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sklearn.linear_model.lars_path

sklearn.linear_model.lars_path(X, y, Xy=None, Gram=None, max_iter=500, alpha_min=0, method='lar', copy_X=True, eps=2.2204460492503131e-16, copy_Gram=True, verbose=0, return_path=True)

Compute Least Angle Regression or Lasso path using LARS algorithm [1]

The optimization objective for the case method=’lasso’ is:

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

in the case of method=’lars’, the objective function is only known in the form of an implicit equation (see discussion in [1])

Parameters:

X : array, shape: (n_samples, n_features)

Input data.

y : array, shape: (n_samples)

Input targets.

max_iter : integer, optional (default=500)

Maximum number of iterations to perform, set to infinity for no limit.

Gram : None, ‘auto’, array, shape: (n_features, n_features), optional

Precomputed Gram matrix (X’ * X), if 'auto', the Gram matrix is precomputed from the given X, if there are more samples than features.

alpha_min : float, optional (default=0)

Minimum correlation along the path. It corresponds to the regularization parameter alpha parameter in the Lasso.

method : {‘lar’, ‘lasso’}, optional (default=’lar’)

Specifies the returned model. Select 'lar' for Least Angle Regression, 'lasso' for the Lasso.

eps : float, optional (default=``np.finfo(np.float).eps``)

The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems.

copy_X : bool, optional (default=True)

If False, X is overwritten.

copy_Gram : bool, optional (default=True)

If False, Gram is overwritten.

verbose : int (default=0)

Controls output verbosity.

return_path: bool, (optional=True) :

If return_path==True returns the entire path, else returns only the last point of the path.

Returns:

alphas: array, shape: [n_alphas + 1] :

Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter, n_features or the number of nodes in the path with alpha >= alpha_min, whichever is smaller.

active: array, shape [n_alphas] :

Indices of active variables at the end of the path.

coefs: array, shape (n_features, n_alphas + 1) :

Coefficients along the path

References

[R133]“Least Angle Regression”, Effron et al. http://www-stat.stanford.edu/~tibs/ftp/lars.pdf
[R134]Wikipedia entry on the Least-angle regression
[R135]Wikipedia entry on the Lasso
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