sklearn.linear_model.ElasticNet¶

class sklearn.linear_model.ElasticNet(alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]

Linear regression with combined L1 and L2 priors as regularizer.

Minimizes the objective function:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2


If you are interested in controlling the L1 and L2 penalty separately, keep in mind that this is equivalent to:

a * L1 + b * L2


where:

alpha = a + b and l1_ratio = a / (a + b)


The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio = 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable, unless you supply your own sequence of alpha.

Read more in the User Guide.

Parameters
alphafloat, optional

Constant that multiplies the penalty terms. Defaults to 1.0. See the notes for the exact mathematical meaning of this parameter. alpha = 0 is equivalent to an ordinary least square, solved by the LinearRegression object. For numerical reasons, using alpha = 0 with the Lasso object is not advised. Given this, you should use the LinearRegression object.

l1_ratiofloat

The ElasticNet mixing parameter, with 0 <= l1_ratio <= 1. For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.

fit_interceptbool

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

normalizeboolean, optional, 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

precomputeTrue | False | array-like

Whether to use a precomputed Gram matrix to speed up calculations. The Gram matrix can also be passed as argument. For sparse input this option is always True to preserve sparsity.

max_iterint, optional

The maximum number of iterations

copy_Xboolean, optional, default True

If True, X will be copied; else, it may be overwritten.

tolfloat, optional

The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.

warm_startbool, optional

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

positivebool, optional

When set to True, forces the coefficients to be positive.

random_stateint, RandomState instance or None, optional, default None

The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.

selectionstr, default ‘cyclic’

If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes
coef_array, shape (n_features,) | (n_targets, n_features)

parameter vector (w in the cost function formula)

sparse_coef_scipy.sparse matrix, shape (n_features, 1) | (n_targets, n_features)

sparse representation of the fitted coef_

intercept_float | array, shape (n_targets,)

independent term in decision function.

n_iter_array-like, shape (n_targets,)

number of iterations run by the coordinate descent solver to reach the specified tolerance.

See also

ElasticNetCV

Elastic net model with best model selection by cross-validation.

SGDRegressor

implements elastic net regression with incremental training.

SGDClassifier

implements logistic regression with elastic net penalty (SGDClassifier(loss="log", penalty="elasticnet")).

Notes

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

Examples

>>> from sklearn.linear_model import ElasticNet
>>> from sklearn.datasets import make_regression

>>> X, y = make_regression(n_features=2, random_state=0)
>>> regr = ElasticNet(random_state=0)
>>> regr.fit(X, y)
ElasticNet(random_state=0)
>>> print(regr.coef_)
[18.83816048 64.55968825]
>>> print(regr.intercept_)
1.451...
>>> print(regr.predict([[0, 0]]))
[1.451...]


Methods

 fit(self, X, y[, check_input]) Fit model with coordinate descent. get_params(self[, deep]) Get parameters for this estimator. path(X, y[, l1_ratio, eps, n_alphas, …]) Compute elastic net path with coordinate descent. predict(self, X) Predict using the linear model. score(self, X, y[, sample_weight]) Return the coefficient of determination R^2 of the prediction. set_params(self, \*\*params) Set the parameters of this estimator.
__init__(self, alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute=False, max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, random_state=None, selection='cyclic')[source]

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y, check_input=True)[source]

Fit model with coordinate descent.

Parameters
Xndarray or scipy.sparse matrix, (n_samples, n_features)

Data

yndarray, shape (n_samples,) or (n_samples, n_targets)

Target. Will be cast to X’s dtype if necessary

check_inputboolean, (default=True)

Allow to bypass several input checking. Don’t use this parameter unless you know what you do.

Notes

Coordinate descent is an algorithm that considers each column of data at a time hence it will automatically convert the X input as a Fortran-contiguous numpy array if necessary.

To avoid memory re-allocation it is advised to allocate the initial data in memory directly using that format.

get_params(self, 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
paramsmapping of string to any

Parameter names mapped to their values.

static path(X, y, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, check_input=True, **params)[source]

Compute elastic net path with coordinate descent.

The elastic net optimization function varies for mono and multi-outputs.

For mono-output tasks it is:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2


For multi-output tasks it is:

(1 / (2 * n_samples)) * ||Y - XW||^Fro_2
+ alpha * l1_ratio * ||W||_21
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2


Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}


i.e. the sum of norm of each row.

Read more in the User Guide.

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

Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If y is mono-output then X can be sparse.

yndarray, shape (n_samples,) or (n_samples, n_outputs)

Target values.

l1_ratiofloat, optional

Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). l1_ratio=1 corresponds to the Lasso.

epsfloat

Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.

n_alphasint, optional

Number of alphas along the regularization path.

alphasndarray, optional

List of alphas where to compute the models. If None alphas are set automatically.

precomputeTrue | False | ‘auto’ | array-like

Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.

Xyarray-like, optional

Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

copy_Xbool, optional, default True

If True, X will be copied; else, it may be overwritten.

coef_initarray, shape (n_features, ) | None

The initial values of the coefficients.

verbosebool or int

Amount of verbosity.

return_n_iterbool

Whether to return the number of iterations or not.

positivebool, default False

If set to True, forces coefficients to be positive. (Only allowed when y.ndim == 1).

check_inputbool, default True

Skip input validation checks, including the Gram matrix when provided assuming there are handled by the caller when check_input=False.

**paramskwargs

Keyword arguments passed to the coordinate descent solver.

Returns
alphasarray, shape (n_alphas,)

The alphas along the path where models are computed.

coefsarray, shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas)

Coefficients along the path.

dual_gapsarray, shape (n_alphas,)

The dual gaps at the end of the optimization for each alpha.

n_itersarray-like, shape (n_alphas,)

The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when return_n_iter is set to True).

Notes

For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

predict(self, 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(self, X, y, sample_weight=None)[source]

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

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

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

set_params(self, **params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). 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
selfobject

Estimator instance.

property sparse_coef_

sparse representation of the fitted coef_