Class ElasticNet

java.lang.Object

smile.regression.ElasticNet

public class ElasticNet
extends Object

Elastic Net regularized linear regression.

Elastic Net linearly combines the L1 (LASSO) and L2 (Ridge) penalties, overcoming limitations of LASSO when features are highly correlated or when the number of features exceeds the sample size (p > n).

The optimization problem can be reformulated as an equivalent LASSO problem on augmented response and covariate matrices. Because the strictly convex L2 penalty guarantees a unique global minimum, the objective remains strictly convex even when the feature matrix is not full rank.

References

• H. Zou and T. Hastie. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 67(2):301-320, 2005.
• K. P. Murphy. Machine Learning: A Probabilistic Perspective, Section 13.5.3. MIT Press, 2012.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	ElasticNet.Options	Hyperparameters for Elastic Net regression.

Method Summary

Modifier and Type	Method	Description
static LinearModel	fit(Formula formula, DataFrame data, double lambda1, double lambda2)	Fits an Elastic Net regularized linear model.
static LinearModel	fit(Formula formula, DataFrame data, ElasticNet.Options options)	Fits an Elastic Net regularized linear model with full options.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

fit

public static LinearModel fit(Formula formula,
 DataFrame data,
 double lambda1,
 double lambda2)

Fits an Elastic Net regularized linear model.

Parameters:

formula - formula specifying response and predictors.

data - training data frame.

lambda1 - L1 penalty coefficient.

lambda2 - L2 penalty coefficient.

Returns:

fitted LinearModel.

fit

public static LinearModel fit(Formula formula,
 DataFrame data,
 ElasticNet.Options options)

Fits an Elastic Net regularized linear model with full options.

Parameters:

formula - formula specifying response and predictors.

data - training data frame.

options - algorithm hyperparameters.

Returns:

fitted LinearModel.