package sklearn

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 <sgd>`.

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 : '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. Also used to compute learning_rate when 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.

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, the iterations 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 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, 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': default 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.

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 is not improving by at least tol for n_iter_no_change consecutive epochs.

.. versionadded:: 0.20

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

n_iter_no_change : int, default=5 Number of iterations with no improvement to wait before early stopping.

.. versionadded:: 0.20

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 <warm_start>`.

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 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.

average_intercept_ : ndarray of shape (1,) The averaged intercept term.

n_iter_ : int The actual number of iterations to reach 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 import linear_model >>> n_samples, n_features = 10, 5 >>> rng = np.random.RandomState(0) >>> y = rng.randn(n_samples) >>> X = rng.randn(n_samples, n_features) >>> clf = linear_model.SGDRegressor(max_iter=1000, tol=1e-3) >>> clf.fit(X, y) SGDRegressor()

See also -------- Ridge, ElasticNet, Lasso, sklearn.svm.SVR

Convert coefficient matrix to dense array format.

Converts the ``coef_`` member (back) to a numpy.ndarray. This is the default format of ``coef_`` and is required for fitting, so calling this method is only required on models that have previously been sparsified; otherwise, it is a no-op.

Returns ------- self Fitted estimator.

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.

Get parameters for this estimator.

Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns ------- params : mapping of string to any Parameter names mapped to their values.

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.

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 the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.

Parameters ---------- X : array-like of shape (n_samples, n_features) Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

y : array-like of shape (n_samples,) or (n_samples, n_outputs) True values for X.

sample_weight : array-like of shape (n_samples,), default=None Sample weights.

Returns ------- score : float R^2 of self.predict(X) wrt. y.

Notes ----- The R2 score used when calling ``score`` on a regressor will use ``multioutput='uniform_average'`` from version 0.23 to keep consistent with :func:`~sklearn.metrics.r2_score`. This will influence the ``score`` method of all the multioutput regressors (except for :class:`~sklearn.multioutput.MultiOutputRegressor`). To specify the default value manually and avoid the warning, please either call :func:`~sklearn.metrics.r2_score` directly or make a custom scorer with :func:`~sklearn.metrics.make_scorer` (the built-in scorer ``'r2'`` uses ``multioutput='uniform_average'``).

Set and validate the parameters of estimator.

Parameters ---------- **kwargs : dict Estimator parameters.

Returns ------- self : object Estimator instance.

Convert coefficient matrix to sparse format.

Converts the ``coef_`` member to a scipy.sparse matrix, which for L1-regularized models can be much more memory- and storage-efficient than the usual numpy.ndarray representation.

The ``intercept_`` member is not converted.

Returns ------- self Fitted estimator.

Notes ----- For non-sparse models, i.e. when there are not many zeros in ``coef_``, this may actually *increase* memory usage, so use this method with care. A rule of thumb is that the number of zero elements, which can be computed with ``(coef_ == 0).sum()``, must be more than 50% for this to provide significant benefits.

After calling this method, further fitting with the partial_fit method (if any) will not work until you call densify.

Attribute coef_: get value or raise Not_found if None.

Attribute coef_: get value as an option.

Attribute intercept_: get value or raise Not_found if None.

Attribute intercept_: get value as an option.

Attribute average_coef_: get value or raise Not_found if None.

Attribute average_coef_: get value as an option.

Attribute average_intercept_: get value or raise Not_found if None.

Attribute average_intercept_: get value as an option.

Attribute n_iter_: get value or raise Not_found if None.

Attribute n_iter_: get value as an option.

Attribute t_: get value or raise Not_found if None.

Attribute t_: get value as an option.

Print the object to a human-readable representation.

Print the object to a human-readable representation.

Pretty-print the object to a formatter.