sklearn.linear_model
.LassoLarsCV¶
- class sklearn.linear_model.LassoLarsCV(*, fit_intercept=True, verbose=False, max_iter=500, normalize='deprecated', precompute='auto', cv=None, max_n_alphas=1000, n_jobs=None, eps=2.220446049250313e-16, copy_X=True, positive=False)[source]¶
Cross-validated Lasso, using the LARS algorithm.
See glossary entry for cross-validation estimator.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Read more in the User Guide.
- Parameters:
- 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.
- max_iterint, default=500
Maximum number of iterations to perform.
- 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 l2-norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
.Changed in version 1.2: default changed from True to False in 1.2.
Deprecated since version 1.2:
normalize
was deprecated in version 1.2 and will be removed in 1.4.- precomputebool or ‘auto’ , default=’auto’
Whether to use a precomputed Gram matrix to speed up calculations. If set to
'auto'
let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X.- cvint, cross-validation generator or an iterable, default=None
Determines the cross-validation splitting strategy. Possible inputs for cv are:
None, to use the default 5-fold cross-validation,
integer, to specify the number of folds.
An iterable yielding (train, test) splits as arrays of indices.
For integer/None inputs,
KFold
is used.Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.22:
cv
default value if None changed from 3-fold to 5-fold.- max_n_alphasint, default=1000
The maximum number of points on the path used to compute the residuals in the cross-validation.
- n_jobsint or None, 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.- 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.
- 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 do 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. As a consequence using LassoLarsCV only makes sense for problems where a sparse solution is expected and/or reached.
- Attributes:
- coef_array-like of shape (n_features,)
parameter vector (w in the formulation formula)
- intercept_float
independent term in decision function.
- coef_path_array-like of shape (n_features, n_alphas)
the varying values of the coefficients along the path
- alpha_float
the estimated regularization parameter alpha
- alphas_array-like of shape (n_alphas,)
the different values of alpha along the path
- cv_alphas_array-like of shape (n_cv_alphas,)
all the values of alpha along the path for the different folds
- mse_path_array-like of shape (n_folds, n_cv_alphas)
the mean square error on left-out for each fold along the path (alpha values given by
cv_alphas
)- n_iter_array-like or int
the number of iterations run by Lars with the optimal alpha.
- active_list of int
Indices of active variables at the end of the path.
- n_features_in_int
Number of features seen during fit.
New in version 0.24.
- feature_names_in_ndarray of shape (
n_features_in_
,) Names of features seen during fit. Defined only when
X
has feature names that are all strings.New in version 1.0.
See also
lars_path
Compute Least Angle Regression or Lasso path using LARS algorithm.
lasso_path
Compute Lasso path with coordinate descent.
Lasso
Linear Model trained with L1 prior as regularizer (aka the Lasso).
LassoCV
Lasso linear model with iterative fitting along a regularization path.
LassoLars
Lasso model fit with Least Angle Regression a.k.a. Lars.
LassoLarsIC
Lasso model fit with Lars using BIC or AIC for model selection.
sklearn.decomposition.sparse_encode
Sparse coding.
Notes
The object solves the same problem as the
LassoCV
object. However, unlike theLassoCV
, it find the relevant alphas values by itself. In general, because of this property, it will be more stable. However, it is more fragile to heavily multicollinear datasets.It is more efficient than the
LassoCV
if only a small number of features are selected compared to the total number, for instance if there are very few samples compared to the number of features.In
fit
, once the best parameteralpha
is found through cross-validation, the model is fit again using the entire training set.Examples
>>> from sklearn.linear_model import LassoLarsCV >>> from sklearn.datasets import make_regression >>> X, y = make_regression(noise=4.0, random_state=0) >>> reg = LassoLarsCV(cv=5).fit(X, y) >>> reg.score(X, y) 0.9993... >>> reg.alpha_ 0.3972... >>> reg.predict(X[:1,]) array([-78.4831...])
Methods
fit
(X, y)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 of the prediction.
set_params
(**params)Set the parameters of this estimator.
- fit(X, y)[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,)
Target values.
- 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 of the prediction.
The coefficient of determination \(R^2\) 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:
- 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)
, wheren_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 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.
Examples using sklearn.linear_model.LassoLarsCV
¶
Lasso model selection: AIC-BIC / cross-validation