8.17.3. sklearn.linear_model.ElasticNet

class sklearn.linear_model.ElasticNet(alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, rho=None)

Linear Model trained with L1 and L2 prior 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.

Parameters:

alpha : float

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 in the scikit. For numerical reasons, using alpha = 0 with the Lasso object is not advised and you should prefer the LinearRegression object.

l1_ratio : float

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_intercept: bool :

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

normalize : boolean, optional, default False

If True, the regressors X will be normalized before regression.

precompute : True | 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. For sparse input this option is always True to preserve sparsity.

max_iter: int, optional :

The maximum number of iterations

copy_X : boolean, optional, default False

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

tol: float, 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_start : bool, optional

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

positive: bool, optional :

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

Notes

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

Attributes

coef_	array, shape = (n_features,)	parameter vector (w in the cost function formula)
sparse_coef_	scipy.sparse matrix, shape = (n_features, 1)	sparse_coef_ is a readonly property derived from coef_
intercept_	float | array, shape = (n_targets,)	independent term in decision function.
dual_gap_	float	the current fit is guaranteed to be epsilon-suboptimal with epsilon := dual_gap_
eps_	float	eps_ is used to check if the fit converged to the requested tol

Methods

decision_function(X)	Decision function of the linear model
fit(X, y[, Xy, coef_init])	Fit model with coordinate descent
get_params([deep])	Get parameters for the estimator
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.

__init__(alpha=1.0, l1_ratio=0.5, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, copy_X=True, tol=0.0001, warm_start=False, positive=False, rho=None)

decision_function(X)

Decision function of the linear model

Parameters:

X : numpy array or scipy.sparse matrix of shape (n_samples, n_features)

Returns:

T : array, shape = (n_samples,)

The predicted decision function

fit(X, y, Xy=None, coef_init=None)

Fit model with coordinate descent

Parameters:

X: ndarray or scipy.sparse matrix, (n_samples, n_features) :

Data

y: ndarray, shape = (n_samples,) or (n_samples, n_targets) :

Target

Xy : array-like, optional

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

coef_init: ndarray of shape n_features or (n_targets, n_features) :

The initial coeffients to warm-start the optimization

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(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.

predict(X)

Predict using the linear model

Parameters:

X : numpy array of shape [n_samples, n_features]

Returns:

C : array, shape = [n_samples]

Returns predicted values.

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_true - 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 :

sparse_coef_

sparse representation of the fitted coef