EmpiricalPenaltySupremumMetrics.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>EmpiricalPenaltySupremumMetrics</i> computes Efron-Stein Metrics for the Penalty Supremum R<sup>x</sup>
* To R<sup>1</sup> Functions.
*
* <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 EmpiricalPenaltySupremumMetrics extends org.drip.sequence.functional.EfronSteinMetrics {
private org.drip.learning.rxtor1.EmpiricalPenaltySupremumEstimator _epse = null;
private org.drip.learning.bound.MeasureConcentrationExpectationBound _mceb = null;
/**
* EmpiricalPenaltySupremumMetrics Constructor
*
* @param epse R^x To R^1 The Empirical Penalty Supremum Estimator Instance
* @param aSSAM Array of the Individual Single Sequence Metrics
* @param mceb The Concentration-of-Measure Loss Expectation Bound Estimator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public EmpiricalPenaltySupremumMetrics (
final org.drip.learning.rxtor1.EmpiricalPenaltySupremumEstimator epse,
final org.drip.sequence.metrics.SingleSequenceAgnosticMetrics[] aSSAM,
final org.drip.learning.bound.MeasureConcentrationExpectationBound mceb)
throws java.lang.Exception
{
super (epse, aSSAM);
if (null == (_epse = epse) || null == (_mceb = mceb))
throw new java.lang.Exception ("EmpiricalPenaltySupremumMetrics ctr: Invalid Inputs");
}
/**
* Retrieve the Empirical Penalty Supremum Function
*
* @return The Empirical Penalty Supremum Function
*/
public org.drip.learning.rxtor1.EmpiricalPenaltySupremumEstimator empiricalPenaltySupremumEstimator()
{
return _epse;
}
/**
* Retrieve the Univariate Sequence Dependent Variance Bound
*
* @param adblVariate The univariate Sequence
*
* @return The Univariate Sequence Dependent Variance Bound
*
* @throws java.lang.Exception Thrown if the Date Dependent Variance Bound cannot be Computed
*/
public double dataDependentVarianceBound (
final double[] adblVariate)
throws java.lang.Exception
{
return _epse.evaluate (adblVariate) / adblVariate.length;
}
/**
* Retrieve the Multivariate Sequence Dependent Variance Bound
*
* @param aadblVariate The Multivariate Sequence
*
* @return The Multivariate Sequence Dependent Variance Bound
*
* @throws java.lang.Exception Thrown if the Date Dependent Variance Bound cannot be Computed
*/
public double dataDependentVarianceBound (
final double[][] aadblVariate)
throws java.lang.Exception
{
return _epse.evaluate (aadblVariate) / aadblVariate.length;
}
/**
* 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.
*
* @param adblVariate The Sample Univariate Array
*
* @return The Lugosi Data-Dependent Variance Bound
*
* @throws java.lang.Exception Thrown if the Lugosi Data-Dependent Variance Bound cannot be computed
*/
public double lugosiVarianceBound (
final double[] adblVariate)
throws java.lang.Exception
{
org.drip.function.definition.R1ToR1 supR1ToR1 = _epse.supremumR1ToR1 (adblVariate);
if (null == supR1ToR1)
throw new java.lang.Exception
("EmpiricalPenaltySupremumMetrics::lugosiVarianceBound => Cannot Find Supremum Classifier");
return dataDependentVarianceBound (adblVariate) + _mceb.constant() + java.lang.Math.pow
(adblVariate.length, _mceb.exponent());
}
/**
* 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.
*
* @param aadblVariate The Sample Multivariate Array
*
* @return The Lugosi Data-Dependent Variance Bound
*
* @throws java.lang.Exception Thrown if the Lugosi Data-Dependent Variance Bound cannot be computed
*/
public double lugosiVarianceBound (
final double[][] aadblVariate)
throws java.lang.Exception
{
org.drip.function.definition.RdToR1 supRdToR1 = _epse.supremumRdToR1 (aadblVariate);
if (null == supRdToR1)
throw new java.lang.Exception
("EmpiricalPenaltySupremumMetrics::lugosiVarianceBound => Cannot Find Supremum Classifier");
return dataDependentVarianceBound (aadblVariate) + _mceb.constant() + java.lang.Math.pow
(aadblVariate.length, _mceb.exponent());
}
}