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=np.float64(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.

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=’lar’, the objective function is only known inthe form of an implicit equation (see discussion in[1]).

Read more in theUser Guide.

Parameters:
Xyndarray of shape (n_features,)

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 theregularization parameter alpha parameter in the Lasso.

method{‘lar’, ‘lasso’}, default=’lar’

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

copy_Xbool, default=True

IfFalse,X is overwritten.

epsfloat, default=np.finfo(float).eps

The machine-precision regularization in the computation of theCholesky diagonal factors. Increase this for very ill-conditionedsystems. Unlike thetol parameter in some iterativeoptimization-based algorithms, this parameter does not controlthe tolerance of the optimization.

copy_Grambool, default=True

IfFalse,Gram is overwritten.

verboseint, default=0

Controls output verbosity.

return_pathbool, default=True

Ifreturn_path==True returns the entire path, else returns only thelast 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 modelcoefficients will not converge to the ordinary-least-squares solutionfor small values of alpha. Only coefficients up to the smallest alphavalue (alphas_[alphas_>0.].min() whenfit_path=True) reached bythe stepwise Lars-Lasso algorithm are typically in congruence with thesolution 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 thenumber of nodes in the path withalpha>=alpha_min, whicheveris 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 ifreturn_n_iter is setto 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

Examples

>>>fromsklearn.linear_modelimportlars_path_gram>>>fromsklearn.datasetsimportmake_regression>>>X,y,true_coef=make_regression(...n_samples=100,n_features=5,n_informative=2,coef=True,random_state=0...)>>>true_coefarray([ 0.        ,  0.        ,  0.        , 97.9, 45.7])>>>alphas,_,estimated_coef=lars_path_gram(X.T@y,X.T@X,n_samples=100)>>>alphas.shape(3,)>>>estimated_coefarray([[ 0.     ,  0.     ,  0.     ],       [ 0.     ,  0.     ,  0.     ],       [ 0.     ,  0.     ,  0.     ],       [ 0.     , 46.96, 97.99],       [ 0.     ,  0.     , 45.70]])
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