Package org.drip.learning.rxtor1

Class ApproximateLipschitzLossLearner

java.lang.Object

org.drip.learning.rxtor1.GeneralizedLearner

org.drip.learning.rxtor1.LipschitzLossLearner

org.drip.learning.rxtor1.ApproximateLipschitzLossLearner

All Implemented Interfaces:

EmpiricalLearningMetricEstimator

public class ApproximateLipschitzLossLearner
extends LipschitzLossLearner

ApproximateLipschitzLossLearner implements the Learner Class that holds the Space of Normed R^d To Normed R¹ Learning Functions for the Family of Loss Functions that are "approximately" Lipschitz, i.e., loss (ep) - loss (ep') Less Than max (C * |ep-ep'|, C')

The References are:

• 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 Penalizer

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
ApproximateLipschitzLossLearner(NormedRxToNormedR1Finite funcClassRxToR1, CoveringNumberLossBound cdpb, RegularizationFunction regularizerFunc, double dblLipschitzSlope, double dblLipschitzFloor)	ApproximateLipschitzLossLearner Constructor

Method Summary

Modifier and Type	Method	Description
double	lipschitzFloor()	Retrieve the Lipschitz Floor
double	lossSampleCoveringNumber(GeneralizedValidatedVector gvvi, double dblEpsilon, boolean bSupremum)	Retrieve the Loss Class Sample Covering Number - L-Infinity or L-p based Based

Methods inherited from class org.drip.learning.rxtor1.LipschitzLossLearner

empiricalLoss, empiricalLoss, empiricalRisk, empiricalRisk, lipschitzSlope

Methods inherited from class org.drip.learning.rxtor1.GeneralizedLearner

coveringLossBoundEvaluator, functionClass, genericCoveringProbabilityBound, genericCoveringProbabilityBound, genericCoveringSampleSize, genericCoveringSampleSize, regressorCoveringProbabilityBound, regressorCoveringProbabilityBound, regressorCoveringSampleSize, regressorCoveringSampleSize, regularizedLoss, regularizedLoss, regularizedRisk, regularizedRisk, regularizerFunction, structuralLoss, structuralLoss, structuralRisk, structuralRisk, supremumEmpiricalLoss, supremumEmpiricalRisk, supremumEmpiricalRisk, supremumRegularizedLoss, supremumRegularizedRisk, supremumRegularizedRisk, supremumStructuralLoss, supremumStructuralRisk, supremumStructuralRisk

Methods inherited from class java.lang.Object

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

Constructor Details

ApproximateLipschitzLossLearner

public ApproximateLipschitzLossLearner(NormedRxToNormedR1Finite funcClassRxToR1,
CoveringNumberLossBound cdpb,
RegularizationFunction regularizerFunc,
double dblLipschitzSlope,
double dblLipschitzFloor)
                                throws java.lang.Exception

ApproximateLipschitzLossLearner Constructor

Parameters:

funcClassRxToR1 - R^x To R^1 Function Class

cdpb - The Covering Number based Deviation Upper Probability Bound Generator

regularizerFunc - The Regularizer Function

dblLipschitzSlope - The Lipschitz Slope Bound

dblLipschitzFloor - The Lipschitz Floor Bound

Throws:

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

Method Details

lipschitzFloor

public double lipschitzFloor()

Retrieve the Lipschitz Floor

Returns:

The Lipschitz Floor

lossSampleCoveringNumber

public double lossSampleCoveringNumber(GeneralizedValidatedVector gvvi,
double dblEpsilon,
boolean bSupremum)
                                throws java.lang.Exception

Description copied from interface: EmpiricalLearningMetricEstimator

Retrieve the Loss Class Sample Covering Number - L-Infinity or L-p based Based

Specified by:

lossSampleCoveringNumber in interface EmpiricalLearningMetricEstimator

Overrides:

lossSampleCoveringNumber in class LipschitzLossLearner

Parameters:

gvvi - The Validated Instance Vector Sequence

dblEpsilon - The Deviation of the Empirical Mean from the Population Mean

bSupremum - TRUE To Use the Supremum Metric in place of the Built-in Metric

Returns:

The Loss Class Sample Covering Number - L-Infinity or L-p based Based

Throws:

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