sklearn.linear_model.lasso_path¶

sklearn.linear_model.lasso_path(X, y, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, fit_intercept=None, normalize=None, copy_X=True, coef_init=None, verbose=False, return_models=False, **params)¶

Compute Lasso path with coordinate descent

The optimization objective for Lasso is:

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

Parameters :

X : {array-like, sparse matrix}, shape (n_samples, n_features)

Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication

y : ndarray, shape = (n_samples,)

Target values

eps : float, optional

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

n_alphas : int, optional

Number of alphas along the regularization path

alphas : ndarray, optional

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

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.

Xy : array-like, optional

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

fit_intercept : bool

Fit or not an intercept. WARNING : will be deprecated in 0.16

normalize : boolean, optional, default False

If True, the regressors X will be normalized before regression. WARNING : will be deprecated in 0.16

copy_X : boolean, optional, default True

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

coef_init : array, shape (n_features, ) | None

The initial values of the coefficients.

verbose : bool or integer

Amount of verbosity

return_models : boolean, optional, default True

If True, the function will return list of models. Setting it to False will change the function output returning the values of the alphas and the coefficients along the path. Returning the model list will be removed in version 0.16.

params : kwargs

keyword arguments passed to the coordinate descent solver.

Returns :

models : a list of models along the regularization path

(Is returned if return_models is set True (default).

alphas : array, shape: [n_alphas + 1]

The alphas along the path where models are computed. (Is returned, along with coefs, when return_models is set to False)

coefs : shape (n_features, n_alphas + 1)

Coefficients along the path. (Is returned, along with alphas, when return_models is set to False).

dual_gaps : shape (n_alphas + 1)

The dual gaps at the end of the optimization for each alpha. (Is returned, along with alphas, when return_models is set to False).

Notes

See examples/linear_model/plot_lasso_coordinate_descent_path.py for an example.

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

Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path

Deprecation Notice: Setting return_models to False will make the Lasso Path return an output in the style used by lars_path. This will be become the norm as of version 0.16. Leaving return_models set to True will let the function return a list of models as before.

Examples

Comparing lasso_path and lars_path with interpolation:

>>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T
>>> y = np.array([1, 2, 3.1])
>>> # Use lasso_path to compute a coefficient path
>>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5],
...                              fit_intercept=False)
>>> print(coef_path)
[[ 0.          0.          0.46874778]
 [ 0.2159048   0.4425765   0.23689075]]

>>> # Now use lars_path and 1D linear interpolation to compute the
>>> # same path
>>> from sklearn.linear_model import lars_path
>>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso')
>>> from scipy import interpolate
>>> coef_path_continuous = interpolate.interp1d(alphas[::-1],
...                                             coef_path_lars[:, ::-1])
>>> print(coef_path_continuous([5., 1., .5]))
[[ 0.          0.          0.46915237]
 [ 0.2159048   0.4425765   0.23668876]]