org.drip.learning.regularization

Class RegularizerRdContinuousToR1Continuous

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedRdToNormedR1

org.drip.spaces.rxtor1.NormedRdContinuousToR1Continuous

org.drip.learning.regularization.RegularizerRdContinuousToR1Continuous

All Implemented Interfaces:

RegularizerRdToR1

public class RegularizerRdContinuousToR1Continuous
extends NormedRdContinuousToR1Continuous
implements RegularizerRdToR1

RegularizerRdContinuousToR1Continuous computes the Structural Loss and Risk for the specified Normed R^d Continuous To Normed R^1 Continuous Learning Function. The References are: 1) Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform Convergence, and Learnability, Journal of Association of Computational Machinery, 44 (4) 615-631. 2) Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations, Cambridge University Press, Cambridge, UK. 3) Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): Towards Efficient Agnostic Learning, Machine Learning, 17 (2) 115-141. 4) Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with Squared Loss, IEEE Transactions on Information Theory, 44 1974-1980. 5) Vapnik, V. N. (1998): Statistical Learning Theory, Wiley, New York.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
RegularizerRdContinuousToR1Continuous(RdToR1 funcRdToR1, RdContinuousBanach rdContinuousInput, R1Continuous r1ContinuousOutput, double dblLambda) RegularizerRdContinuousToR1Continuous Function Space Constructor

Method Summary

Modifier and Type	Method and Description
double	lambda() Retrieve the Regularization Constant Lambda
double	structuralLoss(RdToR1 funcRdToR1, double[][] aadblX) Compute the Regularization Sample Structural Loss
double	structuralRisk(RdR1 distRdR1, RdToR1 funcRdToR1, double[][] aadblX, double[] adblY) Compute the Regularization Sample Structural Loss

Methods inherited from class org.drip.spaces.rxtor1.NormedRdContinuousToR1Continuous

populationMetricNorm

Methods inherited from class org.drip.spaces.rxtor1.NormedRdToNormedR1

function, inputMetricVectorSpace, outputMetricVectorSpace, populationESS, sampleMetricNorm, sampleSupremumNorm

Methods inherited from class org.drip.spaces.rxtor1.NormedRxToNormedR1

populationCoveringNumber, populationSupremumCoveringNumber, populationSupremumMetricNorm, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

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

Constructor Detail

RegularizerRdContinuousToR1Continuous

public RegularizerRdContinuousToR1Continuous(RdToR1 funcRdToR1,
                                             RdContinuousBanach rdContinuousInput,
                                             R1Continuous r1ContinuousOutput,
                                             double dblLambda)
                                      throws java.lang.Exception

RegularizerRdContinuousToR1Continuous Function Space Constructor

Parameters:

funcRdToR1 - The R^d To R^1 Function

rdContinuousInput - The Continuous R^d Input Metric Vector Space

r1ContinuousOutput - The Continuous R^1 Output Metric Vector Space

dblLambda - The Regularization Lambda

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Detail

lambda

public double lambda()

Description copied from interface: RegularizerRdToR1

Retrieve the Regularization Constant Lambda

Specified by:

lambda in interface RegularizerRdToR1

Returns:

The Regularization Constant Lambda

structuralLoss

public double structuralLoss(RdToR1 funcRdToR1,
                             double[][] aadblX)
                      throws java.lang.Exception

Description copied from interface: RegularizerRdToR1

Compute the Regularization Sample Structural Loss

Specified by:

structuralLoss in interface RegularizerRdToR1

Parameters:

funcRdToR1 - R^d To R^1 Function Instance

aadblX - The Sample Instance

Returns:

The Regularization Sample Structural Loss

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

structuralRisk

public double structuralRisk(RdR1 distRdR1,
                             RdToR1 funcRdToR1,
                             double[][] aadblX,
                             double[] adblY)
                      throws java.lang.Exception

Description copied from interface: RegularizerRdToR1

Compute the Regularization Sample Structural Loss

Specified by:

structuralRisk in interface RegularizerRdToR1

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

funcRdToR1 - R^d To R^1 Function Instance

aadblX - The Sample Instance

adblY - The Response Instance

Returns:

The Regularization Sample Structural Loss

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid