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]¶
The 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:
- Xyndarray of shape (n_features,) or (n_features, n_targets)
Xy = X.T @ y
.- Gramndarray of shape (n_features, n_features)
Gram = X.T @ X
.- n_samplesint
Equivalent size of sample.
- max_iterint, default=500
Maximum number of iterations to perform, set to infinity for no limit.
- alpha_minfloat, default=0
Minimum correlation along the path. It corresponds to the regularization parameter alpha parameter in the Lasso.
- method{‘lar’, ‘lasso’}, default=’lar’
Specifies the returned model. Select
'lar'
for Least Angle Regression,'lasso'
for the Lasso.- copy_Xbool, default=True
If
False
,X
is overwritten.- epsfloat, default=np.finfo(float).eps
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the
tol
parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.- copy_Grambool, default=True
If
False
,Gram
is overwritten.- verboseint, default=0
Controls output verbosity.
- return_pathbool, default=True
If
return_path==True
returns the entire path, else returns only the last point of the path.- return_n_iterbool, default=False
Whether to return the number of iterations.
- positivebool, 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()
whenfit_path=True
) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent lasso_path function.
- Returns:
- alphasndarray of shape (n_alphas + 1,)
Maximum of covariances (in absolute value) at each iteration.
n_alphas
is eithermax_iter
,n_features
or the number of nodes in the path withalpha >= alpha_min
, whichever is smaller.- activendarray of shape (n_alphas,)
Indices of active variables at the end of the path.
- coefsndarray of shape (n_features, n_alphas + 1)
Coefficients along the path.
- n_iterint
Number of iterations run. Returned only if
return_n_iter
is set to True.
See also
lars_path_gram
Compute LARS path.
lasso_path
Compute Lasso path with coordinate descent.
LassoLars
Lasso model fit with Least Angle Regression a.k.a. Lars.
Lars
Least Angle Regression model a.k.a. LAR.
LassoLarsCV
Cross-validated Lasso, using the LARS algorithm.
LarsCV
Cross-validated Least Angle Regression model.
sklearn.decomposition.sparse_encode
Sparse coding.
References
[1]“Least Angle Regression”, Efron et al. http://statweb.stanford.edu/~tibs/ftp/lars.pdf