`sklearn.linear_model`.lars_path_gram¶

sklearn.linear_model.lars_path_gram(Xy, Gram, n_samples, max_iter=500, alpha_min=0, method=’lar’, copy_X=True, eps=2.220446049250313e-16, copy_Gram=True, verbose=0, return_path=True, return_n_iter=False, positive=False)[source]¶

lars_path in the sufficient stats mode [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])

Read more in the User Guide.

Parameters:

Xy : array-like, shape (n_samples,) or (n_samples, n_targets): Xy = np.dot(X.T, y).
Gram : array, shape (n_features, n_features): Gram = np.dot(X.T * X).
n_samples : integer or float: Equivalent size of sample.
max_iter : integer, optional (default=500): Maximum number of iterations to perform, set to infinity for no limit.
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.
copy_X : bool, optional (default=True): If False, X is overwritten.
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_Gram : bool, optional (default=True): If False, Gram is overwritten.
verbose : int (default=0): Controls output verbosity.
return_path : bool, optional (default=True): If return_path==True returns the entire path, else returns only the last point of the path.
return_n_iter : bool, optional (default=False): Whether to return the number of iterations.
positive : boolean (default=False): Restrict coefficients to be >= 0. This option is only allowed with method ‘lasso’. Note that the model coefficients will not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ > 0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent lasso_path function.

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
n_iter : int: Number of iterations run. Returned only if return_n_iter is set to True.

sklearn.linear_model.lars_path_gram¶

`sklearn.linear_model`.lars_path_gram¶