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)[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:
alpha : float

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_intercept : boolean

whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).

verbose : boolean or integer, optional

Sets the verbosity amount

normalize : boolean, optional, 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 sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.

precompute : True | False | ‘auto’ | array-like

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_iter : integer, optional

Maximum number of iterations to perform.

eps : float, optional

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_X : boolean, optional, default True

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

fit_path : boolean

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.

positive : boolean (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.
Attributes:
alphas_ : array, shape (n_alphas + 1,) | list of n_targets 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 correlation greater than alpha, whichever is smaller.

active_ : list, length = n_alphas | list of n_targets such lists

Indices of active variables at the end of the path.

coef_path_ : array, shape (n_features, n_alphas + 1) or list

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.

coef_ : array, shape (n_features,) or (n_targets, n_features)

Parameter vector (w in the formulation formula).

intercept_ : float | array, 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, copy_X=True, eps=..., fit_intercept=True,
     fit_path=True, max_iter=500, normalize=True, positive=False,
     precompute='auto', verbose=False)
>>> print(reg.coef_) 
[ 0.         -0.963257...]

Methods

fit(self, X, y[, Xy]) Fit the model using X, y as training data.
get_params(self[, deep]) Get parameters for this estimator.
predict(self, X) Predict using the linear model
score(self, X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction.
set_params(self, \*\*params) Set the parameters of this estimator.
__init__(self, 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)[source]
fit(self, X, y, Xy=None)[source]

Fit the model using X, y as training data.

Parameters:
X : array-like, shape (n_samples, n_features)

Training data.

y : array-like, shape (n_samples,) or (n_samples, n_targets)

Target values.

Xy : array-like, shape (n_samples,) or (n_samples, n_targets), optional

Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
Returns:
self : object

returns an instance of self.
get_params(self, deep=True)[source]

Get parameters for this estimator.

Parameters:
deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:
params : mapping of string to any

Parameter names mapped to their values.
predict(self, X)[source]

Predict using the linear model

Parameters:
X : array_like or sparse matrix, shape (n_samples, n_features)

Samples.
Returns:
C : array, shape (n_samples,)

Returns predicted values.
score(self, X, y, sample_weight=None)[source]

Returns the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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:
X : array-like, shape = (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator.

y : array-like, shape = (n_samples) or (n_samples, n_outputs)

True values for X.

sample_weight : array-like, shape = [n_samples], optional

Sample weights.
Returns:
score : float

R^2 of self.predict(X) wrt. y.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with metrics.r2_score. This will influence the score method of all the multioutput regressors (except for multioutput.MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call metrics.r2_score directly or make a custom scorer with metrics.make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:
self