lasso_path#

sklearn.linear_model.lasso_path(X,y,*,eps=0.001,n_alphas=100,alphas=None,precompute='auto',Xy=None,copy_X=True,coef_init=None,verbose=False,return_n_iter=False,positive=False,**params)[source]#

Compute Lasso path with coordinate descent.

The Lasso optimization function varies for mono and multi-outputs.

For mono-output tasks it is:

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

For multi-output tasks it is:

(1/(2*n_samples))*||Y-XW||^2_Fro+alpha*||W||_21

Where:

||W||_21= \sum_i \sqrt{\sum_jw_{ij}^2}

i.e. the sum of norm of each row.

Read more in theUser Guide.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features)

Training data. Pass directly as Fortran-contiguous data to avoidunnecessary memory duplication. Ify is mono-output thenXcan be sparse.

y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)

Target values.

epsfloat, default=1e-3

Length of the path.eps=1e-3 means thatalpha_min/alpha_max=1e-3.

n_alphasint, default=100

Number of alphas along the regularization path.

alphasarray-like, default=None

List of alphas where to compute the models.IfNone alphas are set automatically.

precompute‘auto’, bool or array-like of shape (n_features, n_features), default=’auto’

Whether to use a precomputed Gram matrix to speed upcalculations. If set to'auto' let us decide. The Grammatrix can also be passed as argument.

Xyarray-like of shape (n_features,) or (n_features, n_targets), default=None

Xy = np.dot(X.T, y) that can be precomputed. It is usefulonly when the Gram matrix is precomputed.

copy_Xbool, default=True

IfTrue, X will be copied; else, it may be overwritten.

coef_initarray-like of shape (n_features, ), default=None

The initial values of the coefficients.

verbosebool or int, default=False

Amount of verbosity.

return_n_iterbool, default=False

Whether to return the number of iterations or not.

positivebool, default=False

If set to True, forces coefficients to be positive.(Only allowed wheny.ndim==1).

**paramskwargs

Keyword arguments passed to the coordinate descent solver.

Returns:

alphasndarray of shape (n_alphas,)

The alphas along the path where models are computed.

coefsndarray of shape (n_features, n_alphas) or (n_targets, n_features, n_alphas)

Coefficients along the path.

dual_gapsndarray of shape (n_alphas,)

The dual gaps at the end of the optimization for each alpha.

n_iterslist of int

The number of iterations taken by the coordinate descent optimizer toreach the specified tolerance for each alpha.

See also

lars_path

Compute Least Angle Regression or Lasso path using LARS algorithm.

Lasso

The Lasso is a linear model that estimates sparse coefficients.

LassoLars

Lasso model fit with Least Angle Regression a.k.a. Lars.

LassoCV

Lasso linear model with iterative fitting along a regularization path.

LassoLarsCV

Cross-validated Lasso using the LARS algorithm.

sklearn.decomposition.sparse_encode

Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

Notes

For an example, seeexamples/linear_model/plot_lasso_lasso_lars_elasticnet_path.py.

To avoid unnecessary memory duplication the X argument of the fit methodshould be directly passed as a Fortran-contiguous numpy array.

Note that in certain cases, the Lars solver may be significantlyfaster to implement this functionality. In particular, linearinterpolation can be used to retrieve model coefficients between thevalues output by lars_path

Examples

Comparing lasso_path and lars_path with interpolation:

>>>importnumpyasnp>>>fromsklearn.linear_modelimportlasso_path>>>X=np.array([[1,2,3.1],[2.3,5.4,4.3]]).T>>>y=np.array([1,2,3.1])>>># Use lasso_path to compute a coefficient path>>>_,coef_path,_=lasso_path(X,y,alphas=[5.,1.,.5])>>>print(coef_path)[[0.         0.         0.46874778] [0.2159048  0.4425765  0.23689075]]

>>># Now use lars_path and 1D linear interpolation to compute the>>># same path>>>fromsklearn.linear_modelimportlars_path>>>alphas,active,coef_path_lars=lars_path(X,y,method='lasso')>>>fromscipyimportinterpolate>>>coef_path_continuous=interpolate.interp1d(alphas[::-1],...coef_path_lars[:,::-1])>>>print(coef_path_continuous([5.,1.,.5]))[[0.         0.         0.46915237] [0.2159048  0.4425765  0.23668876]]

Gallery examples#

Lasso, Lasso-LARS, and Elastic Net paths

Lasso, Lasso-LARS, and Elastic Net paths