8.15.1.18. sklearn.linear_model.SGDRegressor

class sklearn.linear_model.SGDRegressor(loss='squared_loss', penalty='l2', alpha=0.0001, rho=0.85, fit_intercept=True, n_iter=5, shuffle=False, verbose=0, p=0.1, seed=0, learning_rate='invscaling', eta0=0.01, power_t=0.25, warm_start=False)

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.

Parameters :

loss : str, ‘squared_loss’ or ‘huber’

The loss function to be used. Defaults to ‘squared_loss’ which refers to the ordinary least squares fit. ‘huber’ is an epsilon insensitive loss function for robust regression.

penalty : str, ‘l2’ or ‘l1’ or ‘elasticnet’

The penalty (aka regularization term) to be used. Defaults to ‘l2’ which is the standard regularizer for linear SVM models. ‘l1’ and ‘elasticnet’ migh bring sparsity to the model (feature selection) not achievable with ‘l2’.

alpha : float

Constant that multiplies the regularization term. Defaults to 0.0001

rho : float

The Elastic Net mixing parameter, with 0 < rho <= 1. Defaults to 0.85.

fit_intercept: bool :

Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True.

n_iter: int, optional :

The number of passes over the training data (aka epochs). Defaults to 5.

shuffle: bool, optional :

Whether or not the training data should be shuffled after each epoch. Defaults to False.

seed: int, optional :

The seed of the pseudo random number generator to use when shuffling the data.

verbose: integer, optional :

The verbosity level.

p : float

Epsilon in the epsilon-insensitive huber loss function; only if loss==’huber’.

learning_rate : string, optional

The learning rate: constant: eta = eta0 optimal: eta = 1.0/(t+t0) invscaling: eta = eta0 / pow(t, power_t) [default]

eta0 : double, optional

The initial learning rate [default 0.01].

power_t : double, optional

The exponent for inverse scaling learning rate [default 0.25].

warm_start : bool, optional

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution.

See also

Ridge, ElasticNet, Lasso, SVR

Examples

>>> import numpy as np
>>> from sklearn import linear_model
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = linear_model.SGDRegressor()
>>> clf.fit(X, y)
SGDRegressor(alpha=0.0001, eta0=0.01, fit_intercept=True,
       learning_rate='invscaling', loss='squared_loss', n_iter=5, p=0.1,
       penalty='l2', power_t=0.25, rho=0.85, seed=0, shuffle=False,
       verbose=0, warm_start=False)

Attributes

coef_	array, shape = [n_features]	Weights asigned to the features.
intercept_	array, shape = [1]	The intercept term.

Methods

decision_function(X)	Predict using the linear model
fit(X, y[, coef_init, intercept_init, ...])	Fit linear model with Stochastic Gradient Descent.
fit_transform(X[, y])	Fit to data, then transform it
get_params([deep])	Get parameters for the estimator
partial_fit(X, y[, sample_weight])	Fit linear model with Stochastic Gradient Descent.
predict(X)	Predict using the linear model
score(X, y)	Returns the coefficient of determination R^2 of the prediction.
set_params(**params)	Set the parameters of the estimator.
transform(X[, threshold])	Reduce X to its most important features.

__init__(loss='squared_loss', penalty='l2', alpha=0.0001, rho=0.85, fit_intercept=True, n_iter=5, shuffle=False, verbose=0, p=0.1, seed=0, learning_rate='invscaling', eta0=0.01, power_t=0.25, warm_start=False)

decision_function(X)

Predict using the linear model

Parameters :

X : {array-like, sparse matrix}, shape = [n_samples, n_features]

Returns :

array, shape = [n_samples] :

Predicted target values per element in X.

fit(X, y, coef_init=None, intercept_init=None, sample_weight=None)

Fit linear model with Stochastic Gradient Descent.

Parameters :

X : {array-like, sparse matrix}, shape = [n_samples, n_features]

Training data

y : numpy array of shape [n_samples]

Target values

coef_init : array, shape = [n_features]

The initial coeffients to warm-start the optimization.

intercept_init : array, shape = [1]

The initial intercept to warm-start the optimization.

sample_weight : array-like, shape = [n_samples], optional

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

Returns :

self : returns an instance of self.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters :

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns :

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

Notes

This method just calls fit and transform consecutively, i.e., it is not an optimized implementation of fit_transform, unlike other transformers such as PCA.

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

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

partial_fit(X, y, sample_weight=None)

Fit linear model with Stochastic Gradient Descent.

Parameters :

X : {array-like, sparse matrix}, shape = [n_samples, n_features]

Subset of training data

y : numpy array of shape [n_samples]

Subset of target values

sample_weight : array-like, shape = [n_samples], optional

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

Returns :

self : returns an instance of self.

predict(X)

Predict using the linear model

Parameters :

X : {array-like, sparse matrix}, shape = [n_samples, n_features]

Returns :

array, shape = [n_samples] :

Predicted target values per element in X.

score(X, y)

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). Best possible score is 1.0, lower values are worse.

Parameters :

X : array-like, shape = [n_samples, n_features]

Training set.

y : array-like, shape = [n_samples]

Returns :

z : float

set_params(**params)

Set the parameters of the estimator.

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

Returns :self :

transform(X, threshold=None)

Reduce X to its most important features.

Parameters :

X : array or scipy sparse matrix of shape [n_samples, n_features]

The input samples.

threshold : string, float or None, optional (default=None)

The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if available, the object attribute threshold is used. Otherwise, “mean” is used by default.

Returns :

X_r : array of shape [n_samples, n_selected_features]

The input samples with only the selected features.