8.17.29. 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=True, normalize=False, copy_X=True, verbose=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 : ndarray, 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

normalize : boolean, optional, default False

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

copy_X : boolean, optional, default True

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

verbose : bool or integer

Amount of verbosity

params : kwargs

keyword arguments passed to the Lasso objects

Returns:

models : a list of models along the regularization path

See also

lars_path, Lasso, LassoLars, LassoCV, LassoLarsCV, sklearn.decomposition.sparse_encode

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 coefficents between the values output by lars_path

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 = [e.coef_ for e in lasso_path(X, y, alphas=[5., 1., .5], fit_intercept=False)]
>>> print np.array(coef_path).T
[[ 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]]