celer.ElasticNet#

class celer.ElasticNet(alpha=1.0, l1_ratio=1.0, max_iter=100, max_epochs=50000, p0=10, verbose=0, tol=0.0001, prune=True, fit_intercept=True, weights=None, warm_start=False, positive=False)[source]#

ElasticNet scikit-learn estimator based on Celer solver

The optimization objective for ElasticNet is:

1 / (2 * n_samples) * ||y - X w||^2_2
+ alpha * l1_ratio * \sum_j weights_j |w_j|
+ 0.5 * alpha * (1 - l1_ratio) * \sum_j weights_j |w_j|^2)

Parameters:

alphafloat, optional: Constant that multiplies the penalty term. Defaults to 1.0. alpha = 0 is equivalent to an ordinary least square. For numerical reasons, using alpha = 0 with the Lasso object is not advised.
l1_ratiofloat, optional: The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. Defaults to 1.0 which corresponds to L1 penalty (Lasso). l1_ratio = 0 (Ridge regression) is not supported.
max_iterint, optional: The maximum number of iterations (subproblem definitions).
max_epochsint: Maximum number of CD epochs on each subproblem.
p0int: First working set size.
verbosebool or integer: Amount of verbosity.
tolfloat, optional: Stopping criterion for the optimization: the solver runs until the duality gap is smaller than tol * norm(y) ** 2 / len(y) or the maximum number of iteration is reached.
prune0 | 1, optional: Whether or not to use pruning when growing working sets.
fit_interceptbool, optional (default=True): Whether or not to fit an intercept.
weightsarray, shape (n_features,), optional (default=None): Strictly positive weights used in the L1 penalty part of the Lasso objective. If None, weights equal to 1 are used.
warm_startbool, optional (default=False): When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution.
positivebool, optional (default=False): When set to True, forces the coefficients to be positive.

See also

celer_path
LassoCV

References

[1]

M. Massias, A. Gramfort, J. Salmon “Celer: a Fast Solver for the Lasso wit Dual Extrapolation”, ICML 2018, http://proceedings.mlr.press/v80/massias18a.html

Examples

>>> from celer import ElasticNet
>>> clf = ElasticNet(l1_ratio=0.8, alpha=0.1)
>>> clf.fit([[0, 0], [1, 1], [2, 2]], [0, 1, 2])
ElasticNet(alpha=0.1, l1_ratio=0.8)
>>> print(clf.coef_)
[0.43470641 0.43232388]
>>> print(clf.intercept_)
0.13296971635785026

Attributes:

coef_array, shape (n_features,): parameter vector (w in the cost function formula).
sparse_coef_scipy.sparse matrix, shape (n_features, 1): Sparse representation of the fitted coef_.
intercept_float: constant term in decision function.
n_iter_int: Number of subproblems solved by Celer to reach the specified tolerance.

__init__(alpha=1.0, l1_ratio=1.0, max_iter=100, max_epochs=50000, p0=10, verbose=0, tol=0.0001, prune=True, fit_intercept=True, weights=None, warm_start=False, positive=False)[source]#

Methods

`__init__`([alpha, l1_ratio, max_iter, ...])
`fit`(X, y[, sample_weight, check_input])	Fit model with coordinate descent.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`path`(X, y, alphas[, coef_init, return_n_iter])	Compute ElasticNet path with Celer.
`predict`(X)	Predict using the linear model.
`score`(X, y[, sample_weight])	Return the coefficient of determination of the prediction.
`set_fit_request`(*[, check_input, sample_weight])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_score_request`(*[, sample_weight])	Request metadata passed to the `score` method.

Attributes

sparse_coef_

Sparse representation of the fitted coef_.