Package org.drip.learning.regularization

Class RegularizerR1CombinatorialToR1Continuous

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedR1ToNormedR1

org.drip.spaces.rxtor1.NormedR1CombinatorialToR1Continuous

org.drip.learning.regularization.RegularizerR1CombinatorialToR1Continuous

All Implemented Interfaces:

RegularizerR1ToR1

public class RegularizerR1CombinatorialToR1Continuous
extends NormedR1CombinatorialToR1Continuous
implements RegularizerR1ToR1

RegularizerR1CombinatorialToR1Continuous computes the Structural Loss and Risk for the specified Normed R¹ Combinatorial To Normed R¹ Continuous Learning Function.

• 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
• Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations Cambridge University Press Cambridge, UK
• Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): Towards Efficient Agnostic Learning Machine Learning 17 (2) 115-141
• 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
• Vapnik, V. N. (1998): Statistical learning Theory Wiley New York

• Module = Computational Core Module
• Library = Statistical Learning
• Project = Agnostic Learning Bounds under Empirical Loss Minimization Schemes
• Package = Statistical Learning Empirical Loss Regularizer

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
RegularizerR1CombinatorialToR1Continuous(R1ToR1 funcRegularizerR1ToR1, R1Combinatorial r1CombinatorialInput, R1Continuous r1ContinuousOutput, double dblLambda)	RegularizerR1CombinatorialToR1Continuous Function Space Constructor

Method Summary

Modifier and Type	Method	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.NormedR1CombinatorialToR1Continuous

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 Details

RegularizerR1CombinatorialToR1Continuous

public RegularizerR1CombinatorialToR1Continuous(R1ToR1 funcRegularizerR1ToR1,
R1Combinatorial r1CombinatorialInput,
R1Continuous r1ContinuousOutput,
double dblLambda)
                                         throws java.lang.Exception

RegularizerR1CombinatorialToR1Continuous Function Space Constructor

Parameters:

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

r1CombinatorialInput - The Combinatorial 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 Details

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