# 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 ..externals.joblib import Parallel, delayed 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 from ..exceptions import ConvergenceWarning from ..externals import six from .sgd_fast import plain_sgd, average_sgd from ..utils import compute_class_weight from ..utils import deprecated 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 LEARNING_RATE_TYPES = {"constant": 1, "optimal": 2, "invscaling": 3, "pa1": 4, "pa2": 5} PENALTY_TYPES = {"none": 0, "l2": 2, "l1": 1, "elasticnet": 3} DEFAULT_EPSILON = 0.1 # Default value of ``epsilon`` parameter. class BaseSGD(six.with_metaclass(ABCMeta, BaseEstimator, SparseCoefMixin)): """Base class for SGD classification and regression.""" def __init__(self, loss, penalty='l2', alpha=0.0001, C=1.0, l1_ratio=0.15, fit_intercept=True, max_iter=None, tol=None, shuffle=True, verbose=0, epsilon=0.1, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, warm_start=False, average=False, n_iter=None): 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.warm_start = warm_start self.average = average self.n_iter = n_iter 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(set_max_iter=False) def set_params(self, *args, **kwargs): super(BaseSGD, self).set_params(*args, **kwargs) self._validate_params(set_max_iter=False) return self @abstractmethod def fit(self, X, y): """Fit model.""" def _validate_params(self, set_max_iter=True): """Validate input params. """ if not isinstance(self.shuffle, bool): raise ValueError("shuffle must be either True or False") 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.learning_rate in ("constant", "invscaling"): 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) if not set_max_iter: return # n_iter deprecation, set self._max_iter, self._tol self._tol = self.tol if self.n_iter is not None: warnings.warn("n_iter parameter is deprecated in 0.19 and will be" " removed in 0.21. Use max_iter and tol instead.", DeprecationWarning) # Same behavior as before 0.19 max_iter = self.n_iter self._tol = None elif self.tol is None and self.max_iter is None: warnings.warn( "max_iter and tol parameters have been added in %s in 0.19. If" " both are left unset, they default to max_iter=5 and tol=None" ". If tol is not None, max_iter defaults to max_iter=1000. " "From 0.21, default max_iter will be 1000, " "and default tol will be 1e-3." % type(self), FutureWarning) # Before 0.19, default was n_iter=5 max_iter = 5 else: max_iter = self.max_iter if self.max_iter is not None else 1000 self._max_iter = max_iter 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 _validate_sample_weight(self, sample_weight, n_samples): """Set the sample weight array.""" if sample_weight is None: # uniform sample weights sample_weight = np.ones(n_samples, dtype=np.float64, order='C') else: # user-provided array sample_weight = np.asarray(sample_weight, dtype=np.float64, order="C") if sample_weight.shape[0] != n_samples: raise ValueError("Shapes of X and sample_weight do not match.") return sample_weight 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 _prepare_fit_binary(est, y, i): """Initialization for fit_binary. Returns y, coef, 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): """Fit a single binary classifier. The i'th class is considered the "positive" class. """ # 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] dataset, intercept_decay = make_dataset(X, y_i, sample_weight) penalty_type = est._get_penalty_type(est.penalty) learning_rate_type = est._get_learning_rate_type(learning_rate) # XXX should have random_state_! random_state = check_random_state(est.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 = est.tol if est.tol is not None else -np.inf if not est.average: return plain_sgd(coef, intercept, est.loss_function_, penalty_type, alpha, C, est.l1_ratio, dataset, 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) else: standard_coef, standard_intercept, average_coef, average_intercept, \ n_iter_ = average_sgd(coef, intercept, average_coef, average_intercept, est.loss_function_, penalty_type, alpha, C, est.l1_ratio, dataset, 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 len(est.classes_) == 2: est.average_intercept_[0] = average_intercept else: est.average_intercept_[i] = average_intercept return standard_coef, standard_intercept, n_iter_ class BaseSGDClassifier(six.with_metaclass(ABCMeta, BaseSGD, LinearClassifierMixin)): 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 def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=None, tol=None, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, class_weight=None, warm_start=False, average=False, n_iter=None): super(BaseSGDClassifier, self).__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, warm_start=warm_start, average=average, n_iter=n_iter) self.class_weight = class_weight self.n_jobs = int(n_jobs) @property @deprecated("Attribute loss_function was deprecated in version 0.19 and " "will be removed in 0.21. Use ``loss_function_`` instead") def loss_function(self): return self.loss_function_ 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, 'csr', dtype=np.float64, order="C") 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, self.classes_, y) sample_weight = self._validate_sample_weight(sample_weight, n_samples) 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 class labels must be " "greater than one.") 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 = check_X_y(X, y, 'csr', dtype=np.float64, order="C") n_samples, n_features = X.shape # 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) 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. """ # Use joblib to fit OvA in parallel. result = Parallel(n_jobs=self.n_jobs, backend="threading", verbose=self.verbose)( delayed(fit_binary)(self, i, X, y, alpha, C, learning_rate, max_iter, self._expanded_class_weight[i], 1., sample_weight) for i in range(len(self.classes_))) # 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): """Fit linear model with Stochastic Gradient Descent. Parameters ---------- X : {array-like, sparse matrix}, shape (n_samples, n_features) Subset of the training data y : numpy array, shape (n_samples,) Subset of the target values classes : array, shape (n_classes,) 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,), optional Weights applied to individual samples. If not provided, uniform weights are assumed. Returns ------- self : returns an instance of self. """ self._validate_params() 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, 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 : numpy array, shape (n_samples,) Target values coef_init : array, shape (n_classes, n_features) The initial coefficients to warm-start the optimization. intercept_init : array, shape (n_classes,) The initial intercept to warm-start the optimization. sample_weight : array-like, shape (n_samples,), optional 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, a.o.) 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, see 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 SGDRegressor for a description. penalty : str, 'none', 'l2', 'l1', or 'elasticnet' 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 Constant that multiplies the regularization term. Defaults to 0.0001 Also used to compute learning_rate when set to 'optimal'. l1_ratio : float The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1. Defaults to 0.15. fit_intercept : bool Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True. max_iter : int, optional The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the ``fit`` method, and not the `partial_fit`. Defaults to 5. Defaults to 1000 from 0.21, or if tol is not None. .. versionadded:: 0.19 tol : float or None, optional The stopping criterion. If it is not None, the iterations will stop when (loss > previous_loss - tol). Defaults to None. Defaults to 1e-3 from 0.21. .. versionadded:: 0.19 shuffle : bool, optional Whether or not the training data should be shuffled after each epoch. Defaults to True. verbose : integer, optional The verbosity level epsilon : float 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 : integer, optional The number of CPUs to use to do the OVA (One Versus All, for multi-class problems) computation. -1 means 'all CPUs'. Defaults to 1. random_state : int, RandomState instance or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. 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`. learning_rate : string, optional The learning rate schedule: - 'constant': eta = eta0 - 'optimal': eta = 1.0 / (alpha * (t + t0)) [default] - 'invscaling': eta = eta0 / pow(t, power_t) where t0 is chosen by a heuristic proposed by Leon Bottou. eta0 : double The initial learning rate for the 'constant' or 'invscaling' schedules. The default value is 0.0 as eta0 is not used by the default schedule 'optimal'. power_t : double The exponent for inverse scaling learning rate [default 0.5]. class_weight : dict, {class_label: weight} or "balanced" or None, optional 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, optional When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. average : bool or int, optional When set to True, computes the averaged SGD weights 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. n_iter : int, optional The number of passes over the training data (aka epochs). Defaults to None. Deprecated, will be removed in 0.21. .. versionchanged:: 0.19 Deprecated Attributes ---------- coef_ : array, shape (1, n_features) if n_classes == 2 else (n_classes,\ n_features) Weights assigned to the features. intercept_ : array, shape (1,) if n_classes == 2 else (n_classes,) Constants in decision function. n_iter_ : int The actual number of iterations to reach the stopping criterion. For multiclass fits, it is the maximum over every binary fit. loss_function_ : concrete ``LossFunction`` Examples -------- >>> import numpy as np >>> from sklearn import linear_model >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]]) >>> Y = np.array([1, 1, 2, 2]) >>> clf = linear_model.SGDClassifier() >>> clf.fit(X, Y) ... #doctest: +NORMALIZE_WHITESPACE SGDClassifier(alpha=0.0001, average=False, class_weight=None, epsilon=0.1, eta0=0.0, fit_intercept=True, l1_ratio=0.15, learning_rate='optimal', loss='hinge', max_iter=None, n_iter=None, n_jobs=1, penalty='l2', power_t=0.5, random_state=None, shuffle=True, tol=None, verbose=0, warm_start=False) >>> print(clf.predict([[-0.8, -1]])) [1] See also -------- LinearSVC, LogisticRegression, Perceptron """ def __init__(self, loss="hinge", penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=None, tol=None, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, n_jobs=1, random_state=None, learning_rate="optimal", eta0=0.0, power_t=0.5, class_weight=None, warm_start=False, average=False, n_iter=None): super(SGDClassifier, self).__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, class_weight=class_weight, warm_start=warm_start, average=average, n_iter=n_iter) def _check_proba(self): check_is_fitted(self, "t_") 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) Returns ------- array, 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): 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, shape (n_samples, n_features) 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(BaseSGD, RegressorMixin): loss_functions = { "squared_loss": (SquaredLoss, ), "huber": (Huber, DEFAULT_EPSILON), "epsilon_insensitive": (EpsilonInsensitive, DEFAULT_EPSILON), "squared_epsilon_insensitive": (SquaredEpsilonInsensitive, DEFAULT_EPSILON), } @abstractmethod def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=None, tol=None, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, random_state=None, learning_rate="invscaling", eta0=0.01, power_t=0.25, warm_start=False, average=False, n_iter=None): super(BaseSGDRegressor, self).__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, warm_start=warm_start, average=average, n_iter=n_iter) def _partial_fit(self, X, y, alpha, C, loss, learning_rate, max_iter, sample_weight, coef_init, intercept_init): X, y = check_X_y(X, y, "csr", copy=False, order='C', dtype=np.float64) y = y.astype(np.float64, copy=False) n_samples, n_features = X.shape # Allocate datastructures from input arguments sample_weight = self._validate_sample_weight(sample_weight, n_samples) 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): """Fit linear model with Stochastic Gradient Descent. 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,), optional Weights applied to individual samples. If not provided, uniform weights are assumed. Returns ------- self : returns an instance of self. """ self._validate_params() 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 if self.average > 0: self.standard_intercept_ = self.intercept_ self.standard_coef_ = self.coef_ 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, 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 : numpy array, shape (n_samples,) Target values coef_init : array, shape (n_features,) The initial coefficients to warm-start the optimization. intercept_init : array, shape (1,) The initial intercept to warm-start the optimization. sample_weight : array-like, shape (n_samples,), optional 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 ------- array, shape (n_samples,) Predicted target values per element in X. """ check_is_fitted(self, ["t_", "coef_", "intercept_"], all_or_any=all) 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 ------- array, 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 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 > 0: self.standard_coef_, self.standard_intercept_, \ self.average_coef_, self.average_intercept_, self.n_iter_ =\ average_sgd(self.standard_coef_, self.standard_intercept_[0], self.average_coef_, self.average_intercept_[0], loss_function, penalty_type, alpha, C, self.l1_ratio, dataset, 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.average_intercept_ = np.atleast_1d(self.average_intercept_) self.standard_intercept_ = np.atleast_1d(self.standard_intercept_) self.t_ += self.n_iter_ * X.shape[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.intercept_ = self.standard_intercept_ else: self.coef_, self.intercept_, self.n_iter_ = \ plain_sgd(self.coef_, self.intercept_[0], loss_function, penalty_type, alpha, C, self.l1_ratio, dataset, 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.t_ += self.n_iter_ * X.shape[0] self.intercept_ = np.atleast_1d(self.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. penalty : str, 'none', 'l2', 'l1', or 'elasticnet' 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 Constant that multiplies the regularization term. Defaults to 0.0001 Also used to compute learning_rate when set to 'optimal'. l1_ratio : float The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1. Defaults to 0.15. fit_intercept : bool Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True. max_iter : int, optional The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the ``fit`` method, and not the `partial_fit`. Defaults to 5. Defaults to 1000 from 0.21, or if tol is not None. .. versionadded:: 0.19 tol : float or None, optional The stopping criterion. If it is not None, the iterations will stop when (loss > previous_loss - tol). Defaults to None. Defaults to 1e-3 from 0.21. .. versionadded:: 0.19 shuffle : bool, optional Whether or not the training data should be shuffled after each epoch. Defaults to True. verbose : integer, optional The verbosity level. epsilon : float 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 or None, optional (default=None) The seed of the pseudo random number generator to use when shuffling the data. 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`. learning_rate : string, optional The learning rate schedule: - 'constant': eta = eta0 - 'optimal': eta = 1.0 / (alpha * (t + t0)) [default] - 'invscaling': eta = eta0 / pow(t, power_t) where t0 is chosen by a heuristic proposed by Leon Bottou. eta0 : double, optional The initial learning rate [default 0.01]. power_t : double, optional The exponent for inverse scaling learning rate [default 0.25]. warm_start : bool, optional When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. average : bool or int, optional When set to True, computes the averaged SGD weights 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. n_iter : int, optional The number of passes over the training data (aka epochs). Defaults to None. Deprecated, will be removed in 0.21. .. versionchanged:: 0.19 Deprecated Attributes ---------- coef_ : array, shape (n_features,) Weights assigned to the features. intercept_ : array, shape (1,) The intercept term. average_coef_ : array, shape (n_features,) Averaged weights assigned to the features. average_intercept_ : array, shape (1,) The averaged intercept term. n_iter_ : int The actual number of iterations to reach the stopping criterion. Examples -------- >>> import numpy as np >>> from sklearn import linear_model >>> n_samples, n_features = 10, 5 >>> np.random.seed(0) >>> y = np.random.randn(n_samples) >>> X = np.random.randn(n_samples, n_features) >>> clf = linear_model.SGDRegressor() >>> clf.fit(X, y) ... #doctest: +NORMALIZE_WHITESPACE SGDRegressor(alpha=0.0001, average=False, epsilon=0.1, eta0=0.01, fit_intercept=True, l1_ratio=0.15, learning_rate='invscaling', loss='squared_loss', max_iter=None, n_iter=None, penalty='l2', power_t=0.25, random_state=None, shuffle=True, tol=None, verbose=0, warm_start=False) See also -------- Ridge, ElasticNet, Lasso, SVR """ def __init__(self, loss="squared_loss", penalty="l2", alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=None, tol=None, shuffle=True, verbose=0, epsilon=DEFAULT_EPSILON, random_state=None, learning_rate="invscaling", eta0=0.01, power_t=0.25, warm_start=False, average=False, n_iter=None): super(SGDRegressor, self).__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, warm_start=warm_start, average=average, n_iter=n_iter)