org.drip.learning.regularization

Class RegularizerR1ContinuousToR1Continuous

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedR1ToNormedR1

org.drip.spaces.rxtor1.NormedR1ContinuousToR1Continuous

org.drip.learning.regularization.RegularizerR1ContinuousToR1Continuous

All Implemented Interfaces:

RegularizerR1ToR1

public class RegularizerR1ContinuousToR1Continuous
extends NormedR1ContinuousToR1Continuous
implements RegularizerR1ToR1

RegularizerR1ContinuousToR1Continuous computes the Structural Loss and Risk for the specified Normed R^1 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
RegularizerR1ContinuousToR1Continuous(R1ToR1 funcRegularizerR1ToR1, R1Continuous r1ContinuousInput, R1Continuous r1ContinuousOutput, double dblLambda) RegularizerR1ContinuousToR1Continuous Function Space Constructor

Method Summary

Modifier and Type	Method and Description
double	lambda() Retrieve the Regularization Constant Lambda
double	structuralLoss(R1ToR1 funcR1ToR1, double[] adblX) Compute the Regularization Sample Structural Loss
double	structuralRisk(R1R1 distR1R1, R1ToR1 funcR1ToR1, double[] adblX, double[] adblY) Compute the Regularization Sample Structural Loss

Methods inherited from class org.drip.spaces.rxtor1.NormedR1ContinuousToR1Continuous

populationMetricNorm

Methods inherited from class org.drip.spaces.rxtor1.NormedR1ToNormedR1

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

RegularizerR1ContinuousToR1Continuous

public RegularizerR1ContinuousToR1Continuous(R1ToR1 funcRegularizerR1ToR1,
                                             R1Continuous r1ContinuousInput,
                                             R1Continuous r1ContinuousOutput,
                                             double dblLambda)
                                      throws java.lang.Exception

RegularizerR1ContinuousToR1Continuous Function Space Constructor

Parameters:

funcRegularizerR1ToR1 - The R^1 To R^1 Regularizer Function

r1ContinuousInput - The Continuous R^1 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: RegularizerR1ToR1

Retrieve the Regularization Constant Lambda

Specified by:

lambda in interface RegularizerR1ToR1

Returns:

The Regularization Constant Lambda

structuralLoss

public double structuralLoss(R1ToR1 funcR1ToR1,
                             double[] adblX)
                      throws java.lang.Exception

Description copied from interface: RegularizerR1ToR1

Compute the Regularization Sample Structural Loss

Specified by:

structuralLoss in interface RegularizerR1ToR1

Parameters:

funcR1ToR1 - R^1 To R^1 Function Instance

adblX - The Predictor Instance

Returns:

The Regularization Sample Structural Loss

Throws:

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

structuralRisk

public double structuralRisk(R1R1 distR1R1,
                             R1ToR1 funcR1ToR1,
                             double[] adblX,
                             double[] adblY)
                      throws java.lang.Exception

Description copied from interface: RegularizerR1ToR1

Compute the Regularization Sample Structural Loss

Specified by:

structuralRisk in interface RegularizerR1ToR1

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

funcR1ToR1 - R^1 To R^1 Function Instance

adblX - The Predictor Instance

adblY - The Response Instance

Returns:

The Regularization Sample Structural Loss

Throws:

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