# Authors: Peter Prettenhofer (main author) # Mathieu Blondel (partial_fit support) # # License: BSD 3 clause """Classification and regression using Stochastic Gradient Descent (SGD).""" import numpy as np import warnings from abc import ABCMeta, abstractmethod from joblib import Parallel, delayed from ..base import clone, is_classifier from ._base import LinearClassifierMixin, SparseCoefMixin from ._base import make_dataset from ..base import BaseEstimator, RegressorMixin from ..utils import check_array, check_random_state, check_X_y from ..utils.extmath import safe_sparse_dot from ..utils.multiclass import _check_partial_fit_first_call from ..utils.validation import check_is_fitted, _check_sample_weight from ..utils.validation import _deprecate_positional_args from ..exceptions import ConvergenceWarning from ..model_selection import StratifiedShuffleSplit, ShuffleSplit from ._sgd_fast import _plain_sgd from ..utils import compute_class_weight from ._sgd_fast import Hinge from ._sgd_fast import SquaredHinge from ._sgd_fast import Log from ._sgd_fast import ModifiedHuber from ._sgd_fast import SquaredLoss from ._sgd_fast import Huber from ._sgd_fast import EpsilonInsensitive from ._sgd_fast import SquaredEpsilonInsensitive from ..utils.fixes import _joblib_parallel_args from ..utils import deprecated LEARNING_RATE_TYPES = {"constant": 1, "optimal": 2, "invscaling": 3, "adaptive": 4, "pa1": 5, "pa2": 6} PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3} DEFAULT_EPSILON = 0.1 # Default value of ``epsilon`` parameter. MAX_INT = np.iinfo(np.int32).max class _ValidationScoreCallback: """Callback for early stopping based on validation score""" def __init__(self, estimator, X_val, y_val, sample_weight_val, classes=None): self.estimator = clone(estimator) self.estimator.t_ = 1 # to pass check_is_fitted if classes is not None: self.estimator.classes_ = classes self.X_val = X_val self.y_val = y_val self.sample_weight_val = sample_weight_val def __call__(self, coef, intercept): est = self.estimator est.coef_ = coef.reshape(1, -1) est.intercept_ = np.atleast_1d(intercept) return est.score(self.X_val, self.y_val, self.sample_weight_val) class BaseSGD(SparseCoefMixin, BaseEstimator, metaclass=ABCMeta): """Base class for SGD classification and regression.""" @_deprecate_positional_args def __init__(self, loss, *, penalty='l2', alpha=0.0001, C=1.0, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=1e-3, shuffle=True, verbose=0, epsilon=0.1, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, warm_start=False, average=False): self.loss = loss self.penalty = penalty self.learning_rate = learning_rate self.epsilon = epsilon self.alpha = alpha self.C = C self.l1_ratio = l1_ratio self.fit_intercept = fit_intercept self.shuffle = shuffle self.random_state = random_state self.verbose = verbose self.eta0 = eta0 self.power_t = power_t self.early_stopping = early_stopping self.validation_fraction = validation_fraction self.n_iter_no_change = n_iter_no_change self.warm_start = warm_start self.average = average self.max_iter = max_iter self.tol = tol # current tests expect init to do parameter validation # but we are not allowed to set attributes self._validate_params() def set_params(self, **kwargs): """Set and validate the parameters of estimator. Parameters ---------- **kwargs : dict Estimator parameters. Returns ------- self : object Estimator instance. """ super().set_params(**kwargs) self._validate_params() return self @abstractmethod def fit(self, X, y): """Fit model.""" def _validate_params(self, for_partial_fit=False): """Validate input params. """ if not isinstance(self.shuffle, bool): raise ValueError("shuffle must be either True or False") if not isinstance(self.early_stopping, bool): raise ValueError("early_stopping must be either True or False") if self.early_stopping and for_partial_fit: raise ValueError("early_stopping should be False with partial_fit") if self.max_iter is not None and self.max_iter <= 0: raise ValueError("max_iter must be > zero. Got %f" % self.max_iter) if not (0.0 <= self.l1_ratio <= 1.0): raise ValueError("l1_ratio must be in [0, 1]") if self.alpha < 0.0: raise ValueError("alpha must be >= 0") if self.n_iter_no_change < 1: raise ValueError("n_iter_no_change must be >= 1") if not (0.0 < self.validation_fraction < 1.0): raise ValueError("validation_fraction must be in range (0, 1)") if self.learning_rate in ("constant", "invscaling", "adaptive"): if self.eta0 <= 0.0: raise ValueError("eta0 must be > 0") if self.learning_rate == "optimal" and self.alpha == 0: raise ValueError("alpha must be > 0 since " "learning_rate is 'optimal'. alpha is used " "to compute the optimal learning rate.") # raises ValueError if not registered self._get_penalty_type(self.penalty) self._get_learning_rate_type(self.learning_rate) if self.loss not in self.loss_functions: raise ValueError("The loss %s is not supported. " % self.loss) def _get_loss_function(self, loss): """Get concrete ``LossFunction`` object for str ``loss``. """ try: loss_ = self.loss_functions[loss] loss_class, args = loss_[0], loss_[1:] if loss in ('huber', 'epsilon_insensitive', 'squared_epsilon_insensitive'): args = (self.epsilon, ) return loss_class(*args) except KeyError: raise ValueError("The loss %s is not supported. " % loss) def _get_learning_rate_type(self, learning_rate): try: return LEARNING_RATE_TYPES[learning_rate] except KeyError: raise ValueError("learning rate %s " "is not supported. " % learning_rate) def _get_penalty_type(self, penalty): penalty = str(penalty).lower() try: return PENALTY_TYPES[penalty] except KeyError: raise ValueError("Penalty %s is not supported. " % penalty) def _allocate_parameter_mem(self, n_classes, n_features, coef_init=None, intercept_init=None): """Allocate mem for parameters; initialize if provided.""" if n_classes > 2: # allocate coef_ for multi-class if coef_init is not None: coef_init = np.asarray(coef_init, order="C") if coef_init.shape != (n_classes, n_features): raise ValueError("Provided ``coef_`` does not match " "dataset. ") self.coef_ = coef_init else: self.coef_ = np.zeros((n_classes, n_features), dtype=np.float64, order="C") # allocate intercept_ for multi-class if intercept_init is not None: intercept_init = np.asarray(intercept_init, order="C") if intercept_init.shape != (n_classes, ): raise ValueError("Provided intercept_init " "does not match dataset.") self.intercept_ = intercept_init else: self.intercept_ = np.zeros(n_classes, dtype=np.float64, order="C") else: # allocate coef_ for binary problem if coef_init is not None: coef_init = np.asarray(coef_init, dtype=np.float64, order="C") coef_init = coef_init.ravel() if coef_init.shape != (n_features,): raise ValueError("Provided coef_init does not " "match dataset.") self.coef_ = coef_init else: self.coef_ = np.zeros(n_features, dtype=np.float64, order="C") # allocate intercept_ for binary problem if intercept_init is not None: intercept_init = np.asarray(intercept_init, dtype=np.float64) if intercept_init.shape != (1,) and intercept_init.shape != (): raise ValueError("Provided intercept_init " "does not match dataset.") self.intercept_ = intercept_init.reshape(1,) else: self.intercept_ = np.zeros(1, dtype=np.float64, order="C") # initialize average parameters if self.average > 0: self._standard_coef = self.coef_ self._standard_intercept = self.intercept_ self._average_coef = np.zeros(self.coef_.shape, dtype=np.float64, order="C") self._average_intercept = np.zeros(self._standard_intercept.shape, dtype=np.float64, order="C") def _make_validation_split(self, y): """Split the dataset between training set and validation set. Parameters ---------- y : ndarray of shape (n_samples, ) Target values. Returns ------- validation_mask : ndarray of shape (n_samples, ) Equal to 1 on the validation set, 0 on the training set. """ n_samples = y.shape[0] validation_mask = np.zeros(n_samples, dtype=np.uint8) if not self.early_stopping: # use the full set for training, with an empty validation set return validation_mask if is_classifier(self): splitter_type = StratifiedShuffleSplit else: splitter_type = ShuffleSplit cv = splitter_type(test_size=self.validation_fraction, random_state=self.random_state) idx_train, idx_val = next(cv.split(np.zeros(shape=(y.shape[0], 1)), y)) if idx_train.shape[0] == 0 or idx_val.shape[0] == 0: raise ValueError( "Splitting %d samples into a train set and a validation set " "with validation_fraction=%r led to an empty set (%d and %d " "samples). Please either change validation_fraction, increase " "number of samples, or disable early_stopping." % (n_samples, self.validation_fraction, idx_train.shape[0], idx_val.shape[0])) validation_mask[idx_val] = 1 return validation_mask def _make_validation_score_cb(self, validation_mask, X, y, sample_weight, classes=None): if not self.early_stopping: return None return _ValidationScoreCallback( self, X[validation_mask], y[validation_mask], sample_weight[validation_mask], classes=classes) # mypy error: Decorated property not supported @deprecated("Attribute standard_coef_ was deprecated " # type: ignore "in version 0.23 and will be removed in 0.25.") @property def standard_coef_(self): return self._standard_coef # mypy error: Decorated property not supported @deprecated( # type: ignore "Attribute standard_intercept_ was deprecated " "in version 0.23 and will be removed in 0.25." ) @property def standard_intercept_(self): return self._standard_intercept # mypy error: Decorated property not supported @deprecated("Attribute average_coef_ was deprecated " # type: ignore "in version 0.23 and will be removed in 0.25.") @property def average_coef_(self): return self._average_coef # mypy error: Decorated property not supported @deprecated("Attribute average_intercept_ was deprecated " # type: ignore "in version 0.23 and will be removed in 0.25.") @property def average_intercept_(self): return self._average_intercept def _prepare_fit_binary(est, y, i): """Initialization for fit_binary. Returns y, coef, intercept, average_coef, average_intercept. """ y_i = np.ones(y.shape, dtype=np.float64, order="C") y_i[y != est.classes_[i]] = -1.0 average_intercept = 0 average_coef = None if len(est.classes_) == 2: if not est.average: coef = est.coef_.ravel() intercept = est.intercept_[0] else: coef = est._standard_coef.ravel() intercept = est._standard_intercept[0] average_coef = est._average_coef.ravel() average_intercept = est._average_intercept[0] else: if not est.average: coef = est.coef_[i] intercept = est.intercept_[i] else: coef = est._standard_coef[i] intercept = est._standard_intercept[i] average_coef = est._average_coef[i] average_intercept = est._average_intercept[i] return y_i, coef, intercept, average_coef, average_intercept def fit_binary(est, i, X, y, alpha, C, learning_rate, max_iter, pos_weight, neg_weight, sample_weight, validation_mask=None, random_state=None): """Fit a single binary classifier. The i'th class is considered the "positive" class. Parameters ---------- est : Estimator object The estimator to fit i : int Index of the positive class X : numpy array or sparse matrix of shape [n_samples,n_features] Training data y : numpy array of shape [n_samples, ] Target values alpha : float The regularization parameter C : float Maximum step size for passive aggressive learning_rate : string The learning rate. Accepted values are 'constant', 'optimal', 'invscaling', 'pa1' and 'pa2'. max_iter : int The maximum number of iterations (epochs) pos_weight : float The weight of the positive class neg_weight : float The weight of the negative class sample_weight : numpy array of shape [n_samples, ] The weight of each sample validation_mask : numpy array of shape [n_samples, ], default=None Precomputed validation mask in case _fit_binary is called in the context of a one-vs-rest reduction. random_state : int, RandomState instance, default=None If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. """ # if average is not true, average_coef, and average_intercept will be # unused y_i, coef, intercept, average_coef, average_intercept = \ _prepare_fit_binary(est, y, i) assert y_i.shape[0] == y.shape[0] == sample_weight.shape[0] random_state = check_random_state(random_state) dataset, intercept_decay = make_dataset( X, y_i, sample_weight, random_state=random_state) penalty_type = est._get_penalty_type(est.penalty) learning_rate_type = est._get_learning_rate_type(learning_rate) if validation_mask is None: validation_mask = est._make_validation_split(y_i) classes = np.array([-1, 1], dtype=y_i.dtype) validation_score_cb = est._make_validation_score_cb( validation_mask, X, y_i, sample_weight, classes=classes) # numpy mtrand expects a C long which is a signed 32 bit integer under # Windows seed = random_state.randint(MAX_INT) tol = est.tol if est.tol is not None else -np.inf coef, intercept, average_coef, average_intercept, n_iter_ = _plain_sgd( coef, intercept, average_coef, average_intercept, est.loss_function_, penalty_type, alpha, C, est.l1_ratio, dataset, validation_mask, est.early_stopping, validation_score_cb, int(est.n_iter_no_change), max_iter, tol, int(est.fit_intercept), int(est.verbose), int(est.shuffle), seed, pos_weight, neg_weight, learning_rate_type, est.eta0, est.power_t, est.t_, intercept_decay, est.average) if est.average: if len(est.classes_) == 2: est._average_intercept[0] = average_intercept else: est._average_intercept[i] = average_intercept return coef, intercept, n_iter_ class BaseSGDClassifier(LinearClassifierMixin, BaseSGD, metaclass=ABCMeta): loss_functions = { "hinge": (Hinge, 1.0), "squared_hinge": (SquaredHinge, 1.0), "perceptron": (Hinge, 0.0), "log": (Log, ), "modified_huber": (ModifiedHuber, ), "squared_loss": (SquaredLoss, ), "huber": (Huber, DEFAULT_EPSILON), "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON), "squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON), } @abstractmethod @_deprecate_positional_args def __init__(self, loss="hinge", *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=1e-3, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, n_jobs=None, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, class_weight=None, warm_start=False, average=False): super().__init__( loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio, fit_intercept=fit_intercept, max_iter=max_iter, tol=tol, shuffle=shuffle, verbose=verbose, epsilon=epsilon, random_state=random_state, learning_rate=learning_rate, eta0=eta0, power_t=power_t, early_stopping=early_stopping, validation_fraction=validation_fraction, n_iter_no_change=n_iter_no_change, warm_start=warm_start, average=average) self.class_weight = class_weight self.n_jobs = n_jobs def _partial_fit(self, X, y, alpha, C, loss, learning_rate, max_iter, classes, sample_weight, coef_init, intercept_init): X, y = check_X_y(X, y, accept_sparse='csr', dtype=np.float64, order="C", accept_large_sparse=False) n_samples, n_features = X.shape _check_partial_fit_first_call(self, classes) n_classes = self.classes_.shape[0] # Allocate datastructures from input arguments self._expanded_class_weight = compute_class_weight( self.class_weight, classes=self.classes_, y=y) sample_weight = _check_sample_weight(sample_weight, X) if getattr(self, "coef_", None) is None or coef_init is not None: self._allocate_parameter_mem(n_classes, n_features, coef_init, intercept_init) elif n_features != self.coef_.shape[-1]: raise ValueError("Number of features %d does not match previous " "data %d." % (n_features, self.coef_.shape[-1])) self.loss_function_ = self._get_loss_function(loss) if not hasattr(self, "t_"): self.t_ = 1.0 # delegate to concrete training procedure if n_classes > 2: self._fit_multiclass(X, y, alpha=alpha, C=C, learning_rate=learning_rate, sample_weight=sample_weight, max_iter=max_iter) elif n_classes == 2: self._fit_binary(X, y, alpha=alpha, C=C, learning_rate=learning_rate, sample_weight=sample_weight, max_iter=max_iter) else: raise ValueError( "The number of classes has to be greater than one;" " got %d class" % n_classes) return self def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None, intercept_init=None, sample_weight=None): self._validate_params() if hasattr(self, "classes_"): self.classes_ = None X, y = self._validate_data(X, y, accept_sparse='csr', dtype=np.float64, order="C", accept_large_sparse=False) # labels can be encoded as float, int, or string literals # np.unique sorts in asc order; largest class id is positive class classes = np.unique(y) if self.warm_start and hasattr(self, "coef_"): if coef_init is None: coef_init = self.coef_ if intercept_init is None: intercept_init = self.intercept_ else: self.coef_ = None self.intercept_ = None if self.average > 0: self._standard_coef = self.coef_ self._standard_intercept = self.intercept_ self._average_coef = None self._average_intercept = None # Clear iteration count for multiple call to fit. self.t_ = 1.0 self._partial_fit(X, y, alpha, C, loss, learning_rate, self.max_iter, classes, sample_weight, coef_init, intercept_init) if (self.tol is not None and self.tol > -np.inf and self.n_iter_ == self.max_iter): warnings.warn("Maximum number of iteration reached before " "convergence. Consider increasing max_iter to " "improve the fit.", ConvergenceWarning) return self def _fit_binary(self, X, y, alpha, C, sample_weight, learning_rate, max_iter): """Fit a binary classifier on X and y. """ coef, intercept, n_iter_ = fit_binary(self, 1, X, y, alpha, C, learning_rate, max_iter, self._expanded_class_weight[1], self._expanded_class_weight[0], sample_weight, random_state=self.random_state) self.t_ += n_iter_ * X.shape[0] self.n_iter_ = n_iter_ # need to be 2d if self.average > 0: if self.average <= self.t_ - 1: self.coef_ = self._average_coef.reshape(1, -1) self.intercept_ = self._average_intercept else: self.coef_ = self._standard_coef.reshape(1, -1) self._standard_intercept = np.atleast_1d(intercept) self.intercept_ = self._standard_intercept else: self.coef_ = coef.reshape(1, -1) # intercept is a float, need to convert it to an array of length 1 self.intercept_ = np.atleast_1d(intercept) def _fit_multiclass(self, X, y, alpha, C, learning_rate, sample_weight, max_iter): """Fit a multi-class classifier by combining binary classifiers Each binary classifier predicts one class versus all others. This strategy is called OvA (One versus All) or OvR (One versus Rest). """ # Precompute the validation split using the multiclass labels # to ensure proper balancing of the classes. validation_mask = self._make_validation_split(y) # Use joblib to fit OvA in parallel. # Pick the random seed for each job outside of fit_binary to avoid # sharing the estimator random state between threads which could lead # to non-deterministic behavior random_state = check_random_state(self.random_state) seeds = random_state.randint(MAX_INT, size=len(self.classes_)) result = Parallel(n_jobs=self.n_jobs, verbose=self.verbose, **_joblib_parallel_args(require="sharedmem"))( delayed(fit_binary)(self, i, X, y, alpha, C, learning_rate, max_iter, self._expanded_class_weight[i], 1., sample_weight, validation_mask=validation_mask, random_state=seed) for i, seed in enumerate(seeds)) # take the maximum of n_iter_ over every binary fit n_iter_ = 0. for i, (_, intercept, n_iter_i) in enumerate(result): self.intercept_[i] = intercept n_iter_ = max(n_iter_, n_iter_i) self.t_ += n_iter_ * X.shape[0] self.n_iter_ = n_iter_ if self.average > 0: if self.average <= self.t_ - 1.0: self.coef_ = self._average_coef self.intercept_ = self._average_intercept else: self.coef_ = self._standard_coef self._standard_intercept = np.atleast_1d(self.intercept_) self.intercept_ = self._standard_intercept def partial_fit(self, X, y, classes=None, sample_weight=None): """Perform one epoch of stochastic gradient descent on given samples. Internally, this method uses ``max_iter = 1``. Therefore, it is not guaranteed that a minimum of the cost function is reached after calling it once. Matters such as objective convergence and early stopping should be handled by the user. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Subset of the training data. y : ndarray of shape (n_samples,) Subset of the target values. classes : ndarray of shape (n_classes,), default=None Classes across all calls to partial_fit. Can be obtained by via `np.unique(y_all)`, where y_all is the target vector of the entire dataset. This argument is required for the first call to partial_fit and can be omitted in the subsequent calls. Note that y doesn't need to contain all labels in `classes`. sample_weight : array-like, shape (n_samples,), default=None Weights applied to individual samples. If not provided, uniform weights are assumed. Returns ------- self : Returns an instance of self. """ self._validate_params(for_partial_fit=True) if self.class_weight in ['balanced']: raise ValueError("class_weight '{0}' is not supported for " "partial_fit. In order to use 'balanced' weights," " use compute_class_weight('{0}', " "classes=classes, y=y). " "In place of y you can us a large enough sample " "of the full training set target to properly " "estimate the class frequency distributions. " "Pass the resulting weights as the class_weight " "parameter.".format(self.class_weight)) return self._partial_fit(X, y, alpha=self.alpha, C=1.0, loss=self.loss, learning_rate=self.learning_rate, max_iter=1, classes=classes, sample_weight=sample_weight, coef_init=None, intercept_init=None) def fit(self, X, y, coef_init=None, intercept_init=None, sample_weight=None): """Fit linear model with Stochastic Gradient Descent. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Training data. y : ndarray of shape (n_samples,) Target values. coef_init : ndarray of shape (n_classes, n_features), default=None The initial coefficients to warm-start the optimization. intercept_init : ndarray of shape (n_classes,), default=None The initial intercept to warm-start the optimization. sample_weight : array-like, shape (n_samples,), default=None Weights applied to individual samples. If not provided, uniform weights are assumed. These weights will be multiplied with class_weight (passed through the constructor) if class_weight is specified. Returns ------- self : Returns an instance of self. """ return self._fit(X, y, alpha=self.alpha, C=1.0, loss=self.loss, learning_rate=self.learning_rate, coef_init=coef_init, intercept_init=intercept_init, sample_weight=sample_weight) class SGDClassifier(BaseSGDClassifier): """Linear classifiers (SVM, logistic regression, etc.) with SGD training. This estimator implements regularized linear models with stochastic gradient descent (SGD) learning: the gradient of the loss is estimated each sample at a time and the model is updated along the way with a decreasing strength schedule (aka learning rate). SGD allows minibatch (online/out-of-core) learning via the `partial_fit` method. For best results using the default learning rate schedule, the data should have zero mean and unit variance. This implementation works with data represented as dense or sparse arrays of floating point values for the features. The model it fits can be controlled with the loss parameter; by default, it fits a linear support vector machine (SVM). The regularizer is a penalty added to the loss function that shrinks model parameters towards the zero vector using either the squared euclidean norm L2 or the absolute norm L1 or a combination of both (Elastic Net). If the parameter update crosses the 0.0 value because of the regularizer, the update is truncated to 0.0 to allow for learning sparse models and achieve online feature selection. Read more in the :ref:`User Guide `. Parameters ---------- loss : str, default='hinge' The loss function to be used. Defaults to 'hinge', which gives a linear SVM. The possible options are 'hinge', 'log', 'modified_huber', 'squared_hinge', 'perceptron', or a regression loss: 'squared_loss', 'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'. The 'log' loss gives logistic regression, a probabilistic classifier. 'modified_huber' is another smooth loss that brings tolerance to outliers as well as probability estimates. 'squared_hinge' is like hinge but is quadratically penalized. 'perceptron' is the linear loss used by the perceptron algorithm. The other losses are designed for regression but can be useful in classification as well; see :class:`~sklearn.linear_model.SGDRegressor` for a description. More details about the losses formulas can be found in the :ref:`User Guide `. penalty : {'l2', 'l1', 'elasticnet'}, default='l2' The penalty (aka regularization term) to be used. Defaults to 'l2' which is the standard regularizer for linear SVM models. 'l1' and 'elasticnet' might bring sparsity to the model (feature selection) not achievable with 'l2'. alpha : float, default=0.0001 Constant that multiplies the regularization term. The higher the value, the stronger the regularization. Also used to compute the learning rate when set to `learning_rate` is set to 'optimal'. l1_ratio : float, default=0.15 The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1. Only used if `penalty` is 'elasticnet'. fit_intercept : bool, default=True Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. max_iter : int, default=1000 The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the ``fit`` method, and not the :meth:`partial_fit` method. .. versionadded:: 0.19 tol : float, default=1e-3 The stopping criterion. If it is not None, training will stop when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive epochs. .. versionadded:: 0.19 shuffle : bool, default=True Whether or not the training data should be shuffled after each epoch. verbose : int, default=0 The verbosity level. epsilon : float, default=0.1 Epsilon in the epsilon-insensitive loss functions; only if `loss` is 'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'. For 'huber', determines the threshold at which it becomes less important to get the prediction exactly right. For epsilon-insensitive, any differences between the current prediction and the correct label are ignored if they are less than this threshold. n_jobs : int, default=None The number of CPUs to use to do the OVA (One Versus All, for multi-class problems) computation. ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary ` for more details. random_state : int, RandomState instance, default=None Used for shuffling the data, when ``shuffle`` is set to ``True``. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. learning_rate : str, default='optimal' The learning rate schedule: - 'constant': `eta = eta0` - 'optimal': `eta = 1.0 / (alpha * (t + t0))` where t0 is chosen by a heuristic proposed by Leon Bottou. - 'invscaling': `eta = eta0 / pow(t, power_t)` - 'adaptive': eta = eta0, as long as the training keeps decreasing. Each time n_iter_no_change consecutive epochs fail to decrease the training loss by tol or fail to increase validation score by tol if early_stopping is True, the current learning rate is divided by 5. .. versionadded:: 0.20 Added 'adaptive' option eta0 : double, default=0.0 The initial learning rate for the 'constant', 'invscaling' or 'adaptive' schedules. The default value is 0.0 as eta0 is not used by the default schedule 'optimal'. power_t : double, default=0.5 The exponent for inverse scaling learning rate [default 0.5]. early_stopping : bool, default=False Whether to use early stopping to terminate training when validation score is not improving. If set to True, it will automatically set aside a stratified fraction of training data as validation and terminate training when validation score returned by the `score` method is not improving by at least tol for n_iter_no_change consecutive epochs. .. versionadded:: 0.20 Added 'early_stopping' option validation_fraction : float, default=0.1 The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if `early_stopping` is True. .. versionadded:: 0.20 Added 'validation_fraction' option n_iter_no_change : int, default=5 Number of iterations with no improvement to wait before early stopping. .. versionadded:: 0.20 Added 'n_iter_no_change' option class_weight : dict, {class_label: weight} or "balanced", default=None Preset for the class_weight fit parameter. Weights associated with classes. 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))``. warm_start : bool, default=False When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See :term:`the Glossary `. Repeatedly calling fit or partial_fit when warm_start is True can result in a different solution than when calling fit a single time because of the way the data is shuffled. If a dynamic learning rate is used, the learning rate is adapted depending on the number of samples already seen. Calling ``fit`` resets this counter, while ``partial_fit`` will result in increasing the existing counter. average : bool or int, default=False When set to True, computes the averaged SGD weights accross all updates and stores the result in the ``coef_`` attribute. If set to an int greater than 1, averaging will begin once the total number of samples seen reaches `average`. So ``average=10`` will begin averaging after seeing 10 samples. Attributes ---------- coef_ : ndarray of shape (1, n_features) if n_classes == 2 else \ (n_classes, n_features) Weights assigned to the features. intercept_ : ndarray of shape (1,) if n_classes == 2 else (n_classes,) Constants in decision function. n_iter_ : int The actual number of iterations before reaching the stopping criterion. For multiclass fits, it is the maximum over every binary fit. loss_function_ : concrete ``LossFunction`` classes_ : array of shape (n_classes,) t_ : int Number of weight updates performed during training. Same as ``(n_iter_ * n_samples)``. See Also -------- sklearn.svm.LinearSVC: Linear support vector classification. LogisticRegression: Logistic regression. Perceptron: Inherits from SGDClassifier. ``Perceptron()`` is equivalent to ``SGDClassifier(loss="perceptron", eta0=1, learning_rate="constant", penalty=None)``. Examples -------- >>> import numpy as np >>> from sklearn.linear_model import SGDClassifier >>> from sklearn.preprocessing import StandardScaler >>> from sklearn.pipeline import make_pipeline >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) >>> Y = np.array([1, 1, 2, 2]) >>> # Always scale the input. The most convenient way is to use a pipeline. >>> clf = make_pipeline(StandardScaler(), ... SGDClassifier(max_iter=1000, tol=1e-3)) >>> clf.fit(X, Y) Pipeline(steps=[('standardscaler', StandardScaler()), ('sgdclassifier', SGDClassifier())]) >>> print(clf.predict([[-0.8, -1]])) [1] """ @_deprecate_positional_args def __init__(self, loss="hinge", *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=1e-3, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, n_jobs=None, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, class_weight=None, warm_start=False, average=False): super().__init__( loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio, fit_intercept=fit_intercept, max_iter=max_iter, tol=tol, shuffle=shuffle, verbose=verbose, epsilon=epsilon, n_jobs=n_jobs, random_state=random_state, learning_rate=learning_rate, eta0=eta0, power_t=power_t, early_stopping=early_stopping, validation_fraction=validation_fraction, n_iter_no_change=n_iter_no_change, class_weight=class_weight, warm_start=warm_start, average=average) def _check_proba(self): if self.loss not in ("log", "modified_huber"): raise AttributeError("probability estimates are not available for" " loss=%r" % self.loss) @property def predict_proba(self): """Probability estimates. This method is only available for log loss and modified Huber loss. Multiclass probability estimates are derived from binary (one-vs.-rest) estimates by simple normalization, as recommended by Zadrozny and Elkan. Binary probability estimates for loss="modified_huber" are given by (clip(decision_function(X), -1, 1) + 1) / 2. For other loss functions it is necessary to perform proper probability calibration by wrapping the classifier with :class:`sklearn.calibration.CalibratedClassifierCV` instead. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Input data for prediction. Returns ------- ndarray of shape (n_samples, n_classes) Returns the probability of the sample for each class in the model, where classes are ordered as they are in `self.classes_`. References ---------- Zadrozny and Elkan, "Transforming classifier scores into multiclass probability estimates", SIGKDD'02, http://www.research.ibm.com/people/z/zadrozny/kdd2002-Transf.pdf The justification for the formula in the loss="modified_huber" case is in the appendix B in: http://jmlr.csail.mit.edu/papers/volume2/zhang02c/zhang02c.pdf """ self._check_proba() return self._predict_proba def _predict_proba(self, X): check_is_fitted(self) if self.loss == "log": return self._predict_proba_lr(X) elif self.loss == "modified_huber": binary = (len(self.classes_) == 2) scores = self.decision_function(X) if binary: prob2 = np.ones((scores.shape[0], 2)) prob = prob2[:, 1] else: prob = scores np.clip(scores, -1, 1, prob) prob += 1. prob /= 2. if binary: prob2[:, 0] -= prob prob = prob2 else: # the above might assign zero to all classes, which doesn't # normalize neatly; work around this to produce uniform # probabilities prob_sum = prob.sum(axis=1) all_zero = (prob_sum == 0) if np.any(all_zero): prob[all_zero, :] = 1 prob_sum[all_zero] = len(self.classes_) # normalize prob /= prob_sum.reshape((prob.shape[0], -1)) return prob else: raise NotImplementedError("predict_(log_)proba only supported when" " loss='log' or loss='modified_huber' " "(%r given)" % self.loss) @property def predict_log_proba(self): """Log of probability estimates. This method is only available for log loss and modified Huber loss. When loss="modified_huber", probability estimates may be hard zeros and ones, so taking the logarithm is not possible. See ``predict_proba`` for details. Parameters ---------- X : {array-like, sparse matrix} of shape (n_samples, n_features) Input data for prediction. Returns ------- T : array-like, shape (n_samples, n_classes) Returns the log-probability of the sample for each class in the model, where classes are ordered as they are in `self.classes_`. """ self._check_proba() return self._predict_log_proba def _predict_log_proba(self, X): return np.log(self.predict_proba(X)) class BaseSGDRegressor(RegressorMixin, BaseSGD): loss_functions = { "squared_loss": (SquaredLoss, ), "huber": (Huber, DEFAULT_EPSILON), "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON), "squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON), } @abstractmethod @_deprecate_positional_args def __init__(self, loss="squared_loss", *, penalty="l2", alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=1e-3, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, random_state=None, learning_rate="invscaling", eta0=0.01, power_t=0.25, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, warm_start=False, average=False): super().__init__( loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio, fit_intercept=fit_intercept, max_iter=max_iter, tol=tol, shuffle=shuffle, verbose=verbose, epsilon=epsilon, random_state=random_state, learning_rate=learning_rate, eta0=eta0, power_t=power_t, early_stopping=early_stopping, validation_fraction=validation_fraction, n_iter_no_change=n_iter_no_change, warm_start=warm_start, average=average) def _partial_fit(self, X, y, alpha, C, loss, learning_rate, max_iter, sample_weight, coef_init, intercept_init): X, y = self._validate_data(X, y, accept_sparse="csr", copy=False, order='C', dtype=np.float64, accept_large_sparse=False) y = y.astype(np.float64, copy=False) n_samples, n_features = X.shape sample_weight = _check_sample_weight(sample_weight, X) # Allocate datastructures from input arguments if getattr(self, "coef_", None) is None: self._allocate_parameter_mem(1, n_features, coef_init, intercept_init) elif n_features != self.coef_.shape[-1]: raise ValueError("Number of features %d does not match previous " "data %d." % (n_features, self.coef_.shape[-1])) if self.average > 0 and getattr(self, "_average_coef", None) is None: self._average_coef = np.zeros(n_features, dtype=np.float64, order="C") self._average_intercept = np.zeros(1, dtype=np.float64, order="C") self._fit_regressor(X, y, alpha, C, loss, learning_rate, sample_weight, max_iter) return self def partial_fit(self, X, y, sample_weight=None): """Perform one epoch of stochastic gradient descent on given samples. Internally, this method uses ``max_iter = 1``. Therefore, it is not guaranteed that a minimum of the cost function is reached after calling it once. Matters such as objective convergence and early stopping should be handled by the user. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Subset of training data y : numpy array of shape (n_samples,) Subset of target values sample_weight : array-like, shape (n_samples,), default=None Weights applied to individual samples. If not provided, uniform weights are assumed. Returns ------- self : returns an instance of self. """ self._validate_params(for_partial_fit=True) return self._partial_fit(X, y, self.alpha, C=1.0, loss=self.loss, learning_rate=self.learning_rate, max_iter=1, sample_weight=sample_weight, coef_init=None, intercept_init=None) def _fit(self, X, y, alpha, C, loss, learning_rate, coef_init=None, intercept_init=None, sample_weight=None): self._validate_params() if self.warm_start and getattr(self, "coef_", None) is not None: if coef_init is None: coef_init = self.coef_ if intercept_init is None: intercept_init = self.intercept_ else: self.coef_ = None self.intercept_ = None # Clear iteration count for multiple call to fit. self.t_ = 1.0 self._partial_fit(X, y, alpha, C, loss, learning_rate, self.max_iter, sample_weight, coef_init, intercept_init) if (self.tol is not None and self.tol > -np.inf and self.n_iter_ == self.max_iter): warnings.warn("Maximum number of iteration reached before " "convergence. Consider increasing max_iter to " "improve the fit.", ConvergenceWarning) return self def fit(self, X, y, coef_init=None, intercept_init=None, sample_weight=None): """Fit linear model with Stochastic Gradient Descent. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Training data y : ndarray of shape (n_samples,) Target values coef_init : ndarray of shape (n_features,), default=None The initial coefficients to warm-start the optimization. intercept_init : ndarray of shape (1,), default=None The initial intercept to warm-start the optimization. sample_weight : array-like, shape (n_samples,), default=None Weights applied to individual samples (1. for unweighted). Returns ------- self : returns an instance of self. """ return self._fit(X, y, alpha=self.alpha, C=1.0, loss=self.loss, learning_rate=self.learning_rate, coef_init=coef_init, intercept_init=intercept_init, sample_weight=sample_weight) def _decision_function(self, X): """Predict using the linear model Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Returns ------- ndarray of shape (n_samples,) Predicted target values per element in X. """ check_is_fitted(self) X = check_array(X, accept_sparse='csr') scores = safe_sparse_dot(X, self.coef_.T, dense_output=True) + self.intercept_ return scores.ravel() def predict(self, X): """Predict using the linear model Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Returns ------- ndarray of shape (n_samples,) Predicted target values per element in X. """ return self._decision_function(X) def _fit_regressor(self, X, y, alpha, C, loss, learning_rate, sample_weight, max_iter): dataset, intercept_decay = make_dataset(X, y, sample_weight) loss_function = self._get_loss_function(loss) penalty_type = self._get_penalty_type(self.penalty) learning_rate_type = self._get_learning_rate_type(learning_rate) if not hasattr(self, "t_"): self.t_ = 1.0 validation_mask = self._make_validation_split(y) validation_score_cb = self._make_validation_score_cb( validation_mask, X, y, sample_weight) random_state = check_random_state(self.random_state) # numpy mtrand expects a C long which is a signed 32 bit integer under # Windows seed = random_state.randint(0, np.iinfo(np.int32).max) tol = self.tol if self.tol is not None else -np.inf if self.average: coef = self._standard_coef intercept = self._standard_intercept average_coef = self._average_coef average_intercept = self._average_intercept else: coef = self.coef_ intercept = self.intercept_ average_coef = None # Not used average_intercept = [0] # Not used coef, intercept, average_coef, average_intercept, self.n_iter_ = \ _plain_sgd(coef, intercept[0], average_coef, average_intercept[0], loss_function, penalty_type, alpha, C, self.l1_ratio, dataset, validation_mask, self.early_stopping, validation_score_cb, int(self.n_iter_no_change), max_iter, tol, int(self.fit_intercept), int(self.verbose), int(self.shuffle), seed, 1.0, 1.0, learning_rate_type, self.eta0, self.power_t, self.t_, intercept_decay, self.average) self.t_ += self.n_iter_ * X.shape[0] if self.average > 0: self._average_intercept = np.atleast_1d(average_intercept) self._standard_intercept = np.atleast_1d(intercept) if self.average <= self.t_ - 1.0: # made enough updates for averaging to be taken into account self.coef_ = average_coef self.intercept_ = np.atleast_1d(average_intercept) else: self.coef_ = coef self.intercept_ = np.atleast_1d(intercept) else: self.intercept_ = np.atleast_1d(intercept) class SGDRegressor(BaseSGDRegressor): """Linear model fitted by minimizing a regularized empirical loss with SGD SGD stands for Stochastic Gradient Descent: the gradient of the loss is estimated each sample at a time and the model is updated along the way with a decreasing strength schedule (aka learning rate). The regularizer is a penalty added to the loss function that shrinks model parameters towards the zero vector using either the squared euclidean norm L2 or the absolute norm L1 or a combination of both (Elastic Net). If the parameter update crosses the 0.0 value because of the regularizer, the update is truncated to 0.0 to allow for learning sparse models and achieve online feature selection. This implementation works with data represented as dense numpy arrays of floating point values for the features. Read more in the :ref:`User Guide `. Parameters ---------- loss : str, default='squared_loss' The loss function to be used. The possible values are 'squared_loss', 'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive' The 'squared_loss' refers to the ordinary least squares fit. 'huber' modifies 'squared_loss' to focus less on getting outliers correct by switching from squared to linear loss past a distance of epsilon. 'epsilon_insensitive' ignores errors less than epsilon and is linear past that; this is the loss function used in SVR. 'squared_epsilon_insensitive' is the same but becomes squared loss past a tolerance of epsilon. More details about the losses formulas can be found in the :ref:`User Guide `. penalty : {'l2', 'l1', 'elasticnet'}, default='l2' The penalty (aka regularization term) to be used. Defaults to 'l2' which is the standard regularizer for linear SVM models. 'l1' and 'elasticnet' might bring sparsity to the model (feature selection) not achievable with 'l2'. alpha : float, default=0.0001 Constant that multiplies the regularization term. The higher the value, the stronger the regularization. Also used to compute the learning rate when set to `learning_rate` is set to 'optimal'. l1_ratio : float, default=0.15 The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1. Only used if `penalty` is 'elasticnet'. fit_intercept : bool, default=True Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. max_iter : int, default=1000 The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the ``fit`` method, and not the :meth:`partial_fit` method. .. versionadded:: 0.19 tol : float, default=1e-3 The stopping criterion. If it is not None, training will stop when (loss > best_loss - tol) for ``n_iter_no_change`` consecutive epochs. .. versionadded:: 0.19 shuffle : bool, default=True Whether or not the training data should be shuffled after each epoch. verbose : int, default=0 The verbosity level. epsilon : float, default=0.1 Epsilon in the epsilon-insensitive loss functions; only if `loss` is 'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'. For 'huber', determines the threshold at which it becomes less important to get the prediction exactly right. For epsilon-insensitive, any differences between the current prediction and the correct label are ignored if they are less than this threshold. random_state : int, RandomState instance, default=None Used for shuffling the data, when ``shuffle`` is set to ``True``. Pass an int for reproducible output across multiple function calls. See :term:`Glossary `. learning_rate : string, default='invscaling' The learning rate schedule: - 'constant': `eta = eta0` - 'optimal': `eta = 1.0 / (alpha * (t + t0))` where t0 is chosen by a heuristic proposed by Leon Bottou. - 'invscaling': `eta = eta0 / pow(t, power_t)` - 'adaptive': eta = eta0, as long as the training keeps decreasing. Each time n_iter_no_change consecutive epochs fail to decrease the training loss by tol or fail to increase validation score by tol if early_stopping is True, the current learning rate is divided by 5. .. versionadded:: 0.20 Added 'adaptive' option eta0 : double, default=0.01 The initial learning rate for the 'constant', 'invscaling' or 'adaptive' schedules. The default value is 0.01. power_t : double, default=0.25 The exponent for inverse scaling learning rate. early_stopping : bool, default=False Whether to use early stopping to terminate training when validation score is not improving. If set to True, it will automatically set aside a fraction of training data as validation and terminate training when validation score returned by the `score` method is not improving by at least `tol` for `n_iter_no_change` consecutive epochs. .. versionadded:: 0.20 Added 'early_stopping' option validation_fraction : float, default=0.1 The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if `early_stopping` is True. .. versionadded:: 0.20 Added 'validation_fraction' option n_iter_no_change : int, default=5 Number of iterations with no improvement to wait before early stopping. .. versionadded:: 0.20 Added 'n_iter_no_change' option warm_start : bool, default=False When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See :term:`the Glossary `. Repeatedly calling fit or partial_fit when warm_start is True can result in a different solution than when calling fit a single time because of the way the data is shuffled. If a dynamic learning rate is used, the learning rate is adapted depending on the number of samples already seen. Calling ``fit`` resets this counter, while ``partial_fit`` will result in increasing the existing counter. average : bool or int, default=False When set to True, computes the averaged SGD weights accross all updates and stores the result in the ``coef_`` attribute. If set to an int greater than 1, averaging will begin once the total number of samples seen reaches `average`. So ``average=10`` will begin averaging after seeing 10 samples. Attributes ---------- coef_ : ndarray of shape (n_features,) Weights assigned to the features. intercept_ : ndarray of shape (1,) The intercept term. average_coef_ : ndarray of shape (n_features,) Averaged weights assigned to the features. Only available if ``average=True``. .. deprecated:: 0.23 Attribute ``average_coef_`` was deprecated in version 0.23 and will be removed in 0.25. average_intercept_ : ndarray of shape (1,) The averaged intercept term. Only available if ``average=True``. .. deprecated:: 0.23 Attribute ``average_intercept_`` was deprecated in version 0.23 and will be removed in 0.25. n_iter_ : int The actual number of iterations before reaching the stopping criterion. t_ : int Number of weight updates performed during training. Same as ``(n_iter_ * n_samples)``. Examples -------- >>> import numpy as np >>> from sklearn.linear_model import SGDRegressor >>> from sklearn.pipeline import make_pipeline >>> from sklearn.preprocessing import StandardScaler >>> n_samples, n_features = 10, 5 >>> rng = np.random.RandomState(0) >>> y = rng.randn(n_samples) >>> X = rng.randn(n_samples, n_features) >>> # Always scale the input. The most convenient way is to use a pipeline. >>> reg = make_pipeline(StandardScaler(), ... SGDRegressor(max_iter=1000, tol=1e-3)) >>> reg.fit(X, y) Pipeline(steps=[('standardscaler', StandardScaler()), ('sgdregressor', SGDRegressor())]) See also -------- Ridge, ElasticNet, Lasso, sklearn.svm.SVR """ @_deprecate_positional_args def __init__(self, loss="squared_loss", *, penalty="l2", alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=1e-3, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, random_state=None, learning_rate="invscaling", eta0=0.01, power_t=0.25, early_stopping=False, validation_fraction=0.1, n_iter_no_change=5, warm_start=False, average=False): super().__init__( loss=loss, penalty=penalty, alpha=alpha, l1_ratio=l1_ratio, fit_intercept=fit_intercept, max_iter=max_iter, tol=tol, shuffle=shuffle, verbose=verbose, epsilon=epsilon, random_state=random_state, learning_rate=learning_rate, eta0=eta0, power_t=power_t, early_stopping=early_stopping, validation_fraction=validation_fraction, n_iter_no_change=n_iter_no_change, warm_start=warm_start, average=average)