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=2.220446049250313e16, copy_Gram=True, verbose=0, return_path=True, return_n_iter=False, positive=False)[source]¶ 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])
Read more in the User Guide.
 Parameters
 XNone or arraylike of shape (n_samples, n_features)
Input data. Note that if X is None then the Gram matrix must be specified, i.e., cannot be None or False.
Deprecated since version 0.21: The use of
X
isNone
in combination withGram
is notNone
will be removed in v0.23. Uselars_path_gram
instead. yNone or arraylike of shape (n_samples,)
Input targets.
 Xyarraylike of shape (n_samples,) or (n_samples, n_targets), default=None
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
 GramNone, ‘auto’, arraylike of shape (n_features, n_features), default=None
Precomputed Gram matrix (X’ * X), if
'auto'
, the Gram matrix is precomputed from the given X, if there are more samples than features.Deprecated since version 0.21: The use of
X
isNone
in combination withGram
is not None will be removed in v0.23. Uselars_path_gram
instead. 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, optional
The machineprecision regularization in the computation of the Cholesky diagonal factors. Increase this for very illconditioned systems. By default,
np.finfo(np.float).eps
is used. 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 ordinaryleastsquares 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 LarsLasso algorithm are typically in congruence with the solution of the coordinate descent lasso_path function.
 Returns
 alphasarraylike 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. activearraylike of shape (n_alphas,)
Indices of active variables at the end of the path.
 coefsarraylike 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
References
 1
“Least Angle Regression”, Efron et al. http://statweb.stanford.edu/~tibs/ftp/lars.pdf
 2
 3