- RFECV : Recursive feature elimination with built-in cross-validated selection of the best number of features. SelectFromModel : Feature selection based on thresholds of importance weights. SequentialFeatureSelector : Sequential cross-validation based feature selection. Does not rely on importance weights. Notes ----- Allows NaN/Inf in the input if the underlying estimator does as well. 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. 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]) """ _parameter_constraints: dict = { "estimator": [HasMethods(["fit"])], "n_features_to_select": [ None, Interval(RealNotInt, 0, 1, closed="right"), Interval(Integral, 0, None, closed="neither"), ], "step": [ Interval(Integral, 0, None, closed="neither"), Interval(RealNotInt, 0, 1, closed="neither"), ], "verbose": ["verbose"], "importance_getter": [str, callable], } def __init__( self, estimator, *, n_features_to_select=None, step=1, verbose=0, importance_getter="auto", ): self.estimator = estimator self.n_features_to_select = n_features_to_select self.step = step self.importance_getter = importance_getter self.verbose = verbose @property def _estimator_type(self): return self.estimator._estimator_type @property def classes_(self): """Classes labels available when `estimator` is a classifier. Returns ------- ndarray of shape (n_classes,) """ return self.estimator_.classes_ @_fit_context( # RFE.estimator is not validated yet prefer_skip_nested_validation=False ) def fit(self, X, y, **fit_params): """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. **fit_params : dict Additional parameters passed to the `fit` method of the underlying estimator. Returns ------- self : object Fitted estimator. """ _raise_for_unsupported_routing(self, "fit", **fit_params) return self._fit(X, y, **fit_params) def _fit(self, X, y, step_score=None, **fit_params): # Parameter step_score controls the calculation of self.step_scores_ # step_score is not exposed to users and is used when implementing RFECV # self.step_scores_ will not be calculated when calling _fit through fit X, y = self._validate_data( X, y, accept_sparse="csc", ensure_min_features=2, force_all_finite=False, multi_output=True, ) # Initialization n_features = X.shape[1] if self.n_features_to_select is None: n_features_to_select = n_features // 2 elif isinstance(self.n_features_to_select, Integral): # int n_features_to_select = self.n_features_to_select if n_features_to_select > n_features: warnings.warn( ( f"Found {n_features_to_select=} > {n_features=}. There will be" " no feature selection and all features will be kept." ), UserWarning, ) else: # float n_features_to_select = int(n_features * 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) support_ = np.ones(n_features, dtype=bool) ranking_ = np.ones(n_features, dtype=int) if step_score: self.step_n_features_ = [] self.step_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, **fit_params) # Get importance and rank them importances = _get_feature_importances( estimator, self.importance_getter, transform_func="square", ) ranks = np.argsort(importances) # 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.step_n_features_.append(len(features)) self.step_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, **fit_params) # Compute step score when only n_features_to_select features left if step_score: self.step_n_features_.append(len(features)) self.step_scores_.append(step_score(self.estimator_, features)) self.n_features_ = support_.sum() self.support_ = support_ self.ranking_ = ranking_ return self @available_if(_estimator_has("predict")) def predict(self, X): """Reduce X to the selected features and predict using the 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)) @available_if(_estimator_has("score")) def score(self, X, y, **fit_params): """Reduce X to the selected features and return the score of the estimator. Parameters ---------- X : array of shape [n_samples, n_features] The input samples. y : array of shape [n_samples] The target values. **fit_params : dict Parameters to pass to the `score` method of the underlying estimator. .. versionadded:: 1.0 Returns ------- score : float Score of the underlying base estimator computed with the selected features returned by `rfe.transform(X)` and `y`. """ check_is_fitted(self) return self.estimator_.score(self.transform(X), y, **fit_params) def _get_support_mask(self): check_is_fitted(self) return self.support_ @available_if(_estimator_has("decision_function")) 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)) @available_if(_estimator_has("predict_proba")) 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)) @available_if(_estimator_has("predict_log_proba")) 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): tags = { "poor_score": True, "requires_y": True, "allow_nan": True, } # Adjust allow_nan if estimator explicitly defines `allow_nan`. if hasattr(self.estimator, "_get_tags"): tags["allow_nan"] = self.estimator._get_tags()["allow_nan"] return tags class RFECV(RFE): """Recursive feature elimination with cross-validation to select features. The number of features selected is tuned automatically by fitting an :class:`RFE` selector on the different cross-validation splits (provided by the `cv` parameter). The performance of the :class:`RFE` selector are evaluated using `scorer` for different number of selected features and aggregated together. Finally, the scores are averaged across folds and the number of features selected is set to the number of features that maximize the cross-validation score. See glossary entry for :term:`cross-validation estimator`. Read more in the :ref:`User Guide `. Parameters ---------- estimator : ``Estimator`` instance 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, 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, default=None 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 : str, callable or None, 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, 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 importance_getter : str or callable, default='auto' If 'auto', uses the feature importance either through a `coef_` or `feature_importances_` attributes of estimator. Also accepts a string that specifies an attribute name/path for extracting feature importance. For example, give `regressor_.coef_` in case of :class:`~sklearn.compose.TransformedTargetRegressor` or `named_steps.clf.feature_importances_` in case of :class:`~sklearn.pipeline.Pipeline` with its last step named `clf`. If `callable`, overrides the default feature importance getter. The callable is passed with the fitted estimator and it should return importance for each feature. .. versionadded:: 0.24 Attributes ---------- classes_ : ndarray of shape (n_classes,) The classes labels. Only available when `estimator` is a classifier. estimator_ : ``Estimator`` instance The fitted estimator used to select features. cv_results_ : dict of ndarrays All arrays (values of the dictionary) are sorted in ascending order by the number of features used (i.e., the first element of the array represents the models that used the least number of features, while the last element represents the models that used all available features). This dictionary contains the following keys: split(k)_test_score : ndarray of shape (n_subsets_of_features,) The cross-validation scores across (k)th fold. mean_test_score : ndarray of shape (n_subsets_of_features,) Mean of scores over the folds. std_test_score : ndarray of shape (n_subsets_of_features,) Standard deviation of scores over the folds. n_features : ndarray of shape (n_subsets_of_features,) Number of features used at each step. .. versionadded:: 1.0 n_features_ : int The number of selected features with cross-validation. n_features_in_ : int Number of features seen during :term:`fit`. Only defined if the underlying estimator exposes such an attribute when fit. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 ranking_ : narray 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. support_ : ndarray of shape (n_features,) The mask of selected features. See Also -------- RFE : Recursive feature elimination. Notes ----- The size of all values in ``cv_results_`` 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. 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. 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]) """ _parameter_constraints: dict = { **RFE._parameter_constraints, "min_features_to_select": [Interval(Integral, 0, None, closed="neither")], "cv": ["cv_object"], "scoring": [None, str, callable], "n_jobs": [None, Integral], } _parameter_constraints.pop("n_features_to_select") def __init__( self, estimator, *, step=1, min_features_to_select=1, cv=None, scoring=None, verbose=0, n_jobs=None, importance_getter="auto", ): self.estimator = estimator self.step = step self.importance_getter = importance_getter self.cv = cv self.scoring = scoring self.verbose = verbose self.n_jobs = n_jobs self.min_features_to_select = min_features_to_select @_fit_context( # RFECV.estimator is not validated yet prefer_skip_nested_validation=False ) 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, default=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 Returns ------- self : object Fitted estimator. """ _raise_for_unsupported_routing(self, "fit", groups=groups) X, y = self._validate_data( X, y, accept_sparse="csr", ensure_min_features=2, force_all_finite=False, multi_output=True, ) # Initialization cv = check_cv(self.cv, y, classifier=is_classifier(self.estimator)) scorer = check_scoring(self.estimator, scoring=self.scoring) # Build an RFE object, which will evaluate and score each possible # feature count, down to self.min_features_to_select n_features = X.shape[1] if self.min_features_to_select > n_features: warnings.warn( ( f"Found min_features_to_select={self.min_features_to_select} > " f"{n_features=}. There will be no feature selection and all " "features will be kept." ), UserWarning, ) rfe = RFE( estimator=self.estimator, n_features_to_select=min(self.min_features_to_select, n_features), importance_getter=self.importance_getter, 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_features = parallel( func(rfe, self.estimator, X, y, train, test, scorer) for train, test in cv.split(X, y, groups) ) scores, step_n_features = zip(*scores_features) step_n_features_rev = np.array(step_n_features[0])[::-1] scores = np.array(scores) # Reverse order such that lowest number of features is selected in case of tie. scores_sum_rev = np.sum(scores, axis=0)[::-1] n_features_to_select = step_n_features_rev[np.argmax(scores_sum_rev)] # 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, importance_getter=self.importance_getter, 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) # reverse to stay consistent with before scores_rev = scores[:, ::-1] self.cv_results_ = { "mean_test_score": np.mean(scores_rev, axis=0), "std_test_score": np.std(scores_rev, axis=0), **{f"split{i}_test_score": scores_rev[i] for i in range(scores.shape[0])}, "n_features": step_n_features_rev, } return self