from numbers import Integral, Real import numpy as np from ._base import _fit_liblinear, BaseSVC, BaseLibSVM from ..base import BaseEstimator, RegressorMixin, OutlierMixin from ..linear_model._base import LinearClassifierMixin, SparseCoefMixin, LinearModel from ..utils import deprecated from ..utils.validation import _num_samples from ..utils.multiclass import check_classification_targets from ..utils._param_validation import Interval, StrOptions class LinearSVC(LinearClassifierMixin, SparseCoefMixin, BaseEstimator): """Linear Support Vector Classification. Similar to SVC with parameter kernel='linear', but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples. This class supports both dense and sparse input and the multiclass support is handled according to a one-vs-the-rest scheme. Read more in the :ref:`User Guide `. Parameters ---------- penalty : {'l1', 'l2'}, default='l2' Specifies the norm used in the penalization. The 'l2' penalty is the standard used in SVC. The 'l1' leads to ``coef_`` vectors that are sparse. loss : {'hinge', 'squared_hinge'}, default='squared_hinge' Specifies the loss function. 'hinge' is the standard SVM loss (used e.g. by the SVC class) while 'squared_hinge' is the square of the hinge loss. The combination of ``penalty='l1'`` and ``loss='hinge'`` is not supported. dual : bool, default=True Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features. tol : float, default=1e-4 Tolerance for stopping criteria. C : float, default=1.0 Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. multi_class : {'ovr', 'crammer_singer'}, default='ovr' Determines the multi-class strategy if `y` contains more than two classes. ``"ovr"`` trains n_classes one-vs-rest classifiers, while ``"crammer_singer"`` optimizes a joint objective over all classes. While `crammer_singer` is interesting from a theoretical perspective as it is consistent, it is seldom used in practice as it rarely leads to better accuracy and is more expensive to compute. If ``"crammer_singer"`` is chosen, the options loss, penalty and dual will be ignored. fit_intercept : bool, default=True Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered). intercept_scaling : float, default=1.0 When self.fit_intercept is True, instance vector x becomes ``[x, self.intercept_scaling]``, i.e. a "synthetic" feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. class_weight : dict or 'balanced', default=None Set the parameter C of class i to ``class_weight[i]*C`` for SVC. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. verbose : int, default=0 Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generation for shuffling the data for the dual coordinate descent (if ``dual=True``). When ``dual=False`` the underlying implementation of :class:`LinearSVC` is not random and ``random_state`` has no effect on the results. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. max_iter : int, default=1000 The maximum number of iterations to be run. Attributes ---------- coef_ : ndarray of shape (1, n_features) if n_classes == 2 \ else (n_classes, n_features) Weights assigned to the features (coefficients in the primal problem). ``coef_`` is a readonly property derived from ``raw_coef_`` that follows the internal memory layout of liblinear. intercept_ : ndarray of shape (1,) if n_classes == 2 else (n_classes,) Constants in decision function. classes_ : ndarray of shape (n_classes,) The unique classes labels. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : int Maximum number of iterations run across all classes. See Also -------- SVC : Implementation of Support Vector Machine classifier using libsvm: the kernel can be non-linear but its SMO algorithm does not scale to large number of samples as LinearSVC does. Furthermore SVC multi-class mode is implemented using one vs one scheme while LinearSVC uses one vs the rest. It is possible to implement one vs the rest with SVC by using the :class:`~sklearn.multiclass.OneVsRestClassifier` wrapper. Finally SVC can fit dense data without memory copy if the input is C-contiguous. Sparse data will still incur memory copy though. sklearn.linear_model.SGDClassifier : SGDClassifier can optimize the same cost function as LinearSVC by adjusting the penalty and loss parameters. In addition it requires less memory, allows incremental (online) learning, and implements various loss functions and regularization regimes. Notes ----- The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon to have slightly different results for the same input data. If that happens, try with a smaller ``tol`` parameter. The underlying implementation, liblinear, uses a sparse internal representation for the data that will incur a memory copy. Predict output may not match that of standalone liblinear in certain cases. See :ref:`differences from liblinear ` in the narrative documentation. References ---------- `LIBLINEAR: A Library for Large Linear Classification `__ Examples -------- >>> from sklearn.svm import LinearSVC >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> from sklearn.datasets import make_classification >>> X, y = make_classification(n_features=4, random_state=0) >>> clf = make_pipeline(StandardScaler(), ... LinearSVC(random_state=0, tol=1e-5)) >>> clf.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('linearsvc', LinearSVC(random_state=0, tol=1e-05))]) >>> print(clf.named_steps['linearsvc'].coef_) [[0.141... 0.526... 0.679... 0.493...]] >>> print(clf.named_steps['linearsvc'].intercept_) [0.1693...] >>> print(clf.predict([[0, 0, 0, 0]])) [1] """ _parameter_constraints: dict = { "penalty": [StrOptions({"l1", "l2"})], "loss": [StrOptions({"hinge", "squared_hinge"})], "dual": ["boolean"], "tol": [Interval(Real, 0.0, None, closed="neither")], "C": [Interval(Real, 0.0, None, closed="neither")], "multi_class": [StrOptions({"ovr", "crammer_singer"})], "fit_intercept": ["boolean"], "intercept_scaling": [Interval(Real, 0, None, closed="neither")], "class_weight": [None, dict, StrOptions({"balanced"})], "verbose": ["verbose"], "random_state": ["random_state"], "max_iter": [Interval(Integral, 0, None, closed="left")], } def __init__( self, penalty="l2", loss="squared_hinge", *, dual=True, tol=1e-4, C=1.0, multi_class="ovr", fit_intercept=True, intercept_scaling=1, class_weight=None, verbose=0, random_state=None, max_iter=1000, ): self.dual = dual self.tol = tol self.C = C self.multi_class = multi_class self.fit_intercept = fit_intercept self.intercept_scaling = intercept_scaling self.class_weight = class_weight self.verbose = verbose self.random_state = random_state self.max_iter = max_iter self.penalty = penalty self.loss = loss def fit(self, X, y, sample_weight=None): """Fit the model according to the given training data. 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 number of features. y : array-like of shape (n_samples,) Target vector relative to X. sample_weight : array-like of shape (n_samples,), default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. .. versionadded:: 0.18 Returns ------- self : object An instance of the estimator. """ self._validate_params() X, y = self._validate_data( X, y, accept_sparse="csr", dtype=np.float64, order="C", accept_large_sparse=False, ) check_classification_targets(y) self.classes_ = np.unique(y) self.coef_, self.intercept_, n_iter_ = _fit_liblinear( X, y, self.C, self.fit_intercept, self.intercept_scaling, self.class_weight, self.penalty, self.dual, self.verbose, self.max_iter, self.tol, self.random_state, self.multi_class, self.loss, sample_weight=sample_weight, ) # Backward compatibility: _fit_liblinear is used both by LinearSVC/R # and LogisticRegression but LogisticRegression sets a structured # `n_iter_` attribute with information about the underlying OvR fits # while LinearSVC/R only reports the maximum value. self.n_iter_ = n_iter_.max().item() if self.multi_class == "crammer_singer" and len(self.classes_) == 2: self.coef_ = (self.coef_[1] - self.coef_[0]).reshape(1, -1) if self.fit_intercept: intercept = self.intercept_[1] - self.intercept_[0] self.intercept_ = np.array([intercept]) return self def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } class LinearSVR(RegressorMixin, LinearModel): """Linear Support Vector Regression. Similar to SVR with parameter kernel='linear', but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples. This class supports both dense and sparse input. Read more in the :ref:`User Guide `. .. versionadded:: 0.16 Parameters ---------- epsilon : float, default=0.0 Epsilon parameter in the epsilon-insensitive loss function. Note that the value of this parameter depends on the scale of the target variable y. If unsure, set ``epsilon=0``. tol : float, default=1e-4 Tolerance for stopping criteria. C : float, default=1.0 Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. loss : {'epsilon_insensitive', 'squared_epsilon_insensitive'}, \ default='epsilon_insensitive' Specifies the loss function. The epsilon-insensitive loss (standard SVR) is the L1 loss, while the squared epsilon-insensitive loss ('squared_epsilon_insensitive') is the L2 loss. fit_intercept : bool, default=True Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered). intercept_scaling : float, default=1.0 When self.fit_intercept is True, instance vector x becomes [x, self.intercept_scaling], i.e. a "synthetic" feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased. dual : bool, default=True Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features. verbose : int, default=0 Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context. random_state : int, RandomState instance or None, default=None Controls the pseudo random number generation for shuffling the data. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. max_iter : int, default=1000 The maximum number of iterations to be run. Attributes ---------- coef_ : ndarray of shape (n_features) if n_classes == 2 \ else (n_classes, n_features) Weights assigned to the features (coefficients in the primal problem). `coef_` is a readonly property derived from `raw_coef_` that follows the internal memory layout of liblinear. intercept_ : ndarray of shape (1) if n_classes == 2 else (n_classes) Constants in decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : int Maximum number of iterations run across all classes. See Also -------- LinearSVC : Implementation of Support Vector Machine classifier using the same library as this class (liblinear). SVR : Implementation of Support Vector Machine regression using libsvm: the kernel can be non-linear but its SMO algorithm does not scale to large number of samples as LinearSVC does. sklearn.linear_model.SGDRegressor : SGDRegressor can optimize the same cost function as LinearSVR by adjusting the penalty and loss parameters. In addition it requires less memory, allows incremental (online) learning, and implements various loss functions and regularization regimes. Examples -------- >>> from sklearn.svm import LinearSVR >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> from sklearn.datasets import make_regression >>> X, y = make_regression(n_features=4, random_state=0) >>> regr = make_pipeline(StandardScaler(), ... LinearSVR(random_state=0, tol=1e-5)) >>> regr.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('linearsvr', LinearSVR(random_state=0, tol=1e-05))]) >>> print(regr.named_steps['linearsvr'].coef_) [18.582... 27.023... 44.357... 64.522...] >>> print(regr.named_steps['linearsvr'].intercept_) [-4...] >>> print(regr.predict([[0, 0, 0, 0]])) [-2.384...] """ _parameter_constraints: dict = { "epsilon": [Real], "tol": [Interval(Real, 0.0, None, closed="neither")], "C": [Interval(Real, 0.0, None, closed="neither")], "loss": [StrOptions({"epsilon_insensitive", "squared_epsilon_insensitive"})], "fit_intercept": ["boolean"], "intercept_scaling": [Interval(Real, 0, None, closed="neither")], "dual": ["boolean"], "verbose": ["verbose"], "random_state": ["random_state"], "max_iter": [Interval(Integral, 0, None, closed="left")], } def __init__( self, *, epsilon=0.0, tol=1e-4, C=1.0, loss="epsilon_insensitive", fit_intercept=True, intercept_scaling=1.0, dual=True, verbose=0, random_state=None, max_iter=1000, ): self.tol = tol self.C = C self.epsilon = epsilon self.fit_intercept = fit_intercept self.intercept_scaling = intercept_scaling self.verbose = verbose self.random_state = random_state self.max_iter = max_iter self.dual = dual self.loss = loss def fit(self, X, y, sample_weight=None): """Fit the model according to the given training data. 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 number of features. y : array-like of shape (n_samples,) Target vector relative to X. sample_weight : array-like of shape (n_samples,), default=None Array of weights that are assigned to individual samples. If not provided, then each sample is given unit weight. .. versionadded:: 0.18 Returns ------- self : object An instance of the estimator. """ self._validate_params() X, y = self._validate_data( X, y, accept_sparse="csr", dtype=np.float64, order="C", accept_large_sparse=False, ) penalty = "l2" # SVR only accepts l2 penalty self.coef_, self.intercept_, n_iter_ = _fit_liblinear( X, y, self.C, self.fit_intercept, self.intercept_scaling, None, penalty, self.dual, self.verbose, self.max_iter, self.tol, self.random_state, loss=self.loss, epsilon=self.epsilon, sample_weight=sample_weight, ) self.coef_ = self.coef_.ravel() # Backward compatibility: _fit_liblinear is used both by LinearSVC/R # and LogisticRegression but LogisticRegression sets a structured # `n_iter_` attribute with information about the underlying OvR fits # while LinearSVC/R only reports the maximum value. self.n_iter_ = n_iter_.max().item() return self def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } class SVC(BaseSVC): """C-Support Vector Classification. The implementation is based on libsvm. The fit time scales at least quadratically with the number of samples and may be impractical beyond tens of thousands of samples. For large datasets consider using :class:`~sklearn.svm.LinearSVC` or :class:`~sklearn.linear_model.SGDClassifier` instead, possibly after a :class:`~sklearn.kernel_approximation.Nystroem` transformer or other :ref:`kernel_approximation`. The multiclass support is handled according to a one-vs-one scheme. For details on the precise mathematical formulation of the provided kernel functions and how `gamma`, `coef0` and `degree` affect each other, see the corresponding section in the narrative documentation: :ref:`svm_kernels`. Read more in the :ref:`User Guide `. Parameters ---------- C : float, default=1.0 Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. The penalty is a squared l2 penalty. kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'} or callable, \ default='rbf' Specifies the kernel type to be used in the algorithm. If none is given, 'rbf' will be used. If a callable is given it is used to pre-compute the kernel matrix from data matrices; that matrix should be an array of shape ``(n_samples, n_samples)``. degree : int, default=3 Degree of the polynomial kernel function ('poly'). Must be non-negative. Ignored by all other kernels. gamma : {'scale', 'auto'} or float, default='scale' Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. - if ``gamma='scale'`` (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma, - if 'auto', uses 1 / n_features - if float, must be non-negative. .. versionchanged:: 0.22 The default value of ``gamma`` changed from 'auto' to 'scale'. coef0 : float, default=0.0 Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. shrinking : bool, default=True Whether to use the shrinking heuristic. See the :ref:`User Guide `. probability : bool, default=False Whether to enable probability estimates. This must be enabled prior to calling `fit`, will slow down that method as it internally uses 5-fold cross-validation, and `predict_proba` may be inconsistent with `predict`. Read more in the :ref:`User Guide `. tol : float, default=1e-3 Tolerance for stopping criterion. cache_size : float, default=200 Specify the size of the kernel cache (in MB). class_weight : dict or 'balanced', default=None Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as ``n_samples / (n_classes * np.bincount(y))``. verbose : bool, default=False Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context. max_iter : int, default=-1 Hard limit on iterations within solver, or -1 for no limit. decision_function_shape : {'ovo', 'ovr'}, default='ovr' Whether to return a one-vs-rest ('ovr') decision function of shape (n_samples, n_classes) as all other classifiers, or the original one-vs-one ('ovo') decision function of libsvm which has shape (n_samples, n_classes * (n_classes - 1) / 2). However, note that internally, one-vs-one ('ovo') is always used as a multi-class strategy to train models; an ovr matrix is only constructed from the ovo matrix. The parameter is ignored for binary classification. .. versionchanged:: 0.19 decision_function_shape is 'ovr' by default. .. versionadded:: 0.17 *decision_function_shape='ovr'* is recommended. .. versionchanged:: 0.17 Deprecated *decision_function_shape='ovo' and None*. break_ties : bool, default=False If true, ``decision_function_shape='ovr'``, and number of classes > 2, :term:`predict` will break ties according to the confidence values of :term:`decision_function`; otherwise the first class among the tied classes is returned. Please note that breaking ties comes at a relatively high computational cost compared to a simple predict. .. versionadded:: 0.22 random_state : int, RandomState instance or None, default=None Controls the pseudo random number generation for shuffling the data for probability estimates. Ignored when `probability` is False. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Attributes ---------- class_weight_ : ndarray of shape (n_classes,) Multipliers of parameter C for each class. Computed based on the ``class_weight`` parameter. classes_ : ndarray of shape (n_classes,) The classes labels. coef_ : ndarray of shape (n_classes * (n_classes - 1) / 2, n_features) Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. `coef_` is a readonly property derived from `dual_coef_` and `support_vectors_`. dual_coef_ : ndarray of shape (n_classes -1, n_SV) Dual coefficients of the support vector in the decision function (see :ref:`sgd_mathematical_formulation`), multiplied by their targets. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial. See the :ref:`multi-class section of the User Guide ` for details. fit_status_ : int 0 if correctly fitted, 1 otherwise (will raise warning) intercept_ : ndarray of shape (n_classes * (n_classes - 1) / 2,) Constants in decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : ndarray of shape (n_classes * (n_classes - 1) // 2,) Number of iterations run by the optimization routine to fit the model. The shape of this attribute depends on the number of models optimized which in turn depends on the number of classes. .. versionadded:: 1.1 support_ : ndarray of shape (n_SV) Indices of support vectors. support_vectors_ : ndarray of shape (n_SV, n_features) Support vectors. n_support_ : ndarray of shape (n_classes,), dtype=int32 Number of support vectors for each class. probA_ : ndarray of shape (n_classes * (n_classes - 1) / 2) probB_ : ndarray of shape (n_classes * (n_classes - 1) / 2) If `probability=True`, it corresponds to the parameters learned in Platt scaling to produce probability estimates from decision values. If `probability=False`, it's an empty array. Platt scaling uses the logistic function ``1 / (1 + exp(decision_value * probA_ + probB_))`` where ``probA_`` and ``probB_`` are learned from the dataset [2]_. For more information on the multiclass case and training procedure see section 8 of [1]_. shape_fit_ : tuple of int of shape (n_dimensions_of_X,) Array dimensions of training vector ``X``. See Also -------- SVR : Support Vector Machine for Regression implemented using libsvm. LinearSVC : Scalable Linear Support Vector Machine for classification implemented using liblinear. Check the See Also section of LinearSVC for more comparison element. References ---------- .. [1] `LIBSVM: A Library for Support Vector Machines `_ .. [2] `Platt, John (1999). "Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods" `_ Examples -------- >>> import numpy as np >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) >>> y = np.array([1, 1, 2, 2]) >>> from sklearn.svm import SVC >>> clf = make_pipeline(StandardScaler(), SVC(gamma='auto')) >>> clf.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('svc', SVC(gamma='auto'))]) >>> print(clf.predict([[-0.8, -1]])) [1] """ _impl = "c_svc" def __init__( self, *, C=1.0, kernel="rbf", degree=3, gamma="scale", coef0=0.0, shrinking=True, probability=False, tol=1e-3, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape="ovr", break_ties=False, random_state=None, ): super().__init__( kernel=kernel, degree=degree, gamma=gamma, coef0=coef0, tol=tol, C=C, nu=0.0, shrinking=shrinking, probability=probability, cache_size=cache_size, class_weight=class_weight, verbose=verbose, max_iter=max_iter, decision_function_shape=decision_function_shape, break_ties=break_ties, random_state=random_state, ) def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } class NuSVC(BaseSVC): """Nu-Support Vector Classification. Similar to SVC but uses a parameter to control the number of support vectors. The implementation is based on libsvm. Read more in the :ref:`User Guide `. Parameters ---------- nu : float, default=0.5 An upper bound on the fraction of margin errors (see :ref:`User Guide `) and a lower bound of the fraction of support vectors. Should be in the interval (0, 1]. kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'} or callable, \ default='rbf' Specifies the kernel type to be used in the algorithm. If none is given, 'rbf' will be used. If a callable is given it is used to precompute the kernel matrix. degree : int, default=3 Degree of the polynomial kernel function ('poly'). Must be non-negative. Ignored by all other kernels. gamma : {'scale', 'auto'} or float, default='scale' Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. - if ``gamma='scale'`` (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma, - if 'auto', uses 1 / n_features - if float, must be non-negative. .. versionchanged:: 0.22 The default value of ``gamma`` changed from 'auto' to 'scale'. coef0 : float, default=0.0 Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. shrinking : bool, default=True Whether to use the shrinking heuristic. See the :ref:`User Guide `. probability : bool, default=False Whether to enable probability estimates. This must be enabled prior to calling `fit`, will slow down that method as it internally uses 5-fold cross-validation, and `predict_proba` may be inconsistent with `predict`. Read more in the :ref:`User Guide `. tol : float, default=1e-3 Tolerance for stopping criterion. cache_size : float, default=200 Specify the size of the kernel cache (in MB). class_weight : {dict, 'balanced'}, default=None Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The "balanced" mode uses the values of y to automatically adjust weights inversely proportional to class frequencies as ``n_samples / (n_classes * np.bincount(y))``. verbose : bool, default=False Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context. max_iter : int, default=-1 Hard limit on iterations within solver, or -1 for no limit. decision_function_shape : {'ovo', 'ovr'}, default='ovr' Whether to return a one-vs-rest ('ovr') decision function of shape (n_samples, n_classes) as all other classifiers, or the original one-vs-one ('ovo') decision function of libsvm which has shape (n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one ('ovo') is always used as multi-class strategy. The parameter is ignored for binary classification. .. versionchanged:: 0.19 decision_function_shape is 'ovr' by default. .. versionadded:: 0.17 *decision_function_shape='ovr'* is recommended. .. versionchanged:: 0.17 Deprecated *decision_function_shape='ovo' and None*. break_ties : bool, default=False If true, ``decision_function_shape='ovr'``, and number of classes > 2, :term:`predict` will break ties according to the confidence values of :term:`decision_function`; otherwise the first class among the tied classes is returned. Please note that breaking ties comes at a relatively high computational cost compared to a simple predict. .. versionadded:: 0.22 random_state : int, RandomState instance or None, default=None Controls the pseudo random number generation for shuffling the data for probability estimates. Ignored when `probability` is False. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. Attributes ---------- class_weight_ : ndarray of shape (n_classes,) Multipliers of parameter C of each class. Computed based on the ``class_weight`` parameter. classes_ : ndarray of shape (n_classes,) The unique classes labels. coef_ : ndarray of shape (n_classes * (n_classes -1) / 2, n_features) Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. `coef_` is readonly property derived from `dual_coef_` and `support_vectors_`. dual_coef_ : ndarray of shape (n_classes - 1, n_SV) Dual coefficients of the support vector in the decision function (see :ref:`sgd_mathematical_formulation`), multiplied by their targets. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial. See the :ref:`multi-class section of the User Guide ` for details. fit_status_ : int 0 if correctly fitted, 1 if the algorithm did not converge. intercept_ : ndarray of shape (n_classes * (n_classes - 1) / 2,) Constants in decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : ndarray of shape (n_classes * (n_classes - 1) // 2,) Number of iterations run by the optimization routine to fit the model. The shape of this attribute depends on the number of models optimized which in turn depends on the number of classes. .. versionadded:: 1.1 support_ : ndarray of shape (n_SV,) Indices of support vectors. support_vectors_ : ndarray of shape (n_SV, n_features) Support vectors. n_support_ : ndarray of shape (n_classes,), dtype=int32 Number of support vectors for each class. fit_status_ : int 0 if correctly fitted, 1 if the algorithm did not converge. probA_ : ndarray of shape (n_classes * (n_classes - 1) / 2,) probB_ : ndarray of shape (n_classes * (n_classes - 1) / 2,) If `probability=True`, it corresponds to the parameters learned in Platt scaling to produce probability estimates from decision values. If `probability=False`, it's an empty array. Platt scaling uses the logistic function ``1 / (1 + exp(decision_value * probA_ + probB_))`` where ``probA_`` and ``probB_`` are learned from the dataset [2]_. For more information on the multiclass case and training procedure see section 8 of [1]_. shape_fit_ : tuple of int of shape (n_dimensions_of_X,) Array dimensions of training vector ``X``. See Also -------- SVC : Support Vector Machine for classification using libsvm. LinearSVC : Scalable linear Support Vector Machine for classification using liblinear. References ---------- .. [1] `LIBSVM: A Library for Support Vector Machines `_ .. [2] `Platt, John (1999). "Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods" `_ Examples -------- >>> import numpy as np >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) >>> y = np.array([1, 1, 2, 2]) >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> from sklearn.svm import NuSVC >>> clf = make_pipeline(StandardScaler(), NuSVC()) >>> clf.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('nusvc', NuSVC())]) >>> print(clf.predict([[-0.8, -1]])) [1] """ _impl = "nu_svc" _parameter_constraints: dict = { **BaseSVC._parameter_constraints, "nu": [Interval(Real, 0.0, 1.0, closed="right")], } _parameter_constraints.pop("C") def __init__( self, *, nu=0.5, kernel="rbf", degree=3, gamma="scale", coef0=0.0, shrinking=True, probability=False, tol=1e-3, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape="ovr", break_ties=False, random_state=None, ): super().__init__( kernel=kernel, degree=degree, gamma=gamma, coef0=coef0, tol=tol, C=0.0, nu=nu, shrinking=shrinking, probability=probability, cache_size=cache_size, class_weight=class_weight, verbose=verbose, max_iter=max_iter, decision_function_shape=decision_function_shape, break_ties=break_ties, random_state=random_state, ) def _more_tags(self): return { "_xfail_checks": { "check_methods_subset_invariance": ( "fails for the decision_function method" ), "check_class_weight_classifiers": "class_weight is ignored.", "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), "check_classifiers_one_label_sample_weights": ( "specified nu is infeasible for the fit." ), } } class SVR(RegressorMixin, BaseLibSVM): """Epsilon-Support Vector Regression. The free parameters in the model are C and epsilon. The implementation is based on libsvm. The fit time complexity is more than quadratic with the number of samples which makes it hard to scale to datasets with more than a couple of 10000 samples. For large datasets consider using :class:`~sklearn.svm.LinearSVR` or :class:`~sklearn.linear_model.SGDRegressor` instead, possibly after a :class:`~sklearn.kernel_approximation.Nystroem` transformer or other :ref:`kernel_approximation`. Read more in the :ref:`User Guide `. Parameters ---------- kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'} or callable, \ default='rbf' Specifies the kernel type to be used in the algorithm. If none is given, 'rbf' will be used. If a callable is given it is used to precompute the kernel matrix. degree : int, default=3 Degree of the polynomial kernel function ('poly'). Must be non-negative. Ignored by all other kernels. gamma : {'scale', 'auto'} or float, default='scale' Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. - if ``gamma='scale'`` (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma, - if 'auto', uses 1 / n_features - if float, must be non-negative. .. versionchanged:: 0.22 The default value of ``gamma`` changed from 'auto' to 'scale'. coef0 : float, default=0.0 Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. tol : float, default=1e-3 Tolerance for stopping criterion. C : float, default=1.0 Regularization parameter. The strength of the regularization is inversely proportional to C. Must be strictly positive. The penalty is a squared l2 penalty. epsilon : float, default=0.1 Epsilon in the epsilon-SVR model. It specifies the epsilon-tube within which no penalty is associated in the training loss function with points predicted within a distance epsilon from the actual value. Must be non-negative. shrinking : bool, default=True Whether to use the shrinking heuristic. See the :ref:`User Guide `. cache_size : float, default=200 Specify the size of the kernel cache (in MB). verbose : bool, default=False Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context. max_iter : int, default=-1 Hard limit on iterations within solver, or -1 for no limit. Attributes ---------- class_weight_ : ndarray of shape (n_classes,) Multipliers of parameter C for each class. Computed based on the ``class_weight`` parameter. .. deprecated:: 1.2 `class_weight_` was deprecated in version 1.2 and will be removed in 1.4. coef_ : ndarray of shape (1, n_features) Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. `coef_` is readonly property derived from `dual_coef_` and `support_vectors_`. dual_coef_ : ndarray of shape (1, n_SV) Coefficients of the support vector in the decision function. fit_status_ : int 0 if correctly fitted, 1 otherwise (will raise warning) intercept_ : ndarray of shape (1,) Constants in decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : int Number of iterations run by the optimization routine to fit the model. .. versionadded:: 1.1 n_support_ : ndarray of shape (1,), dtype=int32 Number of support vectors. shape_fit_ : tuple of int of shape (n_dimensions_of_X,) Array dimensions of training vector ``X``. support_ : ndarray of shape (n_SV,) Indices of support vectors. support_vectors_ : ndarray of shape (n_SV, n_features) Support vectors. See Also -------- NuSVR : Support Vector Machine for regression implemented using libsvm using a parameter to control the number of support vectors. LinearSVR : Scalable Linear Support Vector Machine for regression implemented using liblinear. References ---------- .. [1] `LIBSVM: A Library for Support Vector Machines `_ .. [2] `Platt, John (1999). "Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods" `_ Examples -------- >>> from sklearn.svm import SVR >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> import numpy as np >>> n_samples, n_features = 10, 5 >>> rng = np.random.RandomState(0) >>> y = rng.randn(n_samples) >>> X = rng.randn(n_samples, n_features) >>> regr = make_pipeline(StandardScaler(), SVR(C=1.0, epsilon=0.2)) >>> regr.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('svr', SVR(epsilon=0.2))]) """ _impl = "epsilon_svr" _parameter_constraints: dict = {**BaseLibSVM._parameter_constraints} for unused_param in ["class_weight", "nu", "probability", "random_state"]: _parameter_constraints.pop(unused_param) def __init__( self, *, kernel="rbf", degree=3, gamma="scale", coef0=0.0, tol=1e-3, C=1.0, epsilon=0.1, shrinking=True, cache_size=200, verbose=False, max_iter=-1, ): super().__init__( kernel=kernel, degree=degree, gamma=gamma, coef0=coef0, tol=tol, C=C, nu=0.0, epsilon=epsilon, verbose=verbose, shrinking=shrinking, probability=False, cache_size=cache_size, class_weight=None, max_iter=max_iter, random_state=None, ) # TODO(1.4): Remove @deprecated( # type: ignore "Attribute `class_weight_` was deprecated in version 1.2 and will be removed in" " 1.4." ) @property def class_weight_(self): return np.empty(0) def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } class NuSVR(RegressorMixin, BaseLibSVM): """Nu Support Vector Regression. Similar to NuSVC, for regression, uses a parameter nu to control the number of support vectors. However, unlike NuSVC, where nu replaces C, here nu replaces the parameter epsilon of epsilon-SVR. The implementation is based on libsvm. Read more in the :ref:`User Guide `. Parameters ---------- nu : float, default=0.5 An upper bound on the fraction of training errors and a lower bound of the fraction of support vectors. Should be in the interval (0, 1]. By default 0.5 will be taken. C : float, default=1.0 Penalty parameter C of the error term. kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'} or callable, \ default='rbf' Specifies the kernel type to be used in the algorithm. If none is given, 'rbf' will be used. If a callable is given it is used to precompute the kernel matrix. degree : int, default=3 Degree of the polynomial kernel function ('poly'). Must be non-negative. Ignored by all other kernels. gamma : {'scale', 'auto'} or float, default='scale' Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. - if ``gamma='scale'`` (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma, - if 'auto', uses 1 / n_features - if float, must be non-negative. .. versionchanged:: 0.22 The default value of ``gamma`` changed from 'auto' to 'scale'. coef0 : float, default=0.0 Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. shrinking : bool, default=True Whether to use the shrinking heuristic. See the :ref:`User Guide `. tol : float, default=1e-3 Tolerance for stopping criterion. cache_size : float, default=200 Specify the size of the kernel cache (in MB). verbose : bool, default=False Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context. max_iter : int, default=-1 Hard limit on iterations within solver, or -1 for no limit. Attributes ---------- class_weight_ : ndarray of shape (n_classes,) Multipliers of parameter C for each class. Computed based on the ``class_weight`` parameter. .. deprecated:: 1.2 `class_weight_` was deprecated in version 1.2 and will be removed in 1.4. coef_ : ndarray of shape (1, n_features) Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. `coef_` is readonly property derived from `dual_coef_` and `support_vectors_`. dual_coef_ : ndarray of shape (1, n_SV) Coefficients of the support vector in the decision function. fit_status_ : int 0 if correctly fitted, 1 otherwise (will raise warning) intercept_ : ndarray of shape (1,) Constants in decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : int Number of iterations run by the optimization routine to fit the model. .. versionadded:: 1.1 n_support_ : ndarray of shape (1,), dtype=int32 Number of support vectors. shape_fit_ : tuple of int of shape (n_dimensions_of_X,) Array dimensions of training vector ``X``. support_ : ndarray of shape (n_SV,) Indices of support vectors. support_vectors_ : ndarray of shape (n_SV, n_features) Support vectors. See Also -------- NuSVC : Support Vector Machine for classification implemented with libsvm with a parameter to control the number of support vectors. SVR : Epsilon Support Vector Machine for regression implemented with libsvm. References ---------- .. [1] `LIBSVM: A Library for Support Vector Machines `_ .. [2] `Platt, John (1999). "Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods" `_ Examples -------- >>> from sklearn.svm import NuSVR >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> import numpy as np >>> n_samples, n_features = 10, 5 >>> np.random.seed(0) >>> y = np.random.randn(n_samples) >>> X = np.random.randn(n_samples, n_features) >>> regr = make_pipeline(StandardScaler(), NuSVR(C=1.0, nu=0.1)) >>> regr.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('nusvr', NuSVR(nu=0.1))]) """ _impl = "nu_svr" _parameter_constraints: dict = {**BaseLibSVM._parameter_constraints} for unused_param in ["class_weight", "epsilon", "probability", "random_state"]: _parameter_constraints.pop(unused_param) def __init__( self, *, nu=0.5, C=1.0, kernel="rbf", degree=3, gamma="scale", coef0=0.0, shrinking=True, tol=1e-3, cache_size=200, verbose=False, max_iter=-1, ): super().__init__( kernel=kernel, degree=degree, gamma=gamma, coef0=coef0, tol=tol, C=C, nu=nu, epsilon=0.0, shrinking=shrinking, probability=False, cache_size=cache_size, class_weight=None, verbose=verbose, max_iter=max_iter, random_state=None, ) # TODO(1.4): Remove @deprecated( # type: ignore "Attribute `class_weight_` was deprecated in version 1.2 and will be removed in" " 1.4." ) @property def class_weight_(self): return np.empty(0) def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } } class OneClassSVM(OutlierMixin, BaseLibSVM): """Unsupervised Outlier Detection. Estimate the support of a high-dimensional distribution. The implementation is based on libsvm. Read more in the :ref:`User Guide `. Parameters ---------- kernel : {'linear', 'poly', 'rbf', 'sigmoid', 'precomputed'} or callable, \ default='rbf' Specifies the kernel type to be used in the algorithm. If none is given, 'rbf' will be used. If a callable is given it is used to precompute the kernel matrix. degree : int, default=3 Degree of the polynomial kernel function ('poly'). Must be non-negative. Ignored by all other kernels. gamma : {'scale', 'auto'} or float, default='scale' Kernel coefficient for 'rbf', 'poly' and 'sigmoid'. - if ``gamma='scale'`` (default) is passed then it uses 1 / (n_features * X.var()) as value of gamma, - if 'auto', uses 1 / n_features - if float, must be non-negative. .. versionchanged:: 0.22 The default value of ``gamma`` changed from 'auto' to 'scale'. coef0 : float, default=0.0 Independent term in kernel function. It is only significant in 'poly' and 'sigmoid'. tol : float, default=1e-3 Tolerance for stopping criterion. nu : float, default=0.5 An upper bound on the fraction of training errors and a lower bound of the fraction of support vectors. Should be in the interval (0, 1]. By default 0.5 will be taken. shrinking : bool, default=True Whether to use the shrinking heuristic. See the :ref:`User Guide `. cache_size : float, default=200 Specify the size of the kernel cache (in MB). verbose : bool, default=False Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context. max_iter : int, default=-1 Hard limit on iterations within solver, or -1 for no limit. Attributes ---------- class_weight_ : ndarray of shape (n_classes,) Multipliers of parameter C for each class. Computed based on the ``class_weight`` parameter. .. deprecated:: 1.2 `class_weight_` was deprecated in version 1.2 and will be removed in 1.4. coef_ : ndarray of shape (1, n_features) Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel. `coef_` is readonly property derived from `dual_coef_` and `support_vectors_`. dual_coef_ : ndarray of shape (1, n_SV) Coefficients of the support vectors in the decision function. fit_status_ : int 0 if correctly fitted, 1 otherwise (will raise warning) intercept_ : ndarray of shape (1,) Constant in the decision function. n_features_in_ : int Number of features seen during :term:`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 n_iter_ : int Number of iterations run by the optimization routine to fit the model. .. versionadded:: 1.1 n_support_ : ndarray of shape (n_classes,), dtype=int32 Number of support vectors for each class. offset_ : float Offset used to define the decision function from the raw scores. We have the relation: decision_function = score_samples - `offset_`. The offset is the opposite of `intercept_` and is provided for consistency with other outlier detection algorithms. .. versionadded:: 0.20 shape_fit_ : tuple of int of shape (n_dimensions_of_X,) Array dimensions of training vector ``X``. support_ : ndarray of shape (n_SV,) Indices of support vectors. support_vectors_ : ndarray of shape (n_SV, n_features) Support vectors. See Also -------- sklearn.linear_model.SGDOneClassSVM : Solves linear One-Class SVM using Stochastic Gradient Descent. sklearn.neighbors.LocalOutlierFactor : Unsupervised Outlier Detection using Local Outlier Factor (LOF). sklearn.ensemble.IsolationForest : Isolation Forest Algorithm. Examples -------- >>> from sklearn.svm import OneClassSVM >>> X = [[0], [0.44], [0.45], [0.46], [1]] >>> clf = OneClassSVM(gamma='auto').fit(X) >>> clf.predict(X) array([-1, 1, 1, 1, -1]) >>> clf.score_samples(X) array([1.7798..., 2.0547..., 2.0556..., 2.0561..., 1.7332...]) """ _impl = "one_class" _parameter_constraints: dict = {**BaseLibSVM._parameter_constraints} for unused_param in ["C", "class_weight", "epsilon", "probability", "random_state"]: _parameter_constraints.pop(unused_param) def __init__( self, *, kernel="rbf", degree=3, gamma="scale", coef0=0.0, tol=1e-3, nu=0.5, shrinking=True, cache_size=200, verbose=False, max_iter=-1, ): super().__init__( kernel, degree, gamma, coef0, tol, 0.0, nu, 0.0, shrinking, False, cache_size, None, verbose, max_iter, random_state=None, ) # TODO(1.4): Remove @deprecated( # type: ignore "Attribute `class_weight_` was deprecated in version 1.2 and will be removed in" " 1.4." ) @property def class_weight_(self): return np.empty(0) def fit(self, X, y=None, sample_weight=None): """Detect the soft boundary of the set of samples X. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Set of samples, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. sample_weight : array-like of shape (n_samples,), default=None Per-sample weights. Rescale C per sample. Higher weights force the classifier to put more emphasis on these points. Returns ------- self : object Fitted estimator. Notes ----- If X is not a C-ordered contiguous array it is copied. """ super().fit(X, np.ones(_num_samples(X)), sample_weight=sample_weight) self.offset_ = -self._intercept_ return self def decision_function(self, X): """Signed distance to the separating hyperplane. Signed distance is positive for an inlier and negative for an outlier. Parameters ---------- X : array-like of shape (n_samples, n_features) The data matrix. Returns ------- dec : ndarray of shape (n_samples,) Returns the decision function of the samples. """ dec = self._decision_function(X).ravel() return dec def score_samples(self, X): """Raw scoring function of the samples. Parameters ---------- X : array-like of shape (n_samples, n_features) The data matrix. Returns ------- score_samples : ndarray of shape (n_samples,) Returns the (unshifted) scoring function of the samples. """ return self.decision_function(X) + self.offset_ def predict(self, X): """Perform classification on samples in X. For a one-class model, +1 or -1 is returned. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) or \ (n_samples_test, n_samples_train) For kernel="precomputed", the expected shape of X is (n_samples_test, n_samples_train). Returns ------- y_pred : ndarray of shape (n_samples,) Class labels for samples in X. """ y = super().predict(X) return np.asarray(y, dtype=np.intp) def _more_tags(self): return { "_xfail_checks": { "check_sample_weights_invariance": ( "zero sample_weight is not equivalent to removing samples" ), } }