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=2.220446049250313e16, 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 byLinearRegression
. For numerical reasons, usingalpha = 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 l2norm. If you wish to standardize, please usesklearn.preprocessing.StandardScaler
before callingfit
on an estimator withnormalize=False
. precompute : True  False  ‘auto’  arraylike
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 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_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 thecoef_path_
attribute. If you compute the solution for a large problem or many targets, settingfit_path
toFalse
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 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.
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 eithermax_iter
,n_features
, or the number of nodes in the path with correlation greater thanalpha
, 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 isFalse
. 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_ : arraylike or int.
The number of iterations taken by lars_path to find the grid of alphas for each target.
See also
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=2.220446049250313e16, 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 : arraylike, shape (n_samples, n_features)
Training data.
 y : arraylike, shape (n_samples,) or (n_samples, n_targets)
Target values.
 Xy : arraylike, 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 : arraylike, 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 : arraylike, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
 sample_weight : arraylike, 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 usemultioutput='uniform_average'
from version 0.23 to keep consistent withmetrics.r2_score
. This will influence thescore
method of all the multioutput regressors (except formultioutput.MultiOutputRegressor
). To specify the default value manually and avoid the warning, please either callmetrics.r2_score
directly or make a custom scorer withmetrics.make_scorer
(the builtin scorer'r2'
usesmultioutput='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