EmpiricalPenaltySupremumEstimator.java
package org.drip.learning.rxtor1;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>EmpiricalPenaltySupremumEstimator</i> 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.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning">Agnostic Learning Bounds under Empirical Loss Minimization Schemes</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning/rxtor1">Statistical Learning Empirical Loss Penalizer</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class EmpiricalPenaltySupremumEstimator extends org.drip.sequence.functional.BoundedMultivariateRandom {
/**
* Supremum Penalty computed off of Empirical Loss
*/
public static final int SUPREMUM_PENALTY_EMPIRICAL_LOSS = 1;
/**
* Supremum Penalty computed off of Structural Loss
*/
public static final int SUPREMUM_PENALTY_STRUCTURAL_LOSS = 2;
/**
* Supremum Penalty computed off of Regularized Loss
*/
public static final int SUPREMUM_PENALTY_REGULARIZED_LOSS = 4;
/**
* Supremum Penalty computed off of Empirical Risk
*/
public static final int SUPREMUM_PENALTY_EMPIRICAL_RISK = 8;
/**
* Supremum Penalty computed off of Structural Risk
*/
public static final int SUPREMUM_PENALTY_STRUCTURAL_RISK = 16;
/**
* Supremum Penalty computed off of Regularized Risk
*/
public static final int SUPREMUM_PENALTY_REGULARIZED_RISK = 32;
private int _iSupremumPenaltyLossMode = -1;
private org.drip.measure.continuous.R1R1 _distR1R1 = null;
private org.drip.measure.continuous.RdR1 _distRdR1 = null;
private org.drip.spaces.rxtor1.NormedR1ToNormedR1[] _aR1ToR1 = null;
private org.drip.spaces.rxtor1.NormedRdToNormedR1[] _aRdToR1 = null;
private org.drip.spaces.instance.GeneralizedValidatedVector _gvviY = null;
private org.drip.learning.rxtor1.EmpiricalLearningMetricEstimator _elme = null;
/**
* EmpiricalPenaltySupremumEstimator Constructor
*
* @param iSupremumPenaltyLossMode Supremum Loss Penalty Mode
* @param elme The Empirical Learning Metric Estimator Instance
* @param gvviY The Validated Outcome Instance
* @param distR1R1 R^1 R^1 Multivariate Measure
* @param distRdR1 R^d R^1 Multivariate Measure
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public EmpiricalPenaltySupremumEstimator (
final int iSupremumPenaltyLossMode,
final org.drip.learning.rxtor1.EmpiricalLearningMetricEstimator elme,
final org.drip.spaces.instance.GeneralizedValidatedVector gvviY,
final org.drip.measure.continuous.R1R1 distR1R1,
final org.drip.measure.continuous.RdR1 distRdR1)
throws java.lang.Exception
{
if (null == (_elme = elme))
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator ctr: Invalid Inputs");
org.drip.spaces.rxtor1.NormedRxToNormedR1[] aRxToR1 = _elme.functionClass().functionSpaces();
if (null == aRxToR1)
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator ctr: Invalid Inputs");
if (aRxToR1 instanceof org.drip.spaces.rxtor1.NormedR1ToNormedR1[])
_aR1ToR1 = (org.drip.spaces.rxtor1.NormedR1ToNormedR1[]) aRxToR1;
else
_aRdToR1 = (org.drip.spaces.rxtor1.NormedRdToNormedR1[]) aRxToR1;
_gvviY = gvviY;
_distR1R1 = distR1R1;
_distRdR1 = distRdR1;
int iNumRxToR1 = aRxToR1.length;
_iSupremumPenaltyLossMode = iSupremumPenaltyLossMode;
if (SUPREMUM_PENALTY_EMPIRICAL_LOSS == _iSupremumPenaltyLossMode && null == _gvviY)
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator ctr: Invalid Inputs");
for (int i = 0; i < iNumRxToR1; ++i) {
if (null == aRxToR1[i])
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator ctr: Invalid Inputs");
}
}
/**
* The Supremum Penalty Loss Mode Flag
*
* @return The Supremum Penalty Loss Mode Flag
*/
public int supremumPenaltyLossMode()
{
return _iSupremumPenaltyLossMode;
}
/**
* Retrieve the Empirical Learning Metric Estimator Instance
*
* @return The Empirical Learning Metric Estimator Instance
*/
public org.drip.learning.rxtor1.EmpiricalLearningMetricEstimator elme()
{
return _elme;
}
/**
* Retrieve the Validated Outcome Instance
*
* @return The Validated Outcome Instance
*/
public org.drip.spaces.instance.GeneralizedValidatedVector empiricalOutcomes()
{
return _gvviY;
}
/**
* Compute the Empirical Penalty Supremum for the specified R^1 Input Space
*
* @param gvviX The R^1 Input Space
*
* @return The Empirical Penalty Supremum for the specified R^1 Input Space
*/
public org.drip.learning.rxtor1.EmpiricalPenaltySupremum supremumR1 (
final org.drip.spaces.instance.GeneralizedValidatedVector gvviX)
{
if (null == _aR1ToR1) return null;
int iSupremumIndex = 0;
int iNumR1ToR1 = _aR1ToR1.length;
double dblSupremumPenaltyLoss = 0.;
for (int i = 0 ; i < iNumR1ToR1; ++i) {
org.drip.function.definition.R1ToR1 funcR1ToR1 = _aR1ToR1[i].function();
if (null == funcR1ToR1) return null;
double dblPenaltyLoss = 0.;
try {
if (SUPREMUM_PENALTY_EMPIRICAL_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.empiricalLoss (funcR1ToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_STRUCTURAL_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.structuralLoss (funcR1ToR1, gvviX);
else if (SUPREMUM_PENALTY_REGULARIZED_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.regularizedLoss (funcR1ToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_EMPIRICAL_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.empiricalRisk (_distR1R1, funcR1ToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_STRUCTURAL_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.structuralRisk (_distR1R1, funcR1ToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_REGULARIZED_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.regularizedRisk (_distR1R1, funcR1ToR1, gvviX, _gvviY);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
if (dblPenaltyLoss > dblSupremumPenaltyLoss) {
iSupremumIndex = i;
dblSupremumPenaltyLoss = dblPenaltyLoss;
}
}
try {
return new org.drip.learning.rxtor1.EmpiricalPenaltySupremum (iSupremumIndex,
dblSupremumPenaltyLoss / gvviX.sampleSize());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Empirical Penalty Supremum for the specified R^d Input Space
*
* @param gvviX The R^d Input Space
*
* @return The Empirical Penalty Supremum for the specified R^d Input Space
*/
public org.drip.learning.rxtor1.EmpiricalPenaltySupremum supremumRd (
final org.drip.spaces.instance.GeneralizedValidatedVector gvviX)
{
if (null == _aRdToR1) return null;
int iSupremumIndex = 0;
int iNumRdToR1 = _aRdToR1.length;
double dblSupremumPenaltyLoss = 0.;
for (int i = 0 ; i < iNumRdToR1; ++i) {
org.drip.function.definition.RdToR1 funcRdToR1 = _aRdToR1[i].function();
if (null == funcRdToR1) return null;
double dblPenaltyLoss = 0.;
try {
if (SUPREMUM_PENALTY_EMPIRICAL_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.empiricalLoss (funcRdToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_STRUCTURAL_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.structuralLoss (funcRdToR1, gvviX);
else if (SUPREMUM_PENALTY_REGULARIZED_LOSS == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.regularizedLoss (funcRdToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_EMPIRICAL_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.empiricalRisk (_distRdR1, funcRdToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_STRUCTURAL_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.structuralRisk (_distRdR1, funcRdToR1, gvviX, _gvviY);
else if (SUPREMUM_PENALTY_REGULARIZED_RISK == _iSupremumPenaltyLossMode)
dblPenaltyLoss += _elme.regularizedRisk (_distRdR1, funcRdToR1, gvviX, _gvviY);
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
if (dblPenaltyLoss > dblSupremumPenaltyLoss) {
iSupremumIndex = i;
dblSupremumPenaltyLoss = dblPenaltyLoss;
}
}
try {
return new org.drip.learning.rxtor1.EmpiricalPenaltySupremum (iSupremumIndex,
dblSupremumPenaltyLoss / gvviX.sampleSize());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Empirical Penalty Supremum for the specified R^1/R^d Input Space
*
* @param gvviX The R^1/R^d Input Space
*
* @return The Empirical Penalty Supremum for the specified R^1/R^d Input Space
*/
public org.drip.learning.rxtor1.EmpiricalPenaltySupremum supremum (
final org.drip.spaces.instance.GeneralizedValidatedVector gvviX)
{
org.drip.learning.rxtor1.EmpiricalPenaltySupremum epsR1 = supremumR1 (gvviX);
return null == epsR1 ? supremumRd (gvviX) : epsR1;
}
/**
* Retrieve the Supremum R^1 To R^1 Function Instance for the specified Variate Sequence
*
* @param adblX The Predictor Instance
*
* @return The Supremum R^1 To R^1 Function Instance
*/
public org.drip.function.definition.R1ToR1 supremumR1ToR1 (
final double[] adblX)
{
org.drip.learning.rxtor1.EmpiricalPenaltySupremum eps = null;
try {
eps = supremumR1 (new org.drip.spaces.instance.ValidatedR1
(org.drip.spaces.tensor.R1ContinuousVector.Standard(), adblX));
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return _aR1ToR1[eps.index()].function();
}
/**
* Retrieve the Supremum R^d To R^1 Function Instance for the specified Variate Sequence
*
* @param aadblX The Predictor Instance
*
* @return The Supremum R^d To R^1 Function Instance
*/
public org.drip.function.definition.RdToR1 supremumRdToR1 (
final double[][] aadblX)
{
org.drip.learning.rxtor1.EmpiricalPenaltySupremum eps = null;
try {
eps = supremumRd (new org.drip.spaces.instance.ValidatedRd
(org.drip.spaces.tensor.RdContinuousVector.Standard (aadblX.length), aadblX));
} catch (java.lang.Exception e) {
e.printStackTrace();
return null;
}
return _aRdToR1[eps.index()].function();
}
@Override public int dimension()
{
return -1;
}
@Override public double evaluate (
final double[] adblX)
throws java.lang.Exception
{
org.drip.learning.rxtor1.EmpiricalPenaltySupremum eps = supremumR1 (new
org.drip.spaces.instance.ValidatedR1 (org.drip.spaces.tensor.R1ContinuousVector.Standard(),
adblX));
if (null == eps)
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator::evaluate => Invalid Inputs");
return eps.value();
}
/**
* Retrieve the Worst-case Loss over the Multivariate Sequence
*
* @param aadblX The Multivariate Array
*
* @return The Worst-case Loss over the Multivariate Sequence
*
* @throws java.lang.Exception Thrown if the Worst-Case Loss cannot be computed
*/
public double evaluate (
final double[][] aadblX)
throws java.lang.Exception
{
if (null == aadblX)
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator::evaluate => Invalid Inputs");
org.drip.learning.rxtor1.EmpiricalPenaltySupremum eps = supremumRd (new
org.drip.spaces.instance.ValidatedRd (org.drip.spaces.tensor.RdContinuousVector.Standard
(aadblX.length), aadblX));
if (null == eps)
throw new java.lang.Exception ("EmpiricalPenaltySupremumEstimator::evaluate => Invalid Inputs");
return eps.value();
}
@Override public double targetVariateVarianceBound (
final int iTargetVariateIndex)
throws java.lang.Exception
{
return 1. / (_gvviY.sampleSize() * _gvviY.sampleSize());
}
}