sklearn.linear_model.LassoLars

class sklearn.linear_model.LassoLars(alpha=1.0, *, fit_intercept=True, verbose=False, normalize=True, precompute='auto', max_iter=500, eps=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.

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 l2-norm. If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False.

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.

New in version 0.23.

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.

New in version 0.23.

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.

See also

lars_path

lasso_path

Lasso

LassoCV

LassoLarsCV

LassoLarsIC

sklearn.decomposition.sparse_encode

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.         -0.963257...]

Methods

fit(X, y[, Xy])	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, 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_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.

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

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 \(R^2\) 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 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) wrt. 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_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.