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());
    }
}