Package org.drip.learning.rxtor1

Class EmpiricalPenaltySupremumMetrics

java.lang.Object

org.drip.sequence.functional.EfronSteinMetrics

org.drip.learning.rxtor1.EmpiricalPenaltySupremumMetrics

public class EmpiricalPenaltySupremumMetrics
extends EfronSteinMetrics

EmpiricalPenaltySupremumMetrics computes Efron-Stein Metrics for the Penalty Supremum R^x To R¹ Functions.

• 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
EmpiricalPenaltySupremumMetrics(EmpiricalPenaltySupremumEstimator epse, SingleSequenceAgnosticMetrics[] aSSAM, MeasureConcentrationExpectationBound mceb)	EmpiricalPenaltySupremumMetrics Constructor

Method Summary

Modifier and Type	Method	Description
double	dataDependentVarianceBound(double[] adblVariate)	Retrieve the Univariate Sequence Dependent Variance Bound
double	dataDependentVarianceBound(double[][] aadblVariate)	Retrieve the Multivariate Sequence Dependent Variance Bound
EmpiricalPenaltySupremumEstimator	empiricalPenaltySupremumEstimator()	Retrieve the Empirical Penalty Supremum Function
double	lugosiVarianceBound(double[] adblVariate)	Compute the Lugosi Data-Dependent Variance Bound from the Sample and the Classifier Class Asymptotic Behavior.
double	lugosiVarianceBound(double[][] aadblVariate)	Compute the Lugosi Data-Dependent Variance Bound from the Sample and the Classifier Class Asymptotic Behavior.

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

boundedVarianceUpperBound, efronSteinSteeleBound, function, ghostVarianceUpperBound, ghostVariateVarianceMetrics, martingaleVarianceUpperBound, pivotedDifferenceSequenceMetrics, pivotVarianceUpperBound, separableVarianceUpperBound, sequenceMetrics, symmetrizedDifferenceSequenceMetrics, variateFunctionVarianceMetrics, variateSequence

Methods inherited from class java.lang.Object

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

Constructor Details

EmpiricalPenaltySupremumMetrics

public EmpiricalPenaltySupremumMetrics(EmpiricalPenaltySupremumEstimator epse,
SingleSequenceAgnosticMetrics[] aSSAM,
MeasureConcentrationExpectationBound mceb)
                                throws java.lang.Exception

EmpiricalPenaltySupremumMetrics Constructor

Parameters:

epse - R^x To R^1 The Empirical Penalty Supremum Estimator Instance

aSSAM - Array of the Individual Single Sequence Metrics

mceb - The Concentration-of-Measure Loss Expectation Bound Estimator

Throws:

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

Method Details

empiricalPenaltySupremumEstimator

public EmpiricalPenaltySupremumEstimator empiricalPenaltySupremumEstimator()

Retrieve the Empirical Penalty Supremum Function

Returns:

The Empirical Penalty Supremum Function

dataDependentVarianceBound

public double dataDependentVarianceBound(double[] adblVariate)
                                  throws java.lang.Exception

Retrieve the Univariate Sequence Dependent Variance Bound

Parameters:

adblVariate - The univariate Sequence

Returns:

The Univariate Sequence Dependent Variance Bound

Throws:

java.lang.Exception - Thrown if the Date Dependent Variance Bound cannot be Computed

dataDependentVarianceBound

public double dataDependentVarianceBound(double[][] aadblVariate)
                                  throws java.lang.Exception

Retrieve the Multivariate Sequence Dependent Variance Bound

Parameters:

aadblVariate - The Multivariate Sequence

Returns:

The Multivariate Sequence Dependent Variance Bound

Throws:

java.lang.Exception - Thrown if the Date Dependent Variance Bound cannot be Computed

lugosiVarianceBound

public double lugosiVarianceBound(double[] adblVariate)
                           throws java.lang.Exception

Compute the Lugosi Data-Dependent Variance Bound from the Sample and the Classifier Class Asymptotic Behavior. The Reference is: G. Lugosi (2002): Pattern Classification and Learning Theory, in: L.Gyorfi, editor, Principles of Non-parametric Learning, 5-62, Springer, Wien.

Parameters:

adblVariate - The Sample Univariate Array

Returns:

The Lugosi Data-Dependent Variance Bound

Throws:

java.lang.Exception - Thrown if the Lugosi Data-Dependent Variance Bound cannot be computed

lugosiVarianceBound

public double lugosiVarianceBound(double[][] aadblVariate)
                           throws java.lang.Exception

Compute the Lugosi Data-Dependent Variance Bound from the Sample and the Classifier Class Asymptotic Behavior. The Reference is: G. Lugosi (2002): Pattern Classification and Learning Theory, in: L.Gyorfi, editor, Principles of Non-parametric Learning, 5-62, Springer, Wien.

Parameters:

aadblVariate - The Sample Multivariate Array

Returns:

The Lugosi Data-Dependent Variance Bound

Throws:

java.lang.Exception - Thrown if the Lugosi Data-Dependent Variance Bound cannot be computed