smile.regression

Class ElasticNet

java.lang.Object

smile.regression.ElasticNet

All Implemented Interfaces:

java.io.Serializable, Regression<double[]>

public class ElasticNet
extends java.lang.Object
implements Regression<double[]>

Elastic Net regularization. The elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods.

The elastic net problem can be reduced to a lasso problem on modified data and response. And note that the penalty function of Elastic Net is strictly convex so there is a unique global minimum, even if input data matrix is not full rank.

References

1. Kevin P. Murphy: Machine Learning A Probabilistic Perspective, Section 13.5.3, 2012
2. Zou, Hui, Hastie, Trevor: Regularization and Variable Selection via the Elastic Net, 2005

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ElasticNet(double[][] x, double[] y, double lambda1, double lambda2) Constructor.
ElasticNet(double[][] x, double[] y, double lambda1, double lambda2, double tol, int maxIter) Constructor.

Method Summary

Modifier and Type	Method and Description
double[]	coefficients()
double	intercept() Returns the intercept.
LASSO	lasso()
double	predict(double[] x) Predicts the dependent variable of an instance.

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.regression.Regression

predict

Constructor Detail

ElasticNet

public ElasticNet(double[][] x,
                  double[] y,
                  double lambda1,
                  double lambda2)

Constructor. Learn the Elastic Net regularized least squares model.

Parameters:

x - a matrix containing the explanatory variables. NO NEED to include a constant column of 1s for bias.

y - the response values.

lambda1 - the shrinkage/regularization parameter for L1

lambda2 - the shrinkage/regularization parameter for L2

ElasticNet

public ElasticNet(double[][] x,
                  double[] y,
                  double lambda1,
                  double lambda2,
                  double tol,
                  int maxIter)

Constructor. Learn the Elastic Net regularized least squares model.

Parameters:

x - a matrix containing the explanatory variables. NO NEED to include a constant column of 1s for bias.

y - the response values.

lambda1 - the shrinkage/regularization parameter for L1

lambda2 - the shrinkage/regularization parameter for L2

tol - the tolerance for stopping iterations (relative target duality gap).

maxIter - the maximum number of IPM (Newton) iterations.

Method Detail

predict

public double predict(double[] x)

Description copied from interface: Regression

Predicts the dependent variable of an instance.

Specified by:

predict in interface Regression<double[]>

Parameters:

x - the instance.

Returns:

the predicted value of dependent variable.

coefficients

public double[] coefficients()

Returns:

the linear coefficients.

intercept

public double intercept()

Returns the intercept.

lasso

public LASSO lasso()

Returns:

the reduced LASSO model