sklearn.linear_model
.LassoLarsIC¶
- class sklearn.linear_model.LassoLarsIC(criterion='aic', *, fit_intercept=True, verbose=False, normalize='deprecated', precompute='auto', max_iter=500, eps=2.220446049250313e-16, copy_X=True, positive=False, noise_variance=None)[source]¶
Lasso model fit with Lars using BIC or AIC for model selection.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
AIC is the Akaike information criterion [2] and BIC is the Bayes Information criterion [3]. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.
Read more in the User Guide.
- Parameters:
- criterion{‘aic’, ‘bic’}, default=’aic’
The type of criterion to use.
- 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=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, ‘auto’ or array-like, 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. Can be used for early stopping.
- 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 LassoLarsIC only makes sense for problems where a sparse solution is expected and/or reached.- noise_variancefloat, default=None
The estimated noise variance of the data. If
None
, an unbiased estimate is computed by an OLS model. However, it is only possible in the case wheren_samples > n_features + fit_intercept
.New in version 1.1.
- Attributes:
- coef_array-like of shape (n_features,)
parameter vector (w in the formulation formula)
- intercept_float
independent term in decision function.
- alpha_float
the alpha parameter chosen by the information criterion
- alphas_array-like 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 a list, it will be of lengthn_targets
.- n_iter_int
number of iterations run by lars_path to find the grid of alphas.
- criterion_array-like of shape (n_alphas,)
The value of the information criteria (‘aic’, ‘bic’) across all alphas. The alpha which has the smallest information criterion is chosen, as specified in [1].
- noise_variance_float
The estimated noise variance from the data used to compute the criterion.
New in version 1.1.
- 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.
LassoLarsCV
Cross-validated Lasso, using the LARS algorithm.
sklearn.decomposition.sparse_encode
Sparse coding.
Notes
The number of degrees of freedom is computed as in [1].
To have more details regarding the mathematical formulation of the AIC and BIC criteria, please refer to User Guide.
References
Examples
>>> from sklearn import linear_model >>> reg = linear_model.LassoLarsIC(criterion='bic') >>> X = [[-2, 2], [-1, 1], [0, 0], [1, 1], [2, 2]] >>> y = [-2.2222, -1.1111, 0, -1.1111, -2.2222] >>> reg.fit(X, y) LassoLarsIC(criterion='bic') >>> print(reg.coef_) [ 0. -1.11...]
Methods
fit
(X, y[, copy_X])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, copy_X=None)[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. Will be cast to X’s dtype if necessary.
- copy_Xbool, default=None
If provided, this parameter will override the choice of copy_X made at instance creation. If
True
, X will be copied; else, it may be overwritten.
- 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.LassoLarsIC
¶
Lasso model selection via information criteria
Lasso model selection: AIC-BIC / cross-validation