org.drip.learning.rxtor1

Class GeneralizedLearner

java.lang.Object

org.drip.learning.rxtor1.GeneralizedLearner

All Implemented Interfaces:

EmpiricalLearningMetricEstimator

Direct Known Subclasses:

L1LossLearner, LipschitzLossLearner, LpLossLearner

public abstract class GeneralizedLearner
extends java.lang.Object
implements EmpiricalLearningMetricEstimator

GeneralizedLearner implements the Learner Class that holds the Space of Normed R^x To Normed R^1 Learning Functions along with their Custom Empirical Loss. Class-Specific Asymptotic Sample, Covering Number based Upper Probability Bounds and other Parameters are also maintained. 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
GeneralizedLearner(NormedRxToNormedR1Finite funcClassRxToR1, CoveringNumberLossBound funcClassCNLB, RegularizationFunction regularizerFunc) GeneralizedLearner Constructor

Method Summary

Modifier and Type	Method and Description
CoveringNumberLossBound	coveringLossBoundEvaluator() Retrieve the Covering Number based Deviation Upper Probability Bound Generator
NormedRxToNormedR1Finite	functionClass() Retrieve the Underlying Learner Function Class
double	genericCoveringProbabilityBound(GeneralizedValidatedVector gvvi, int iSampleSize, double dblEpsilon, boolean bSupremum) Compute the Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for General-Purpose Learning
double	genericCoveringProbabilityBound(int iSampleSize, double dblEpsilon, boolean bSupremum) Compute the Upper Bound of the Probability of the Absolute Deviation of the Empirical Mean from the Population Mean using the Function Class Supremum Covering Number for General-Purpose Learning
double	genericCoveringSampleSize(double dblEpsilon, double dblDeviationUpperProbabilityBound, boolean bSupremum) Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds.
double	genericCoveringSampleSize(GeneralizedValidatedVector gvvi, double dblEpsilon, double dblDeviationUpperProbabilityBound, boolean bSupremum) Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds.
double	regressorCoveringProbabilityBound(GeneralizedValidatedVector gvvi, int iSampleSize, double dblEpsilon, boolean bSupremum) Compute the Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning
double	regressorCoveringProbabilityBound(int iSampleSize, double dblEpsilon, boolean bSupremum) Compute the Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning
double	regressorCoveringSampleSize(double dblEpsilon, double dblDeviationUpperProbabilityBound, boolean bSupremum) Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds for Regression Learning.
double	regressorCoveringSampleSize(GeneralizedValidatedVector gvvi, double dblEpsilon, double dblDeviationUpperProbabilityBound, boolean bSupremum) Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds for Regression Learning.
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

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.drip.learning.rxtor1.EmpiricalLearningMetricEstimator

empiricalLoss, empiricalLoss, empiricalRisk, empiricalRisk, lossSampleCoveringNumber

Constructor Detail

GeneralizedLearner

public GeneralizedLearner(NormedRxToNormedR1Finite funcClassRxToR1,
                          CoveringNumberLossBound funcClassCNLB,
                          RegularizationFunction regularizerFunc)
                   throws java.lang.Exception

GeneralizedLearner Constructor

Parameters:

funcClassRxToR1 - R^x To R^1 Function Class

funcClassCNLB - The Function Class Covering Number based Deviation Upper Probability Bound Generator

regularizerFunc - The Regularizer Function

Throws:

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

Method Detail

functionClass

public NormedRxToNormedR1Finite functionClass()

Description copied from interface: EmpiricalLearningMetricEstimator

Retrieve the Underlying Learner Function Class

Specified by:

functionClass in interface EmpiricalLearningMetricEstimator

Returns:

The Underlying Learner Function Class

regularizerFunction

public RegularizationFunction regularizerFunction()

Description copied from interface: EmpiricalLearningMetricEstimator

Retrieve the Regularizer Function

Specified by:

regularizerFunction in interface EmpiricalLearningMetricEstimator

Returns:

The Regularizer Function

supremumEmpiricalLoss

public EmpiricalPenaltySupremum supremumEmpiricalLoss(GeneralizedValidatedVector gvviX,
                                                      GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Empirical Sample Loss

Specified by:

supremumEmpiricalLoss in interface EmpiricalLearningMetricEstimator

Parameters:

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

structuralLoss

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Structural Sample Loss

Specified by:

structuralLoss in interface EmpiricalLearningMetricEstimator

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

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Structural Sample Loss

Specified by:

structuralLoss in interface EmpiricalLearningMetricEstimator

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

public EmpiricalPenaltySupremum supremumStructuralLoss(GeneralizedValidatedVector gvviX)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Structural Sample Loss

Specified by:

supremumStructuralLoss in interface EmpiricalLearningMetricEstimator

Parameters:

gvviX - The Validated Predictor Instance

Returns:

The Supremum Structural Sample Loss

regularizedLoss

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Regularized Sample Loss (Empirical + Structural)

Specified by:

regularizedLoss in interface EmpiricalLearningMetricEstimator

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

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Regularized Sample Loss (Empirical + Structural)

Specified by:

regularizedLoss in interface EmpiricalLearningMetricEstimator

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

public EmpiricalPenaltySupremum supremumRegularizedLoss(GeneralizedValidatedVector gvviX,
                                                        GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Regularized Sample Loss

Specified by:

supremumRegularizedLoss in interface EmpiricalLearningMetricEstimator

Parameters:

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Loss

supremumEmpiricalRisk

public EmpiricalPenaltySupremum supremumEmpiricalRisk(R1R1 distR1R1,
                                                      GeneralizedValidatedVector gvviX,
                                                      GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Empirical Sample Risk

Specified by:

supremumEmpiricalRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

supremumEmpiricalRisk

public EmpiricalPenaltySupremum supremumEmpiricalRisk(RdR1 distRdR1,
                                                      GeneralizedValidatedVector gvviX,
                                                      GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Empirical Sample Risk

Specified by:

supremumEmpiricalRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Empirical Sample Loss

structuralRisk

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Structural Sample Risk

Specified by:

structuralRisk in interface EmpiricalLearningMetricEstimator

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

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Structural Sample Risk

Specified by:

structuralRisk in interface EmpiricalLearningMetricEstimator

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

public EmpiricalPenaltySupremum supremumStructuralRisk(R1R1 distR1R1,
                                                       GeneralizedValidatedVector gvviX,
                                                       GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Structural Sample Risk

Specified by:

supremumStructuralRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Structural Sample Loss

supremumStructuralRisk

public EmpiricalPenaltySupremum supremumStructuralRisk(RdR1 distRdR1,
                                                       GeneralizedValidatedVector gvviX,
                                                       GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Structural Sample Risk

Specified by:

supremumStructuralRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Structural Sample Risk

regularizedRisk

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Regularized Sample Risk (Empirical + Structural)

Specified by:

regularizedRisk in interface EmpiricalLearningMetricEstimator

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

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

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Regularized Sample Risk (Empirical + Structural)

Specified by:

regularizedRisk in interface EmpiricalLearningMetricEstimator

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

public EmpiricalPenaltySupremum supremumRegularizedRisk(R1R1 distR1R1,
                                                        GeneralizedValidatedVector gvviX,
                                                        GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Regularized Sample Risk

Specified by:

supremumRegularizedRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distR1R1 - R^1 R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Risk

supremumRegularizedRisk

public EmpiricalPenaltySupremum supremumRegularizedRisk(RdR1 distRdR1,
                                                        GeneralizedValidatedVector gvviX,
                                                        GeneralizedValidatedVector gvviY)

Description copied from interface: EmpiricalLearningMetricEstimator

Compute the Supremum Regularized Sample Risk

Specified by:

supremumRegularizedRisk in interface EmpiricalLearningMetricEstimator

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

gvviX - The Validated Predictor Instance

gvviY - The Validated Response Instance

Returns:

The Supremum Regularized Sample Risk

coveringLossBoundEvaluator

public CoveringNumberLossBound coveringLossBoundEvaluator()

Retrieve the Covering Number based Deviation Upper Probability Bound Generator

Returns:

The Covering Number based Deviation Upper Probability Bound Generator

genericCoveringProbabilityBound

public double genericCoveringProbabilityBound(int iSampleSize,
                                              double dblEpsilon,
                                              boolean bSupremum)
                                       throws java.lang.Exception

Compute the Upper Bound of the Probability of the Absolute Deviation of the Empirical Mean from the Population Mean using the Function Class Supremum Covering Number for General-Purpose Learning

Parameters:

iSampleSize - The Sample Size

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 Upper Bound of the Probability of the Absolute Deviation of the Empirical Mean from the Population Mean using the Function Class Supremum Covering Number for General-Purpose Learning

Throws:

java.lang.Exception - Thrown if the Upper Probability Bound cannot be computed

genericCoveringSampleSize

public double genericCoveringSampleSize(double dblEpsilon,
                                        double dblDeviationUpperProbabilityBound,
                                        boolean bSupremum)
                                 throws java.lang.Exception

Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds.

Parameters:

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

dblDeviationUpperProbabilityBound - The Upper Bound of the Probability for the given Deviation

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

Returns:

The Minimum Possible Sample Size

Throws:

java.lang.Exception - Thrown if the Minimum Sample Size cannot be computed

genericCoveringProbabilityBound

public double genericCoveringProbabilityBound(GeneralizedValidatedVector gvvi,
                                              int iSampleSize,
                                              double dblEpsilon,
                                              boolean bSupremum)
                                       throws java.lang.Exception

Compute the Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for General-Purpose Learning

Parameters:

gvvi - The Validated Instance Vector Sequence

iSampleSize - The Sample Size

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 Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for General-Purpose Learning

Throws:

java.lang.Exception - Thrown if the Upper Probability Bound cannot be computed

genericCoveringSampleSize

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

Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds.

Parameters:

gvvi - The Validated Instance Vector Sequence

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

dblDeviationUpperProbabilityBound - The Upper Bound of the Probability for the given Deviation

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

Returns:

The Minimum Possible Sample Size

Throws:

java.lang.Exception - Thrown if the Minimum Sample Size cannot be computed

regressorCoveringProbabilityBound

public double regressorCoveringProbabilityBound(int iSampleSize,
                                                double dblEpsilon,
                                                boolean bSupremum)
                                         throws java.lang.Exception

Compute the Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning

Parameters:

iSampleSize - The Sample Size

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 Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning

Throws:

java.lang.Exception - Thrown if the Upper Probability Bound cannot be computed

regressorCoveringSampleSize

public double regressorCoveringSampleSize(double dblEpsilon,
                                          double dblDeviationUpperProbabilityBound,
                                          boolean bSupremum)
                                   throws java.lang.Exception

Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds for Regression Learning.

Parameters:

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

dblDeviationUpperProbabilityBound - The Upper Bound of the Probability for the given Deviation

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

Returns:

The Minimum Possible Sample Size

Throws:

java.lang.Exception - Thrown if the Minimum Sample Size cannot be computed

regressorCoveringProbabilityBound

public double regressorCoveringProbabilityBound(GeneralizedValidatedVector gvvi,
                                                int iSampleSize,
                                                double dblEpsilon,
                                                boolean bSupremum)
                                         throws java.lang.Exception

Compute the Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning

Parameters:

gvvi - The Validated Instance Vector Sequence

iSampleSize - The Sample Size

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 Sample/Data Dependent Upper Bound of the Probability of the Absolute Deviation between the Empirical and the Population Means using the Function Class Supremum Covering Number for Regression Learning

Throws:

java.lang.Exception - Thrown if the Upper Probability Bound cannot be computed

regressorCoveringSampleSize

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

Compute the Minimum Possible Sample Size needed to generate the required Upper Probability Bound for the Specified Empirical Deviation using the Covering Number Convergence Bounds for Regression Learning.

Parameters:

gvvi - The Validated Instance Vector Sequence

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

dblDeviationUpperProbabilityBound - The Upper Bound of the Probability for the given Deviation

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

Returns:

The Minimum Possible Sample Size

Throws:

java.lang.Exception - Thrown if the Minimum Sample Size cannot be computed