celer.Lasso#

class celer.Lasso(alpha=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]#

Lasso scikit-learn estimator based on Celer solver

The optimization objective for Lasso is:

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

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 Lasso
>>> clf = Lasso(alpha=0.1)
>>> clf.fit([[0, 0], [1, 1], [2, 2]], [0, 1, 2])
Lasso(alpha=0.1, max_epochs=50000, max_iter=100,
p0=10, prune=0, tol=1e-06, verbose=0)
>>> print(clf.coef_)
[0.85 0.  ]
>>> print(clf.intercept_)
0.15
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, 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, max_iter, max_epochs, p0, ...])

fit(X, y[, sample_weight, check_input])

Fit model with coordinate descent.

get_params([deep])

Get parameters for this estimator.

path(X, y, alphas[, coef_init, return_n_iter])

Compute Lasso path with Celer.

predict(X)

Predict using the linear model.

score(X, y[, sample_weight])

Return the coefficient of determination of the prediction.

set_params(**params)

Set the parameters of this estimator.

Attributes

sparse_coef_

Sparse representation of the fitted coef_.