fit(X, y, sample_weight=None) [source]

Fit Ridge classifier with cv.  Parameters

Xndarray of shape (n_samples, n_features)

Training vectors, where n_samples is the number of samples and n_features is the number of features. When using GCV, will be cast to float64 if necessary.
yndarray of shape (n_samples,)

Target values. Will be cast to X’s dtype if necessary.
sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.    Returns

selfobject


get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.


predict(X) [source]

Predict class labels for samples in X.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape [n_samples]

Predicted class label per sample.


score(X, y, sample_weight=None) [source]

Return the mean accuracy on the given test data and labels. In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.  Parameters

Xarray-like of shape (n_samples, n_features)

Test samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True labels for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

Mean accuracy of self.predict(X) wrt. y.


set_params(**params) [source]

Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters

**paramsdict

Estimator parameters.    Returns

selfestimator instance

Estimator instance.


class sklearn.linear_model.RidgeCV(alphas=0.1, 1.0, 10.0, *, fit_intercept=True, normalize=False, scoring=None, cv=None, gcv_mode=None, store_cv_values=False, alpha_per_target=False) [source]

Ridge regression with built-in cross-validation. See glossary entry for cross-validation estimator. By default, it performs efficient Leave-One-Out Cross-Validation. Read more in the User Guide.  Parameters

alphasndarray of shape (n_alphas,), default=(0.1, 1.0, 10.0)

Array of alpha values to try. Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to 1 / (2C) in other linear models such as LogisticRegression or LinearSVC. If using Leave-One-Out cross-validation, alphas must be positive.
fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
normalizebool, default=False

This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
scoringstring, callable, default=None

A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). If None, the negative mean squared error if cv is ‘auto’ or None (i.e. when using leave-one-out cross-validation), and r2 score otherwise.
cvint, cross-validation generator or an iterable, default=None

Determines the cross-validation splitting strategy. Possible inputs for cv are:  None, to use the efficient Leave-One-Out cross-validation integer, to specify the number of folds.
CV splitter, An iterable yielding (train, test) splits as arrays of indices.  For integer/None inputs, if y is binary or multiclass, StratifiedKFold is used, else, KFold is used. Refer User Guide for the various cross-validation strategies that can be used here.
gcv_mode{‘auto’, ‘svd’, eigen’}, default=’auto’

Flag indicating which strategy to use when performing Leave-One-Out Cross-Validation. Options are: 'auto' : use 'svd' if n_samples > n_features, otherwise use 'eigen'
'svd' : force use of singular value decomposition of X when X is
    dense, eigenvalue decomposition of X^T.X when X is sparse.
'eigen' : force computation via eigendecomposition of X.X^T
 The ‘auto’ mode is the default and is intended to pick the cheaper option of the two depending on the shape of the training data.
store_cv_valuesbool, default=False

Flag indicating if the cross-validation values corresponding to each alpha should be stored in the cv_values_ attribute (see below). This flag is only compatible with cv=None (i.e. using Leave-One-Out Cross-Validation).
alpha_per_targetbool, default=False

Flag indicating whether to optimize the alpha value (picked from the alphas parameter list) for each target separately (for multi-output settings: multiple prediction targets). When set to True, after fitting, the alpha_ attribute will contain a value for each target. When set to False, a single alpha is used for all targets.  New in version 0.24.     Attributes

cv_values_ndarray of shape (n_samples, n_alphas) or shape (n_samples, n_targets, n_alphas), optional

Cross-validation values for each alpha (only available if store_cv_values=True and cv=None). After fit() has been called, this attribute will contain the mean squared errors (by default) or the values of the {loss,score}_func function (if provided in the constructor).
coef_ndarray of shape (n_features) or (n_targets, n_features)

Weight vector(s).
intercept_float or ndarray of shape (n_targets,)

Independent term in decision function. Set to 0.0 if fit_intercept = False.
alpha_float or ndarray of shape (n_targets,)

Estimated regularization parameter, or, if alpha_per_target=True, the estimated regularization parameter for each target.
best_score_float or ndarray of shape (n_targets,)

Score of base estimator with best alpha, or, if alpha_per_target=True, a score for each target.  New in version 0.23.       See also
Ridge

Ridge regression.
RidgeClassifier

Ridge classifier.
RidgeClassifierCV

Ridge classifier with built-in cross validation.    Examples >>> from sklearn.datasets import load_diabetes
>>> from sklearn.linear_model import RidgeCV
>>> X, y = load_diabetes(return_X_y=True)
>>> clf = RidgeCV(alphas=[1e-3, 1e-2, 1e-1, 1]).fit(X, y)
>>> clf.score(X, y)
0.5166...
 Methods
fit(X, y[, sample_weight]) Fit Ridge regression model with cv.
get_params([deep]) Get parameters for this estimator.
predict(X) Predict using the linear model.
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params) Set the parameters of this estimator.
fit(X, y, sample_weight=None) [source]

Fit Ridge regression model with cv.  Parameters

Xndarray of shape (n_samples, n_features)

Training data. If using GCV, will be cast to float64 if necessary.
yndarray of shape (n_samples,) or (n_samples, n_targets)

Target values. Will be cast to X’s dtype if necessary.
sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.    Returns

selfobject
   Notes When sample_weight is provided, the selected hyperparameter may depend on whether we use leave-one-out cross-validation (cv=None or cv=’auto’) or another form of cross-validation, because only leave-one-out cross-validation takes the sample weights into account when computing the validation score.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

predict(X) [source]

Predict using the linear model.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params) [source]

Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters

**paramsdict

Estimator parameters.    Returns

selfestimator instance

Estimator instance.


sklearn.linear_model.RidgeCV
class sklearn.linear_model.RidgeCV(alphas=0.1, 1.0, 10.0, *, fit_intercept=True, normalize=False, scoring=None, cv=None, gcv_mode=None, store_cv_values=False, alpha_per_target=False) [source]

Ridge regression with built-in cross-validation. See glossary entry for cross-validation estimator. By default, it performs efficient Leave-One-Out Cross-Validation. Read more in the User Guide.  Parameters

alphasndarray of shape (n_alphas,), default=(0.1, 1.0, 10.0)

Array of alpha values to try. Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to 1 / (2C) in other linear models such as LogisticRegression or LinearSVC. If using Leave-One-Out cross-validation, alphas must be positive.
fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
normalizebool, default=False

This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.
scoringstring, callable, default=None

A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). If None, the negative mean squared error if cv is ‘auto’ or None (i.e. when using leave-one-out cross-validation), and r2 score otherwise.
cvint, cross-validation generator or an iterable, default=None

Determines the cross-validation splitting strategy. Possible inputs for cv are:  None, to use the efficient Leave-One-Out cross-validation integer, to specify the number of folds.
CV splitter, An iterable yielding (train, test) splits as arrays of indices.  For integer/None inputs, if y is binary or multiclass, StratifiedKFold is used, else, KFold is used. Refer User Guide for the various cross-validation strategies that can be used here.
gcv_mode{‘auto’, ‘svd’, eigen’}, default=’auto’

Flag indicating which strategy to use when performing Leave-One-Out Cross-Validation. Options are: 'auto' : use 'svd' if n_samples > n_features, otherwise use 'eigen'
'svd' : force use of singular value decomposition of X when X is
    dense, eigenvalue decomposition of X^T.X when X is sparse.
'eigen' : force computation via eigendecomposition of X.X^T
 The ‘auto’ mode is the default and is intended to pick the cheaper option of the two depending on the shape of the training data.
store_cv_valuesbool, default=False

Flag indicating if the cross-validation values corresponding to each alpha should be stored in the cv_values_ attribute (see below). This flag is only compatible with cv=None (i.e. using Leave-One-Out Cross-Validation).
alpha_per_targetbool, default=False

Flag indicating whether to optimize the alpha value (picked from the alphas parameter list) for each target separately (for multi-output settings: multiple prediction targets). When set to True, after fitting, the alpha_ attribute will contain a value for each target. When set to False, a single alpha is used for all targets.  New in version 0.24.     Attributes

cv_values_ndarray of shape (n_samples, n_alphas) or shape (n_samples, n_targets, n_alphas), optional

Cross-validation values for each alpha (only available if store_cv_values=True and cv=None). After fit() has been called, this attribute will contain the mean squared errors (by default) or the values of the {loss,score}_func function (if provided in the constructor).
coef_ndarray of shape (n_features) or (n_targets, n_features)

Weight vector(s).
intercept_float or ndarray of shape (n_targets,)

Independent term in decision function. Set to 0.0 if fit_intercept = False.
alpha_float or ndarray of shape (n_targets,)

Estimated regularization parameter, or, if alpha_per_target=True, the estimated regularization parameter for each target.
best_score_float or ndarray of shape (n_targets,)

Score of base estimator with best alpha, or, if alpha_per_target=True, a score for each target.  New in version 0.23.       See also
Ridge

Ridge regression.
RidgeClassifier

Ridge classifier.
RidgeClassifierCV

Ridge classifier with built-in cross validation.    Examples >>> from sklearn.datasets import load_diabetes
>>> from sklearn.linear_model import RidgeCV
>>> X, y = load_diabetes(return_X_y=True)
>>> clf = RidgeCV(alphas=[1e-3, 1e-2, 1e-1, 1]).fit(X, y)
>>> clf.score(X, y)
0.5166...
 Methods
fit(X, y[, sample_weight]) Fit Ridge regression model with cv.
get_params([deep]) Get parameters for this estimator.
predict(X) Predict using the linear model.
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params) Set the parameters of this estimator.
fit(X, y, sample_weight=None) [source]

Fit Ridge regression model with cv.  Parameters

Xndarray of shape (n_samples, n_features)

Training data. If using GCV, will be cast to float64 if necessary.
yndarray of shape (n_samples,) or (n_samples, n_targets)

Target values. Will be cast to X’s dtype if necessary.
sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.    Returns

selfobject
   Notes When sample_weight is provided, the selected hyperparameter may depend on whether we use leave-one-out cross-validation (cv=None or cv=’auto’) or another form of cross-validation, because only leave-one-out cross-validation takes the sample weights into account when computing the validation score.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

predict(X) [source]

Predict using the linear model.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params) [source]

Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters

**paramsdict

Estimator parameters.    Returns

selfestimator instance

Estimator instance.

 Examples using sklearn.linear_model.RidgeCV

  Combine predictors using stacking

  Common pitfalls in interpretation of coefficients of linear models

  Face completion with a multi-output estimators

  Effect of transforming the targets in regression model


fit(X, y, sample_weight=None) [source]

Fit Ridge regression model with cv.  Parameters

Xndarray of shape (n_samples, n_features)

Training data. If using GCV, will be cast to float64 if necessary.
yndarray of shape (n_samples,) or (n_samples, n_targets)

Target values. Will be cast to X’s dtype if necessary.
sample_weightfloat or ndarray of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight.    Returns

selfobject
   Notes When sample_weight is provided, the selected hyperparameter may depend on whether we use leave-one-out cross-validation (cv=None or cv=’auto’) or another form of cross-validation, because only leave-one-out cross-validation takes the sample weights into account when computing the validation score.


predict(X) [source]

Predict using the linear model.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape (n_samples,)

Returns predicted values.


score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).


sklearn.linear_model.ridge_regression(X, y, alpha, *, sample_weight=None, solver='auto', max_iter=None, tol=0.001, verbose=0, random_state=None, return_n_iter=False, return_intercept=False, check_input=True) [source]

Solve the ridge equation by the method of normal equations. Read more in the User Guide.  Parameters

X{ndarray, sparse matrix, LinearOperator} of shape (n_samples, n_features)

Training data
yndarray of shape (n_samples,) or (n_samples, n_targets)

Target values
alphafloat or array-like of shape (n_targets,)

Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to 1 / (2C) in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.
sample_weightfloat or array-like of shape (n_samples,), default=None

Individual weights for each sample. If given a float, every sample will have the same weight. If sample_weight is not None and solver=’auto’, the solver will be set to ‘cholesky’.  New in version 0.17.
solver{‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}, default=’auto’

Solver to use in the computational routines:  ‘auto’ chooses the solver automatically based on the type of data. ‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’. ‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution via a Cholesky decomposition of dot(X.T, X) ‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter). ‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure. ‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its improved, unbiased version named SAGA. Both methods also use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.  All last five solvers support both dense and sparse data. However, only ‘sag’ and ‘sparse_cg’ supports sparse input when fit_intercept is True.  New in version 0.17: Stochastic Average Gradient descent solver.   New in version 0.19: SAGA solver.
max_iterint, default=None

Maximum number of iterations for conjugate gradient solver. For the ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined by scipy.sparse.linalg. For ‘sag’ and saga solver, the default value is 1000.
tolfloat, default=1e-3

Precision of the solution.
verboseint, default=0

Verbosity level. Setting verbose > 0 will display additional information depending on the solver used.
random_stateint, RandomState instance, default=None

Used when solver == ‘sag’ or ‘saga’ to shuffle the data. See Glossary for details.
return_n_iterbool, default=False

If True, the method also returns n_iter, the actual number of iteration performed by the solver.  New in version 0.17.
return_interceptbool, default=False

If True and if X is sparse, the method also returns the intercept, and the solver is automatically changed to ‘sag’. This is only a temporary fix for fitting the intercept with sparse data. For dense data, use sklearn.linear_model._preprocess_data before your regression.  New in version 0.17.
check_inputbool, default=True

If False, the input arrays X and y will not be checked.  New in version 0.21.     Returns

coefndarray of shape (n_features,) or (n_targets, n_features)

Weight vector(s).
n_iterint, optional

The actual number of iteration performed by the solver. Only returned if return_n_iter is True.
interceptfloat or ndarray of shape (n_targets,)

The intercept of the model. Only returned if return_intercept is True and if X is a scipy sparse array.     Notes This function won’t compute the intercept.


class sklearn.linear_model.SGDClassifier(loss='hinge', *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=0.001, shuffle=True, verbose=0, epsilon=0.1, 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) [source]

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 User Guide.  Parameters

lossstr, 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. More details about the losses formulas can be found in the 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’.
alphafloat, 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_ratiofloat, 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_interceptbool, default=True

Whether the intercept should be estimated or not. If False, the data is assumed to be already centered.
max_iterint, 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 partial_fit method.  New in version 0.19.
tolfloat, 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.  New in version 0.19.
shufflebool, default=True

Whether or not the training data should be shuffled after each epoch.
verboseint, default=0

The verbosity level.
epsilonfloat, 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_jobsint, 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 joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_stateint, 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 Glossary.
learning_ratestr, 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.  New in version 0.20: Added ‘adaptive’ option
eta0double, 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_tdouble, default=0.5

The exponent for inverse scaling learning rate [default 0.5].
early_stoppingbool, 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.  New in version 0.20: Added ‘early_stopping’ option
validation_fractionfloat, 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.  New in version 0.20: Added ‘validation_fraction’ option
n_iter_no_changeint, default=5

Number of iterations with no improvement to wait before early stopping.  New in version 0.20: Added ‘n_iter_no_change’ option
class_weightdict, {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_startbool, default=False

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See 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.
averagebool 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]
 Methods
decision_function(X) Predict confidence scores for samples.
densify() Convert coefficient matrix to dense array format.
fit(X, y[, coef_init, intercept_init, …]) Fit linear model with Stochastic Gradient Descent.
get_params([deep]) Get parameters for this estimator.
partial_fit(X, y[, classes, sample_weight]) Perform one epoch of stochastic gradient descent on given samples.
predict(X) Predict class labels for samples in X.
score(X, y[, sample_weight]) Return the mean accuracy on the given test data and labels.
set_params(**kwargs) Set and validate the parameters of estimator.
sparsify() Convert coefficient matrix to sparse format.
decision_function(X) [source]

Predict confidence scores for samples. The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns
 array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)

Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.

densify() [source]

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(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data.
yndarray of shape (n_samples,)

Target values.
coef_initndarray of shape (n_classes, n_features), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (n_classes,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-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.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

partial_fit(X, y, classes=None, sample_weight=None) [source]

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.
yndarray of shape (n_samples,)

Subset of the target values.
classesndarray 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_weightarray-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(X) [source]

Predict class labels for samples in X.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape [n_samples]

Predicted class label per sample.

property predict_log_proba
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

Tarray-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_.

property predict_proba
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 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

score(X, y, sample_weight=None) [source]

Return the mean accuracy on the given test data and labels. In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.  Parameters

Xarray-like of shape (n_samples, n_features)

Test samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True labels for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

Mean accuracy of self.predict(X) wrt. y.

set_params(**kwargs) [source]

Set and validate the parameters of estimator.  Parameters

**kwargsdict

Estimator parameters.    Returns

selfobject

Estimator instance.

sparsify() [source]

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.


sklearn.linear_model.SGDClassifier
class sklearn.linear_model.SGDClassifier(loss='hinge', *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=0.001, shuffle=True, verbose=0, epsilon=0.1, 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) [source]

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 User Guide.  Parameters

lossstr, 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. More details about the losses formulas can be found in the 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’.
alphafloat, 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_ratiofloat, 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_interceptbool, default=True

Whether the intercept should be estimated or not. If False, the data is assumed to be already centered.
max_iterint, 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 partial_fit method.  New in version 0.19.
tolfloat, 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.  New in version 0.19.
shufflebool, default=True

Whether or not the training data should be shuffled after each epoch.
verboseint, default=0

The verbosity level.
epsilonfloat, 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_jobsint, 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 joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_stateint, 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 Glossary.
learning_ratestr, 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.  New in version 0.20: Added ‘adaptive’ option
eta0double, 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_tdouble, default=0.5

The exponent for inverse scaling learning rate [default 0.5].
early_stoppingbool, 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.  New in version 0.20: Added ‘early_stopping’ option
validation_fractionfloat, 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.  New in version 0.20: Added ‘validation_fraction’ option
n_iter_no_changeint, default=5

Number of iterations with no improvement to wait before early stopping.  New in version 0.20: Added ‘n_iter_no_change’ option
class_weightdict, {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_startbool, default=False

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See 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.
averagebool 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]
 Methods
decision_function(X) Predict confidence scores for samples.
densify() Convert coefficient matrix to dense array format.
fit(X, y[, coef_init, intercept_init, …]) Fit linear model with Stochastic Gradient Descent.
get_params([deep]) Get parameters for this estimator.
partial_fit(X, y[, classes, sample_weight]) Perform one epoch of stochastic gradient descent on given samples.
predict(X) Predict class labels for samples in X.
score(X, y[, sample_weight]) Return the mean accuracy on the given test data and labels.
set_params(**kwargs) Set and validate the parameters of estimator.
sparsify() Convert coefficient matrix to sparse format.
decision_function(X) [source]

Predict confidence scores for samples. The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns
 array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)

Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.

densify() [source]

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(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data.
yndarray of shape (n_samples,)

Target values.
coef_initndarray of shape (n_classes, n_features), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (n_classes,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-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.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

partial_fit(X, y, classes=None, sample_weight=None) [source]

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.
yndarray of shape (n_samples,)

Subset of the target values.
classesndarray 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_weightarray-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(X) [source]

Predict class labels for samples in X.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape [n_samples]

Predicted class label per sample.

property predict_log_proba
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

Tarray-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_.

property predict_proba
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 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

score(X, y, sample_weight=None) [source]

Return the mean accuracy on the given test data and labels. In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted.  Parameters

Xarray-like of shape (n_samples, n_features)

Test samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True labels for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

Mean accuracy of self.predict(X) wrt. y.

set_params(**kwargs) [source]

Set and validate the parameters of estimator.  Parameters

**kwargsdict

Estimator parameters.    Returns

selfobject

Estimator instance.

sparsify() [source]

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.

 Examples using sklearn.linear_model.SGDClassifier

  Model Complexity Influence

  Out-of-core classification of text documents

  SGD: Maximum margin separating hyperplane

  SGD: convex loss functions

  SGD: Penalties

  SGD: Weighted samples

  Comparing various online solvers

  Plot multi-class SGD on the iris dataset

  Early stopping of Stochastic Gradient Descent

  Explicit feature map approximation for RBF kernels

  Comparing randomized search and grid search for hyperparameter estimation

  Sample pipeline for text feature extraction and evaluation

  Semi-supervised Classification on a Text Dataset

  Classification of text documents using sparse features


decision_function(X) [source]

Predict confidence scores for samples. The confidence score for a sample is proportional to the signed distance of that sample to the hyperplane.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns
 array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)

Confidence scores per (sample, class) combination. In the binary case, confidence score for self.classes_[1] where >0 means this class would be predicted.


densify() [source]

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(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data.
yndarray of shape (n_samples,)

Target values.
coef_initndarray of shape (n_classes, n_features), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (n_classes,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-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.


partial_fit(X, y, classes=None, sample_weight=None) [source]

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.
yndarray of shape (n_samples,)

Subset of the target values.
classesndarray 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_weightarray-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.


property predict_log_proba
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

Tarray-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_.


property predict_proba
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 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


set_params(**kwargs) [source]

Set and validate the parameters of estimator.  Parameters

**kwargsdict

Estimator parameters.    Returns

selfobject

Estimator instance.


sparsify() [source]

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.


class sklearn.linear_model.SGDRegressor(loss='squared_loss', *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=0.001, shuffle=True, verbose=0, epsilon=0.1, 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) [source]

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 User Guide.  Parameters

lossstr, 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 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’.
alphafloat, 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_ratiofloat, 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_interceptbool, default=True

Whether the intercept should be estimated or not. If False, the data is assumed to be already centered.
max_iterint, 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 partial_fit method.  New in version 0.19.
tolfloat, 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.  New in version 0.19.
shufflebool, default=True

Whether or not the training data should be shuffled after each epoch.
verboseint, default=0

The verbosity level.
epsilonfloat, 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_stateint, 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 Glossary.
learning_ratestring, 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.  New in version 0.20: Added ‘adaptive’ option
eta0double, default=0.01

The initial learning rate for the ‘constant’, ‘invscaling’ or ‘adaptive’ schedules. The default value is 0.01.
power_tdouble, default=0.25

The exponent for inverse scaling learning rate.
early_stoppingbool, 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.  New in version 0.20: Added ‘early_stopping’ option
validation_fractionfloat, 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.  New in version 0.20: Added ‘validation_fraction’ option
n_iter_no_changeint, default=5

Number of iterations with no improvement to wait before early stopping.  New in version 0.20: Added ‘n_iter_no_change’ option
warm_startbool, default=False

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See 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.
averagebool 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 since version 0.23: Attribute average_coef_ was deprecated in version 0.23 and will be removed in 1.0 (renaming of 0.25).
average_intercept_ndarray of shape (1,)

The averaged intercept term. Only available if average=True.  Deprecated since version 0.23: Attribute average_intercept_ was deprecated in version 0.23 and will be removed in 1.0 (renaming of 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).      See also
Ridge, ElasticNet, Lasso, sklearn.svm.SVR

  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())])
 Methods
densify() Convert coefficient matrix to dense array format.
fit(X, y[, coef_init, intercept_init, …]) Fit linear model with Stochastic Gradient Descent.
get_params([deep]) Get parameters for this estimator.
partial_fit(X, y[, sample_weight]) Perform one epoch of stochastic gradient descent on given samples.
predict(X) Predict using the linear model
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.
set_params(**kwargs) Set and validate the parameters of estimator.
sparsify() Convert coefficient matrix to sparse format.
densify() [source]

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(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data
yndarray of shape (n_samples,)

Target values
coef_initndarray of shape (n_features,), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (1,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).    Returns

selfreturns an instance of self.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

partial_fit(X, y, sample_weight=None) [source]

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
ynumpy array of shape (n_samples,)

Subset of target values
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples. If not provided, uniform weights are assumed.    Returns

selfreturns an instance of self.

predict(X) [source]

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.

score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**kwargs) [source]

Set and validate the parameters of estimator.  Parameters

**kwargsdict

Estimator parameters.    Returns

selfobject

Estimator instance.

sparsify() [source]

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.


sklearn.linear_model.SGDRegressor
class sklearn.linear_model.SGDRegressor(loss='squared_loss', *, penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, max_iter=1000, tol=0.001, shuffle=True, verbose=0, epsilon=0.1, 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) [source]

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 User Guide.  Parameters

lossstr, 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 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’.
alphafloat, 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_ratiofloat, 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_interceptbool, default=True

Whether the intercept should be estimated or not. If False, the data is assumed to be already centered.
max_iterint, 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 partial_fit method.  New in version 0.19.
tolfloat, 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.  New in version 0.19.
shufflebool, default=True

Whether or not the training data should be shuffled after each epoch.
verboseint, default=0

The verbosity level.
epsilonfloat, 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_stateint, 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 Glossary.
learning_ratestring, 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.  New in version 0.20: Added ‘adaptive’ option
eta0double, default=0.01

The initial learning rate for the ‘constant’, ‘invscaling’ or ‘adaptive’ schedules. The default value is 0.01.
power_tdouble, default=0.25

The exponent for inverse scaling learning rate.
early_stoppingbool, 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.  New in version 0.20: Added ‘early_stopping’ option
validation_fractionfloat, 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.  New in version 0.20: Added ‘validation_fraction’ option
n_iter_no_changeint, default=5

Number of iterations with no improvement to wait before early stopping.  New in version 0.20: Added ‘n_iter_no_change’ option
warm_startbool, default=False

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See 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.
averagebool 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 since version 0.23: Attribute average_coef_ was deprecated in version 0.23 and will be removed in 1.0 (renaming of 0.25).
average_intercept_ndarray of shape (1,)

The averaged intercept term. Only available if average=True.  Deprecated since version 0.23: Attribute average_intercept_ was deprecated in version 0.23 and will be removed in 1.0 (renaming of 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).      See also
Ridge, ElasticNet, Lasso, sklearn.svm.SVR

  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())])
 Methods
densify() Convert coefficient matrix to dense array format.
fit(X, y[, coef_init, intercept_init, …]) Fit linear model with Stochastic Gradient Descent.
get_params([deep]) Get parameters for this estimator.
partial_fit(X, y[, sample_weight]) Perform one epoch of stochastic gradient descent on given samples.
predict(X) Predict using the linear model
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.
set_params(**kwargs) Set and validate the parameters of estimator.
sparsify() Convert coefficient matrix to sparse format.
densify() [source]

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(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data
yndarray of shape (n_samples,)

Target values
coef_initndarray of shape (n_features,), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (1,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).    Returns

selfreturns an instance of self.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

partial_fit(X, y, sample_weight=None) [source]

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
ynumpy array of shape (n_samples,)

Subset of target values
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples. If not provided, uniform weights are assumed.    Returns

selfreturns an instance of self.

predict(X) [source]

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.

score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**kwargs) [source]

Set and validate the parameters of estimator.  Parameters

**kwargsdict

Estimator parameters.    Returns

selfobject

Estimator instance.

sparsify() [source]

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.

 Examples using sklearn.linear_model.SGDRegressor

  Prediction Latency

  SGD: Penalties


fit(X, y, coef_init=None, intercept_init=None, sample_weight=None) [source]

Fit linear model with Stochastic Gradient Descent.  Parameters

X{array-like, sparse matrix}, shape (n_samples, n_features)

Training data
yndarray of shape (n_samples,)

Target values
coef_initndarray of shape (n_features,), default=None

The initial coefficients to warm-start the optimization.
intercept_initndarray of shape (1,), default=None

The initial intercept to warm-start the optimization.
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples (1. for unweighted).    Returns

selfreturns an instance of self.


get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.


partial_fit(X, y, sample_weight=None) [source]

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
ynumpy array of shape (n_samples,)

Subset of target values
sample_weightarray-like, shape (n_samples,), default=None

Weights applied to individual samples. If not provided, uniform weights are assumed.    Returns

selfreturns an instance of self.


predict(X) [source]

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.


score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).


class sklearn.linear_model.TheilSenRegressor(*, fit_intercept=True, copy_X=True, max_subpopulation=10000.0, n_subsamples=None, max_iter=300, tol=0.001, random_state=None, n_jobs=None, verbose=False) [source]

Theil-Sen Estimator: robust multivariate regression model. The algorithm calculates least square solutions on subsets with size n_subsamples of the samples in X. Any value of n_subsamples between the number of features and samples leads to an estimator with a compromise between robustness and efficiency. Since the number of least square solutions is “n_samples choose n_subsamples”, it can be extremely large and can therefore be limited with max_subpopulation. If this limit is reached, the subsets are chosen randomly. In a final step, the spatial median (or L1 median) is calculated of all least square solutions. Read more in the User Guide.  Parameters

fit_interceptbool, default=True

Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations.
copy_Xbool, default=True

If True, X will be copied; else, it may be overwritten.
max_subpopulationint, default=1e4

Instead of computing with a set of cardinality ‘n choose k’, where n is the number of samples and k is the number of subsamples (at least number of features), consider only a stochastic subpopulation of a given maximal size if ‘n choose k’ is larger than max_subpopulation. For other than small problem sizes this parameter will determine memory usage and runtime if n_subsamples is not changed.
n_subsamplesint, default=None

Number of samples to calculate the parameters. This is at least the number of features (plus 1 if fit_intercept=True) and the number of samples as a maximum. A lower number leads to a higher breakdown point and a low efficiency while a high number leads to a low breakdown point and a high efficiency. If None, take the minimum number of subsamples leading to maximal robustness. If n_subsamples is set to n_samples, Theil-Sen is identical to least squares.
max_iterint, default=300

Maximum number of iterations for the calculation of spatial median.
tolfloat, default=1.e-3

Tolerance when calculating spatial median.
random_stateint, RandomState instance or None, default=None

A random number generator instance to define the state of the random permutations generator. Pass an int for reproducible output across multiple function calls. See Glossary
n_jobsint, default=None

Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
verbosebool, default=False

Verbose mode when fitting the model.    Attributes

coef_ndarray of shape (n_features,)

Coefficients of the regression model (median of distribution).
intercept_float

Estimated intercept of regression model.
breakdown_float

Approximated breakdown point.
n_iter_int

Number of iterations needed for the spatial median.
n_subpopulation_int

Number of combinations taken into account from ‘n choose k’, where n is the number of samples and k is the number of subsamples.     References  Theil-Sen Estimators in a Multiple Linear Regression Model, 2009 Xin Dang, Hanxiang Peng, Xueqin Wang and Heping Zhang http://home.olemiss.edu/~xdang/papers/MTSE.pdf
  Examples >>> from sklearn.linear_model import TheilSenRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(
...     n_samples=200, n_features=2, noise=4.0, random_state=0)
>>> reg = TheilSenRegressor(random_state=0).fit(X, y)
>>> reg.score(X, y)
0.9884...
>>> reg.predict(X[:1,])
array([-31.5871...])
 Methods
fit(X, y) Fit linear model.
get_params([deep]) Get parameters for this estimator.
predict(X) Predict using the linear model.
score(X, y[, sample_weight]) Return the coefficient of determination \(R^2\) of the prediction.
set_params(**params) Set the parameters of this estimator.
fit(X, y) [source]

Fit linear model.  Parameters

Xndarray of shape (n_samples, n_features)

Training data.
yndarray of shape (n_samples,)

Target values.    Returns

selfreturns an instance of self.

get_params(deep=True) [source]

Get parameters for this estimator.  Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns

paramsdict

Parameter names mapped to their values.

predict(X) [source]

Predict using the linear model.  Parameters

Xarray-like or sparse matrix, shape (n_samples, n_features)

Samples.    Returns

Carray, shape (n_samples,)

Returns predicted values.

score(X, y, sample_weight=None) [source]

Return the coefficient of determination \(R^2\) of the prediction. The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), 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

Xarray-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 with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.
yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.
sample_weightarray-like of shape (n_samples,), default=None

Sample weights.    Returns

scorefloat

\(R^2\) of self.predict(X) wrt. y.     Notes The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params) [source]

Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters

**paramsdict

Estimator parameters.    Returns

selfestimator instance

Estimator instance.