Package org.drip.learning.rxtor1

Class LpLossLearner

java.lang.Object

org.drip.learning.rxtor1.GeneralizedLearner

org.drip.learning.rxtor1.LpLossLearner

All Implemented Interfaces:

EmpiricalLearningMetricEstimator

public class LpLossLearner
extends GeneralizedLearner

LpLossLearner implements the Learner Class that holds the Space of Normed R^x To Normed R¹ Learning Functions for the Family of Loss Functions that are Polynomial, i.e., loss (eta) = (eta ^ p) / p, for p greater than 1. This is Lipschitz, with a Lipschitz Slope of C = (b - a) ^ (p - 1)

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
LpLossLearner(NormedRxToNormedR1Finite funcClassRxToR1, CoveringNumberLossBound cdpb, RegularizationFunction regularizerFunc, double dblLossExponent)	LpLossLearner Constructor

Method Summary

Modifier and Type	Method	Description
double	empiricalLoss(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY)	Compute the Empirical Sample Loss
double	empiricalLoss(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY)	Compute the Empirical Sample Loss
double	empiricalRisk(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY)	Compute the Empirical Sample Risk
double	empiricalRisk(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY)	Compute the Empirical Sample Risk
double	lipschitzSlope()	Retrieve the Lipschitz Slope Bound
double	lossExponent()	Retrieve the Loss Exponent
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.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

LpLossLearner

public LpLossLearner(NormedRxToNormedR1Finite funcClassRxToR1,
CoveringNumberLossBound cdpb,
RegularizationFunction regularizerFunc,
double dblLossExponent)
              throws java.lang.Exception

LpLossLearner Constructor

Parameters:

funcClassRxToR1 - R^x To R^1 Function Class

cdpb - The Covering Number based Deviation Upper Probability Bound Generator

regularizerFunc - The Regularizer Function

dblLossExponent - The Loss Exponent

Throws:

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

Method Details

lossExponent

public double lossExponent()

Retrieve the Loss Exponent

Returns:

The Loss Exponent

lipschitzSlope

public double lipschitzSlope()

Retrieve the Lipschitz Slope Bound

Returns:

The Lipschitz Slope Bound

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

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

empiricalLoss

public double empiricalLoss(R1ToR1 funcLearnerR1ToR1,
GeneralizedValidatedVector gvviX,
GeneralizedValidatedVector gvviY)
                     throws java.lang.Exception

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Empirical Sample Loss

Parameters:

funcLearnerR1ToR1 - The R^1 To R^1 Learner Function

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Empirical Loss

Throws:

java.lang.Exception - Thrown if the Empirical Loss cannot be computed

empiricalLoss

public double empiricalLoss(RdToR1 funcLearnerRdToR1,
GeneralizedValidatedVector gvviX,
GeneralizedValidatedVector gvviY)
                     throws java.lang.Exception

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Empirical Sample Loss

Parameters:

funcLearnerRdToR1 - The R^d To R^1 Learner Function

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Empirical Loss

Throws:

java.lang.Exception - Thrown if the Empirical Loss cannot be computed

empiricalRisk

public double empiricalRisk(R1R1 distR1R1,
R1ToR1 funcLearnerR1ToR1,
GeneralizedValidatedVector gvviX,
GeneralizedValidatedVector gvviY)
                     throws java.lang.Exception

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Empirical Sample Risk

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

funcLearnerR1ToR1 - The R^1 To R^1 Learner Function

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Empirical Sample Risk

Throws:

java.lang.Exception - Thrown if the Empirical Sample Risk cannot be computed

empiricalRisk

public double empiricalRisk(RdR1 distRdR1,
RdToR1 funcLearnerRdToR1,
GeneralizedValidatedVector gvviX,
GeneralizedValidatedVector gvviY)
                     throws java.lang.Exception

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Empirical Sample Risk

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

funcLearnerRdToR1 - The R^d To R^1 Learner Function

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Empirical Sample Risk

Throws:

java.lang.Exception - Thrown if the Empirical Sample Risk cannot be computed