smile.regression

Class RidgeRegression

java.lang.Object

smile.regression.RidgeRegression

All Implemented Interfaces:

Regression<double[]>

public class RidgeRegression
extends Object
implements Regression<double[]>

Ridge Regression. When the predictor variables are highly correlated amongst themselves, the coefficients of the resulting least squares fit may be very imprecise. By allowing a small amount of bias in the estimates, more reasonable coefficients may often be obtained. Ridge regression is one method to address these issues. Often, small amounts of bias lead to dramatic reductions in the variance of the estimated model coefficients. Ridge regression is such a technique which shrinks the regression coefficients by imposing a penalty on their size. Ridge regression was originally developed to overcome the singularity of the X'X matrix. This matrix is perturbed so as to make its determinant appreciably different from 0.

Ridge regression is a kind of Tikhonov regularization, which is the most commonly used method of regularization of ill-posed problems. Another interpretation of ridge regression is available through Bayesian estimation. In this setting the belief that weight should be small is coded into a prior distribution.

Author:

Haifeng Li

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	RidgeRegression.Trainer Trainer for ridge regression.

Constructor Summary

Constructors

Constructor and Description
RidgeRegression(double[][] x, double[] y, double lambda) Constructor.

Method Summary

Modifier and Type	Method and Description
double[]	coefficients() Returns the (scaled) linear coefficients.
double	intercept() Returns the (centered) intercept.
double	predict(double[] x) Predicts the dependent variable of an instance.
double	shrinkage() Returns the shrinkage parameter.

Methods inherited from class java.lang.Object

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

Constructor Detail

RidgeRegression

public RidgeRegression(double[][] x,
                       double[] y,
                       double lambda)

Constructor. Learn the ridge regression model.

Parameters:

x - a matrix containing the explanatory variables.

y - the response values.

lambda - the shrinkage/regularization parameter.

Method Detail

coefficients

public double[] coefficients()

Returns the (scaled) linear coefficients.

intercept

public double intercept()

Returns the (centered) intercept.

shrinkage

public double shrinkage()

Returns the shrinkage parameter.

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.