# LassoLars#

class sklearn.linear_model.LassoLars(alpha=1.0, *, fit_intercept=True, verbose=False, precompute='auto', max_iter=500, eps=np.float64(2.220446049250313e-16), copy_X=True, fit_path=True, positive=False, jitter=None, random_state=None)[source]#

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

It is a Linear Model trained with an L1 prior as regularizer.

The optimization objective for Lasso is:

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


Read more in the User Guide.

Parameters:
alphafloat, default=1.0

Constant that multiplies the penalty term. Defaults to 1.0. alpha = 0 is equivalent to an ordinary least square, solved by LinearRegression. For numerical reasons, using alpha = 0 with the LassoLars object is not advised and you should prefer the LinearRegression object.

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.

precomputebool, ‘auto’ or array-like, default=’auto’

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

max_iterint, default=500

Maximum number of iterations to perform.

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_Xbool, default=True

If True, X will be copied; else, it may be overwritten.

fit_pathbool, default=True

If True the full path is stored in the coef_path_ attribute. If you compute the solution for a large problem or many targets, setting fit_path to False will lead to a speedup, especially with a small alpha.

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 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() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator.

jitterfloat, default=None

Upper bound on a uniform noise parameter to be added to the y values, to satisfy the model’s assumption of one-at-a-time computations. Might help with stability.

random_stateint, RandomState instance or None, default=None

Determines random number generation for jittering. Pass an int for reproducible output across multiple function calls. See Glossary. Ignored if jitter is None.

Attributes:
alphas_array-like of shape (n_alphas + 1,) or list of such arrays

Maximum of covariances (in absolute value) at each iteration. n_alphas is either max_iter, n_features or the number of nodes in the path with alpha >= alpha_min, whichever is smaller. If this is a list of array-like, the length of the outer list is n_targets.

active_list of length n_alphas or list of such lists

Indices of active variables at the end of the path. If this is a list of list, the length of the outer list is n_targets.

coef_path_array-like of shape (n_features, n_alphas + 1) or list of such arrays

If a list is passed it’s expected to be one of n_targets such arrays. The varying values of the coefficients along the path. It is not present if the fit_path parameter is False. If this is a list of array-like, the length of the outer list is n_targets.

coef_array-like of shape (n_features,) or (n_targets, n_features)

Parameter vector (w in the formulation formula).

intercept_float or array-like of shape (n_targets,)

Independent term in decision function.

n_iter_array-like or int

The number of iterations taken by lars_path to find the grid of alphas for each target.

n_features_in_int

Number of features seen during fit.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

lars_path

Compute Least Angle Regression or Lasso path using LARS algorithm.

lasso_path

Compute Lasso path with coordinate descent.

Lasso

Linear Model trained with L1 prior as regularizer (aka the Lasso).

LassoCV

Lasso linear model with iterative fitting along a regularization path.

LassoLarsCV

Cross-validated Lasso, using the LARS algorithm.

LassoLarsIC

Lasso model fit with Lars using BIC or AIC for model selection.

sklearn.decomposition.sparse_encode

Sparse coding.

Examples

>>> from sklearn import linear_model
>>> reg = linear_model.LassoLars(alpha=0.01)
>>> reg.fit([[-1, 1], [0, 0], [1, 1]], [-1, 0, -1])
LassoLars(alpha=0.01)
>>> print(reg.coef_)
[ 0.         -0.955...]

fit(X, y, Xy=None)[source]#

Fit the model using X, y as training data.

Parameters:
Xarray-like of shape (n_samples, n_features)

Training data.

yarray-like of shape (n_samples,) or (n_samples, n_targets)

Target values.

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 useful only when the Gram matrix is precomputed.

Returns:
selfobject

Returns an instance of self.

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

A MetadataRequest encapsulating routing information.

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:
Xarray-like 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 of the prediction.

The coefficient of determination $$R^2$$ 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 of y, disregarding the input features, would get a $$R^2$$ score of 0.0.

Parameters:
Xarray-like 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), where n_samples_fitted is the number of samples used in the fitting for the estimator.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:
scorefloat

$$R^2$$ of self.predict(X) w.r.t. y.

Notes

The $$R^2$$ score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_fit_request(*, Xy: = '$UNCHANGED$') [source]#

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:
Xystr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for Xy parameter in fit.

Returns:
selfobject

The updated object.

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.

set_score_request(*, sample_weight: = '$UNCHANGED$') [source]#

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to score.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:
sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for sample_weight parameter in score.

Returns:
selfobject

The updated object.