sklearn.linear_model
.LassoLarsCV¶

class
sklearn.linear_model.
LassoLarsCV
(*, fit_intercept=True, verbose=False, max_iter=500, normalize=True, precompute='auto', cv=None, max_n_alphas=1000, n_jobs=None, eps=2.220446049250313e16, copy_X=True, positive=False)[source]¶ Crossvalidated Lasso, using the LARS algorithm.
See glossary entry for crossvalidation estimator.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * y  Xw^2_2 + alpha * w_1
Read more in the User Guide.
 Parameters
 fit_interceptbool, default=True
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
 verbosebool or int, default=False
Sets the verbosity amount.
 max_iterint, default=500
Maximum number of iterations to perform.
 normalizebool, default=True
This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
. precomputebool or ‘auto’ , default=’auto’
Whether to use a precomputed Gram matrix to speed up calculations. If set to
'auto'
let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X. cvint, crossvalidation generator or an iterable, default=None
Determines the crossvalidation splitting strategy. Possible inputs for cv are:
None, to use the default 5fold crossvalidation,
integer, to specify the number of folds.
An iterable yielding (train, test) splits as arrays of indices.
For integer/None inputs,
KFold
is used.Refer User Guide for the various crossvalidation strategies that can be used here.
Changed in version 0.22:
cv
default value if None changed from 3fold to 5fold. max_n_alphasint, default=1000
The maximum number of points on the path used to compute the residuals in the crossvalidation
 n_jobsint or None, default=None
Number of CPUs to use during the cross validation.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. epsfloat, default=np.finfo(float).eps
The machineprecision regularization in the computation of the Cholesky diagonal factors. Increase this for very illconditioned systems. Unlike the
tol
parameter in some iterative optimizationbased algorithms, this parameter does not control the tolerance of the optimization. copy_Xbool, default=True
If True, X will be copied; else, it may be overwritten.
 positivebool, default=False
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do 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 estimator. As a consequence using LassoLarsCV only makes sense for problems where a sparse solution is expected and/or reached.
 Attributes
 coef_arraylike of shape (n_features,)
parameter vector (w in the formulation formula)
 intercept_float
independent term in decision function.
 coef_path_arraylike of shape (n_features, n_alphas)
the varying values of the coefficients along the path
 alpha_float
the estimated regularization parameter alpha
 alphas_arraylike of shape (n_alphas,)
the different values of alpha along the path
 cv_alphas_arraylike of shape (n_cv_alphas,)
all the values of alpha along the path for the different folds
 mse_path_arraylike of shape (n_folds, n_cv_alphas)
the mean square error on leftout for each fold along the path (alpha values given by
cv_alphas
) n_iter_arraylike or int
the number of iterations run by Lars with the optimal alpha.
 active_list of int
Indices of active variables at the end of the path.
Notes
The object solves the same problem as the LassoCV object. However, unlike the LassoCV, it find the relevant alphas values by itself. In general, because of this property, it will be more stable. However, it is more fragile to heavily multicollinear datasets.
It is more efficient than the LassoCV if only a small number of features are selected compared to the total number, for instance if there are very few samples compared to the number of features.
Examples
>>> from sklearn.linear_model import LassoLarsCV >>> from sklearn.datasets import make_regression >>> X, y = make_regression(noise=4.0, random_state=0) >>> reg = LassoLarsCV(cv=5).fit(X, y) >>> reg.score(X, y) 0.9992... >>> reg.alpha_ 0.0484... >>> reg.predict(X[:1,]) array([77.8723...])
Methods
fit
(X, y)Fit the model using X, y as training data.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict using the linear model.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.

fit
(X, y)[source]¶ Fit the model using X, y as training data.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training data.
 yarraylike of shape (n_samples,)
Target values.
 Returns
 selfobject
returns an instance of self.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
 Parameters
 deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
 Returns
 paramsdict
Parameter names mapped to their values.

predict
(X)[source]¶ Predict using the linear model.
 Parameters
 Xarraylike or sparse matrix, shape (n_samples, n_features)
Samples.
 Returns
 Carray, shape (n_samples,)
Returns predicted values.

score
(X, y, sample_weight=None)[source]¶ Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1  \frac{u}{v})\), where \(u\) is the residual sum of squares
((y_true  y_pred) ** 2).sum()
and \(v\) is the total sum of squares((y_true  y_true.mean()) ** 2).sum()
. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value ofy
, disregarding the input features, would get a \(R^2\) score of 0.0. Parameters
 Xarraylike of shape (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape
(n_samples, n_samples_fitted)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator. yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
. sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
\(R^2\) of
self.predict(X)
wrt.y
.
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfestimator instance
Estimator instance.