Package org.drip.learning.rxtor1

Class EmpiricalPenaltySupremumEstimator

java.lang.Object

org.drip.function.definition.RdToR1

org.drip.sequence.functional.MultivariateRandom

org.drip.sequence.functional.BoundedMultivariateRandom

org.drip.learning.rxtor1.EmpiricalPenaltySupremumEstimator

public class EmpiricalPenaltySupremumEstimator
extends BoundedMultivariateRandom

EmpiricalPenaltySupremumEstimator contains the Implementation of the Empirical Penalty Supremum Estimator dependent on Multivariate Random Variables where the Multivariate Function is a Linear Combination of Bounded Univariate Functions acting on each Random Variate.

• 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

Field Summary

Fields

Modifier and Type	Field	Description
static int	SUPREMUM_PENALTY_EMPIRICAL_LOSS	Supremum Penalty computed off of Empirical Loss
static int	SUPREMUM_PENALTY_EMPIRICAL_RISK	Supremum Penalty computed off of Empirical Risk
static int	SUPREMUM_PENALTY_REGULARIZED_LOSS	Supremum Penalty computed off of Regularized Loss
static int	SUPREMUM_PENALTY_REGULARIZED_RISK	Supremum Penalty computed off of Regularized Risk
static int	SUPREMUM_PENALTY_STRUCTURAL_LOSS	Supremum Penalty computed off of Structural Loss
static int	SUPREMUM_PENALTY_STRUCTURAL_RISK	Supremum Penalty computed off of Structural Risk

Constructor Summary

Constructors

Constructor	Description
EmpiricalPenaltySupremumEstimator(int iSupremumPenaltyLossMode, EmpiricalLearningMetricEstimator elme, GeneralizedValidatedVector gvviY, R1R1 distR1R1, RdR1 distRdR1)	EmpiricalPenaltySupremumEstimator Constructor

Method Summary

Modifier and Type	Method	Description
int	dimension()	Retrieve the Dimension of the Input Variate
EmpiricalLearningMetricEstimator	elme()	Retrieve the Empirical Learning Metric Estimator Instance
GeneralizedValidatedVector	empiricalOutcomes()	Retrieve the Validated Outcome Instance
double	evaluate(double[] adblX)	Evaluate for the given Input Variates
double	evaluate(double[][] aadblX)	Retrieve the Worst-case Loss over the Multivariate Sequence
EmpiricalPenaltySupremum	supremum(GeneralizedValidatedVector gvviX)	Compute the Empirical Penalty Supremum for the specified R^1/R^d Input Space
int	supremumPenaltyLossMode()	The Supremum Penalty Loss Mode Flag
EmpiricalPenaltySupremum	supremumR1(GeneralizedValidatedVector gvviX)	Compute the Empirical Penalty Supremum for the specified R^1 Input Space
R1ToR1	supremumR1ToR1(double[] adblX)	Retrieve the Supremum R^1 To R^1 Function Instance for the specified Variate Sequence
EmpiricalPenaltySupremum	supremumRd(GeneralizedValidatedVector gvviX)	Compute the Empirical Penalty Supremum for the specified R^d Input Space
RdToR1	supremumRdToR1(double[][] aadblX)	Retrieve the Supremum R^d To R^1 Function Instance for the specified Variate Sequence
double	targetVariateVarianceBound(int iTargetVariateIndex)	Retrieve the Maximal Agnostic Variance Bound over the Non-target Variate Space for the Target Variate

Methods inherited from class org.drip.sequence.functional.MultivariateRandom

conditionalTargetVariateMetrics, conditionalTargetVariateMetrics, ghostTargetVariateMetrics, ghostTargetVariateMetrics, ghostTargetVariateMetrics, unconditionalTargetVariateMetrics

Methods inherited from class org.drip.function.definition.RdToR1

conditionNumber, conditionNumberL2, conditionNumberLInfinity, conditionNumberLp, derivative, differential, gradient, gradientModulus, gradientModulusFunction, hessian, integrate, jacobian, maxima, minima, ValidateInput

Methods inherited from class java.lang.Object

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

Field Details

SUPREMUM_PENALTY_EMPIRICAL_LOSS

public static final int SUPREMUM_PENALTY_EMPIRICAL_LOSS

Supremum Penalty computed off of Empirical Loss

See Also:

Constant Field Values

SUPREMUM_PENALTY_STRUCTURAL_LOSS

public static final int SUPREMUM_PENALTY_STRUCTURAL_LOSS

Supremum Penalty computed off of Structural Loss

See Also:

Constant Field Values

SUPREMUM_PENALTY_REGULARIZED_LOSS

public static final int SUPREMUM_PENALTY_REGULARIZED_LOSS

Supremum Penalty computed off of Regularized Loss

See Also:

Constant Field Values

SUPREMUM_PENALTY_EMPIRICAL_RISK

public static final int SUPREMUM_PENALTY_EMPIRICAL_RISK

Supremum Penalty computed off of Empirical Risk

See Also:

Constant Field Values

SUPREMUM_PENALTY_STRUCTURAL_RISK

public static final int SUPREMUM_PENALTY_STRUCTURAL_RISK

Supremum Penalty computed off of Structural Risk

See Also:

Constant Field Values

SUPREMUM_PENALTY_REGULARIZED_RISK

public static final int SUPREMUM_PENALTY_REGULARIZED_RISK

Supremum Penalty computed off of Regularized Risk

See Also:

Constant Field Values

Constructor Details

EmpiricalPenaltySupremumEstimator

public EmpiricalPenaltySupremumEstimator(int iSupremumPenaltyLossMode,
EmpiricalLearningMetricEstimator elme,
GeneralizedValidatedVector gvviY,
R1R1 distR1R1,
RdR1 distRdR1)
                                  throws java.lang.Exception

EmpiricalPenaltySupremumEstimator Constructor

Parameters:

iSupremumPenaltyLossMode - Supremum Loss Penalty Mode

elme - The Empirical Learning Metric Estimator Instance

gvviY - The Validated Outcome Instance

distR1R1 - R^1 R^1 Multivariate Measure

distRdR1 - R^d R^1 Multivariate Measure

Throws:

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

Method Details

supremumPenaltyLossMode

public int supremumPenaltyLossMode()

The Supremum Penalty Loss Mode Flag

Returns:

The Supremum Penalty Loss Mode Flag

elme

public EmpiricalLearningMetricEstimator elme()

Retrieve the Empirical Learning Metric Estimator Instance

Returns:

The Empirical Learning Metric Estimator Instance

empiricalOutcomes

public GeneralizedValidatedVector empiricalOutcomes()

Retrieve the Validated Outcome Instance

Returns:

The Validated Outcome Instance

supremumR1

public EmpiricalPenaltySupremum supremumR1(GeneralizedValidatedVector gvviX)

Compute the Empirical Penalty Supremum for the specified R^1 Input Space

Parameters:

gvviX - The R^1 Input Space

Returns:

The Empirical Penalty Supremum for the specified R^1 Input Space

supremumRd

public EmpiricalPenaltySupremum supremumRd(GeneralizedValidatedVector gvviX)

Compute the Empirical Penalty Supremum for the specified R^d Input Space

Parameters:

gvviX - The R^d Input Space

Returns:

The Empirical Penalty Supremum for the specified R^d Input Space

supremum

public EmpiricalPenaltySupremum supremum(GeneralizedValidatedVector gvviX)

Compute the Empirical Penalty Supremum for the specified R^1/R^d Input Space

Parameters:

gvviX - The R^1/R^d Input Space

Returns:

The Empirical Penalty Supremum for the specified R^1/R^d Input Space

supremumR1ToR1

public R1ToR1 supremumR1ToR1(double[] adblX)

Retrieve the Supremum R^1 To R^1 Function Instance for the specified Variate Sequence

Parameters:

adblX - The Predictor Instance

Returns:

The Supremum R^1 To R^1 Function Instance

supremumRdToR1

public RdToR1 supremumRdToR1(double[][] aadblX)

Retrieve the Supremum R^d To R^1 Function Instance for the specified Variate Sequence

Parameters:

aadblX - The Predictor Instance

Returns:

The Supremum R^d To R^1 Function Instance

dimension

public int dimension()

Description copied from class: RdToR1

Retrieve the Dimension of the Input Variate

Specified by:

dimension in class RdToR1

Returns:

The Dimension of the Input Variate

evaluate

public double evaluate(double[] adblX)
                throws java.lang.Exception

Description copied from class: RdToR1

Evaluate for the given Input Variates

Specified by:

evaluate in class RdToR1

Parameters:

adblX - Array of Input Variates

Returns:

The Calculated Value

Throws:

java.lang.Exception - Thrown if the Evaluation cannot be done

evaluate

public double evaluate(double[][] aadblX)
                throws java.lang.Exception

Retrieve the Worst-case Loss over the Multivariate Sequence

Parameters:

aadblX - The Multivariate Array

Returns:

The Worst-case Loss over the Multivariate Sequence

Throws:

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

targetVariateVarianceBound

public double targetVariateVarianceBound(int iTargetVariateIndex)
                                  throws java.lang.Exception

Description copied from class: BoundedMultivariateRandom

Retrieve the Maximal Agnostic Variance Bound over the Non-target Variate Space for the Target Variate

Specified by:

targetVariateVarianceBound in class BoundedMultivariateRandom

Parameters:

iTargetVariateIndex - The Index corresponding to the Variate on which the Bound is sought

Returns:

The Maximal Agnostic Bound over the Non-target Variate Space for the Target Variate

Throws:

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