sklearn.linear_model
.LassoCV¶

class
sklearn.linear_model.
LassoCV
(*, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, normalize=False, precompute='auto', max_iter=1000, tol=0.0001, copy_X=True, cv=None, verbose=False, n_jobs=None, positive=False, random_state=None, selection='cyclic')[source]¶ Lasso linear model with iterative fitting along a regularization path.
See glossary entry for crossvalidation estimator.
The best model is selected by crossvalidation.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * y  Xw^2_2 + alpha * w_1
Read more in the User Guide.
 Parameters
 epsfloat, default=1e3
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
. n_alphasint, default=100
Number of alphas along the regularization path.
 alphasndarray, default=None
List of alphas where to compute the models. If
None
alphas are set automatically. 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).
 normalizebool, default=False
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
. precompute‘auto’, bool or arraylike of shape (n_features, n_features), 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=1000
The maximum number of iterations.
 tolfloat, default=1e4
The tolerance for the optimization: if the updates are smaller than
tol
, the optimization code checks the dual gap for optimality and continues until it is smaller thantol
. copy_Xbool, default=True
If
True
, X will be copied; else, it may be overwritten. cvint, crossvalidation generator or iterable, default=None
Determines the crossvalidation splitting strategy. Possible inputs for cv are:
None, to use the default 5fold crossvalidation,
int, to specify the number of folds.
An iterable yielding (train, test) splits as arrays of indices.
For int/None inputs,
KFold
is used.Refer User Guide for the various crossvalidation strategies that can be used here.
Changed in version 0.22:
cv
default value if None changed from 3fold to 5fold. verbosebool or int, default=False
Amount of verbosity.
 n_jobsint, default=None
Number of CPUs to use during the cross validation.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. positivebool, default=False
If positive, restrict regression coefficients to be positive.
 random_stateint, RandomState instance, default=None
The seed of the pseudo random number generator that selects a random feature to update. Used when
selection
== ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary. selection{‘cyclic’, ‘random’}, default=’cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e4.
 Attributes
 alpha_float
The amount of penalization chosen by cross validation.
 coef_ndarray of shape (n_features,) or (n_targets, n_features)
Parameter vector (w in the cost function formula).
 intercept_float or ndarray of shape (n_targets,)
Independent term in decision function.
 mse_path_ndarray of shape (n_alphas, n_folds)
Mean square error for the test set on each fold, varying alpha.
 alphas_ndarray of shape (n_alphas,)
The grid of alphas used for fitting.
 dual_gap_float or ndarray of shape (n_targets,)
The dual gap at the end of the optimization for the optimal alpha (
alpha_
). n_iter_int
Number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.
See also
Notes
For an example, see examples/linear_model/plot_lasso_model_selection.py.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortrancontiguous numpy array.
Examples
>>> from sklearn.linear_model import LassoCV >>> from sklearn.datasets import make_regression >>> X, y = make_regression(noise=4, random_state=0) >>> reg = LassoCV(cv=5, random_state=0).fit(X, y) >>> reg.score(X, y) 0.9993... >>> reg.predict(X[:1,]) array([78.4951...])
Methods
fit
(X, y)Fit linear model with coordinate descent.
get_params
([deep])Get parameters for this estimator.
path
(*args, **kwargs)Compute Lasso path with coordinate descent
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)[source]¶ Fit linear model with coordinate descent.
Fit is on grid of alphas and best alpha estimated by crossvalidation.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If y is monooutput, X can be sparse.
 yarraylike of shape (n_samples,) or (n_samples, n_targets)
Target values.

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.

static
path
(*args, **kwargs)[source]¶ Compute Lasso path with coordinate descent
The Lasso optimization function varies for mono and multioutputs.
For monooutput tasks it is:
(1 / (2 * n_samples)) * y  Xw^2_2 + alpha * w_1
For multioutput tasks it is:
(1 / (2 * n_samples)) * Y  XW^2_Fro + alpha * W_21
Where:
W_21 = \sum_i \sqrt{\sum_j w_{ij}^2}
i.e. the sum of norm of each row.
Read more in the User Guide.
 Parameters
 X{arraylike, sparse matrix} of shape (n_samples, n_features)
Training data. Pass directly as Fortrancontiguous data to avoid unnecessary memory duplication. If
y
is monooutput thenX
can be sparse. y{arraylike, sparse matrix} of shape (n_samples,) or (n_samples, n_outputs)
Target values
 epsfloat, default=1e3
Length of the path.
eps=1e3
means thatalpha_min / alpha_max = 1e3
 n_alphasint, default=100
Number of alphas along the regularization path
 alphasndarray, default=None
List of alphas where to compute the models. If
None
alphas are set automatically precompute‘auto’, bool or arraylike of shape (n_features, n_features), 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. Xyarraylike of shape (n_features,) or (n_features, n_outputs), default=None
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
 copy_Xbool, default=True
If
True
, X will be copied; else, it may be overwritten. coef_initndarray of shape (n_features, ), default=None
The initial values of the coefficients.
 verbosebool or int, default=False
Amount of verbosity.
 return_n_iterbool, default=False
whether to return the number of iterations or not.
 positivebool, default=False
If set to True, forces coefficients to be positive. (Only allowed when
y.ndim == 1
). **paramskwargs
keyword arguments passed to the coordinate descent solver.
 Returns
 alphasndarray of shape (n_alphas,)
The alphas along the path where models are computed.
 coefsndarray of shape (n_features, n_alphas) or (n_outputs, n_features, n_alphas)
Coefficients along the path.
 dual_gapsndarray of shape (n_alphas,)
The dual gaps at the end of the optimization for each alpha.
 n_iterslist of int
The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha.
Notes
For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.
To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortrancontiguous numpy array.
Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path
Examples
Comparing lasso_path and lars_path with interpolation:
>>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T >>> y = np.array([1, 2, 3.1]) >>> # Use lasso_path to compute a coefficient path >>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5]) >>> print(coef_path) [[0. 0. 0.46874778] [0.2159048 0.4425765 0.23689075]]
>>> # Now use lars_path and 1D linear interpolation to compute the >>> # same path >>> from sklearn.linear_model import lars_path >>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso') >>> from scipy import interpolate >>> coef_path_continuous = interpolate.interp1d(alphas[::1], ... coef_path_lars[:, ::1]) >>> print(coef_path_continuous([5., 1., .5])) [[0. 0. 0.46915237] [0.2159048 0.4425765 0.23668876]]

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.