`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.

sklearn.linear_model.LassoLars¶

`sklearn.linear_model`.LassoLars¶