org.drip.learning.rxtor1

Interface EmpiricalLearningMetricEstimator

All Known Implementing Classes:

ApproximateLipschitzLossLearner, GeneralizedLearner, L1LossLearner, LipschitzLossLearner, LpLossLearner

public interface EmpiricalLearningMetricEstimator

EmpiricalLearningMetricEstimator is the Estimator of the Empirical Loss and Risk, as well as the corresponding Covering Numbers. 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

Method Summary

Modifier and Type	Method and 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
NormedRxToNormedR1Finite	functionClass() Retrieve the Underlying Learner Function Class
double	lossSampleCoveringNumber(GeneralizedValidatedVector gvvi, double dblEpsilon, boolean bSupremum) Retrieve the Loss Class Sample Covering Number - L-Infinity or L-p based Based
double	regularizedLoss(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Regularized Sample Loss (Empirical + Structural)
double	regularizedLoss(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Regularized Sample Loss (Empirical + Structural)
double	regularizedRisk(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Regularized Sample Risk (Empirical + Structural)
double	regularizedRisk(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Regularized Sample Risk (Empirical + Structural)
RegularizationFunction	regularizerFunction() Retrieve the Regularizer Function
double	structuralLoss(R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvvi) Compute the Structural Sample Loss
double	structuralLoss(RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvvi) Compute the Structural Sample Loss
double	structuralRisk(R1R1 distR1R1, R1ToR1 funcLearnerR1ToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Structural Sample Risk
double	structuralRisk(RdR1 distRdR1, RdToR1 funcLearnerRdToR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Structural Sample Risk
EmpiricalPenaltySupremum	supremumEmpiricalLoss(GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Empirical Sample Loss
EmpiricalPenaltySupremum	supremumEmpiricalRisk(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Empirical Sample Risk
EmpiricalPenaltySupremum	supremumEmpiricalRisk(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Empirical Sample Risk
EmpiricalPenaltySupremum	supremumRegularizedLoss(GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Regularized Sample Loss
EmpiricalPenaltySupremum	supremumRegularizedRisk(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Regularized Sample Risk
EmpiricalPenaltySupremum	supremumRegularizedRisk(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Regularized Sample Risk
EmpiricalPenaltySupremum	supremumStructuralLoss(GeneralizedValidatedVector gvviX) Compute the Supremum Structural Sample Loss
EmpiricalPenaltySupremum	supremumStructuralRisk(R1R1 distR1R1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Structural Sample Risk
EmpiricalPenaltySupremum	supremumStructuralRisk(RdR1 distRdR1, GeneralizedValidatedVector gvviX, GeneralizedValidatedVector gvviY) Compute the Supremum Structural Sample Risk

Method Detail

functionClass

NormedRxToNormedR1Finite functionClass()

Retrieve the Underlying Learner Function Class

Returns:

The Underlying Learner Function Class

regularizerFunction

RegularizationFunction regularizerFunction()

Retrieve the Regularizer Function

Returns:

The Regularizer Function

lossSampleCoveringNumber

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

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

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

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

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

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

supremumEmpiricalLoss

EmpiricalPenaltySupremum supremumEmpiricalLoss(GeneralizedValidatedVector gvviX,
                                               GeneralizedValidatedVector gvviY)
                                        throws java.lang.Exception

Compute the Supremum Empirical Sample Loss

Parameters:

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

Throws:

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

structuralLoss

double structuralLoss(R1ToR1 funcLearnerR1ToR1,
                      GeneralizedValidatedVector gvvi)
               throws java.lang.Exception

Compute the Structural Sample Loss

Parameters:

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

gvvi - The Validated Predictor Instance

Returns:

The Structural Loss

Throws:

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

structuralLoss

double structuralLoss(RdToR1 funcLearnerRdToR1,
                      GeneralizedValidatedVector gvvi)
               throws java.lang.Exception

Compute the Structural Sample Loss

Parameters:

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

gvvi - The Validated Predictor Instance

Returns:

The Structural Loss

Throws:

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

supremumStructuralLoss

EmpiricalPenaltySupremum supremumStructuralLoss(GeneralizedValidatedVector gvviX)
                                         throws java.lang.Exception

Compute the Supremum Structural Sample Loss

Parameters:

gvviX - The Validated Predictor Instance

Returns:

The Supremum Structural Sample Loss

Throws:

java.lang.Exception - Thrown if the Supremum Structural Sample Loss cannot be computed

regularizedLoss

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

Compute the Regularized Sample Loss (Empirical + Structural)

Parameters:

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

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Regularized Loss

Throws:

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

regularizedLoss

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

Compute the Regularized Sample Loss (Empirical + Structural)

Parameters:

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

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Regularized Loss

Throws:

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

supremumRegularizedLoss

EmpiricalPenaltySupremum supremumRegularizedLoss(GeneralizedValidatedVector gvviX,
                                                 GeneralizedValidatedVector gvviY)
                                          throws java.lang.Exception

Compute the Supremum Regularized Sample Loss

Parameters:

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Loss

Throws:

java.lang.Exception - Thrown if the Supremum Regularized Sample Loss cannot be computed

empiricalRisk

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

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

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

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

supremumEmpiricalRisk

EmpiricalPenaltySupremum supremumEmpiricalRisk(R1R1 distR1R1,
                                               GeneralizedValidatedVector gvviX,
                                               GeneralizedValidatedVector gvviY)
                                        throws java.lang.Exception

Compute the Supremum Empirical Sample Risk

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

Throws:

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

supremumEmpiricalRisk

EmpiricalPenaltySupremum supremumEmpiricalRisk(RdR1 distRdR1,
                                               GeneralizedValidatedVector gvviX,
                                               GeneralizedValidatedVector gvviY)
                                        throws java.lang.Exception

Compute the Supremum Empirical Sample Risk

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

Throws:

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

structuralRisk

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

Compute the Structural 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 Structural Risk

Throws:

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

structuralRisk

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

Compute the Structural 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 Structural Risk

Throws:

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

supremumStructuralRisk

EmpiricalPenaltySupremum supremumStructuralRisk(R1R1 distR1R1,
                                                GeneralizedValidatedVector gvviX,
                                                GeneralizedValidatedVector gvviY)
                                         throws java.lang.Exception

Compute the Supremum Structural Sample Risk

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Structural Sample Loss

Throws:

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

supremumStructuralRisk

EmpiricalPenaltySupremum supremumStructuralRisk(RdR1 distRdR1,
                                                GeneralizedValidatedVector gvviX,
                                                GeneralizedValidatedVector gvviY)
                                         throws java.lang.Exception

Compute the Supremum Structural Sample Risk

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Structural Sample Risk

Throws:

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

regularizedRisk

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

Compute the Regularized Sample Risk (Empirical + Structural)

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 Regularized Sample Risk

Throws:

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

regularizedRisk

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

Compute the Regularized Sample Risk (Empirical + Structural)

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 Regularized Sample Risk

Throws:

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

supremumRegularizedRisk

EmpiricalPenaltySupremum supremumRegularizedRisk(R1R1 distR1R1,
                                                 GeneralizedValidatedVector gvviX,
                                                 GeneralizedValidatedVector gvviY)
                                          throws java.lang.Exception

Compute the Supremum Regularized Sample Risk

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Risk

Throws:

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

supremumRegularizedRisk

EmpiricalPenaltySupremum supremumRegularizedRisk(RdR1 distRdR1,
                                                 GeneralizedValidatedVector gvviX,
                                                 GeneralizedValidatedVector gvviY)
                                          throws java.lang.Exception

Compute the Supremum Regularized Sample Risk

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Risk

Throws:

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