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, 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 byLinearRegression
. For numerical reasons, usingalpha = 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 l2norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
. precomputebool, ‘auto’ or arraylike, 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 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_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 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. 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 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. jitterfloat, default=None
Upper bound on a uniform noise parameter to be added to the
y
values, to satisfy the model’s assumption of oneatatime 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_arraylike of shape (n_alphas + 1,) or list of 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 withalpha >= alpha_min
, whichever is smaller. If this is a list of arraylike, the length of the outer list isn_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_arraylike 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 isFalse
. If this is a list of arraylike, the length of the outer list isn_targets
. coef_arraylike of shape (n_features,) or (n_targets, n_features)
Parameter vector (w in the formulation formula).
 intercept_float or arraylike of 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) >>> 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
 Xarraylike of shape (n_samples, n_features)
Training data.
 yarraylike of shape (n_samples,) or (n_samples, n_targets)
Target values.
 Xyarraylike 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
 Xarraylike 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 ofy
, disregarding the input features, would get a \(R^2\) score of 0.0. Parameters
 Xarraylike 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)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator. yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
. sample_weightarraylike 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 usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).

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.