Struct PyElasticNet Copy item path

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.

§Parameters

alpha : float, default=1.0 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 :class:LinearRegression object. For numerical reasons, using alpha = 0 with the Lasso object is not advised. Given this, you should use the :class:LinearRegression object.

l1_ratio : float, default=0.5 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, 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).

copy_X : bool, default=True If True, X will be copied; else, it may be overwritten.

max_iter : int, default=1000 The maximum number of iterations for the optimization algorithm.

tol : float, default=1e-4 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, see Notes below.

warm_start : bool, default=False When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See :term:the Glossary <warm_start>.

positive : bool, default=False When set to True, forces the coefficients to be positive.

random_state : int, RandomState instance, default=None The seed of the pseudo random number generator that selects a random feature to update. Used when selection == ‘random’. Pass an int for reproducible output across multiple function calls. See :term:Glossary <random_state>.

selection : {‘cyclic’, ‘random’}, 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_ : ndarray of shape (n_features,) or (n_targets, n_features) Parameter vector (w in the cost function formula).

sparse_coef_ : sparse matrix of shape (n_features,) or
(n_targets, n_features) Sparse representation of the fitted coef_.

intercept_ : float or ndarray of shape (n_targets,) Independent term in decision function.

n_features_in_ : int Number of features seen during :term:fit.

n_iter_ : list of int Number of iterations run by the coordinate descent solver to reach the specified tolerance.

§Examples

from sklears_python 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_) [18.83816119 64.55968437] print(regr.intercept_) 1.451… print(regr.predict([[0, 0]])) [1.451…]

§Notes

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

The precise stopping criteria based on tol are the following: First, check that that maximum coordinate update, i.e. :math:\\max_j |w_j^{new} - w_j^{old}| is smaller than tol times the maximum absolute coefficient, :math:\\max_j |w_j|. If so, then additionally check whether the dual gap is smaller than tol times :math:||y||_2^2 / n_\\text{samples}.