MeasureConcentrationExpectationBound.java

package org.drip.learning.bound;

/*
 * -*- 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>MeasureConcentrationExpectationBound</i> provides the Upper Bound of the Expected Loss between
 * Empirical Outcome and the Prediction of the given Learner Class using the Concentration of Measure
 * Inequalities. This is expressed as C n<sup>a</sup>, where n is the Size of the Sample, and 'C' and 'a' are
 * Constants specific to the Learning Class. The References are:
 * <br><br>
 * <ul>
 *  <li>
 *      Boucheron, S., G. Lugosi, and P. Massart (2003): Concentration Inequalities Using the Entropy Method
 *          <i>Annals of Probability</i> <b>31</b> 1583-1614
 *  </li>
 *  <li>
 *      Lugosi, G. (2002): Pattern Classification and Learning Theory, in: <i>L. Györ, editor, Principles
 *          of Non-parametric Learning</i> <b>Springer</b> Wien 5-62
 *  </li>
 * </ul>
 *
 *  <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/bound">Covering Numbers, Concentration, Lipschitz Bounds</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class MeasureConcentrationExpectationBound {
    private double _dblConstant = java.lang.Double.NaN;
    private double _dblExponent = java.lang.Double.NaN;

    /**
     * MeasureConcentrationExpectationBound Constructor
     * 
     * @param dblConstant Asymptote Constant
     * @param dblExponent Asymptote Exponent
     * 
     * @throws java.lang.Exception Thrown if the Constant and/or Exponent is Invalid
     */

    public MeasureConcentrationExpectationBound (
        final double dblConstant,
        final double dblExponent)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (_dblConstant = dblConstant) ||
            !org.drip.numerical.common.NumberUtil.IsValid (_dblExponent = dblExponent))
            throw new java.lang.Exception ("MeasureConcentrationExpectationBound ctr: Invalid Inputs!");
    }

    /**
     * Retrieve the Asymptote Constant
     * 
     * @return The Asymptote Constant
     */

    public double constant()
    {
        return _dblConstant;
    }

    /**
     * Retrieve the Asymptote Exponent
     * 
     * @return The Asymptote Exponent
     */

    public double exponent()
    {
        return _dblExponent;
    }

    /**
     * Compute the Expected Loss Upper Bound between the Sample and the Population for the specified Sample
     *  Size
     * 
     * @param iSampleSize The Sample Size
     * 
     * @return The Expected Loss Upper Bound the Sample and the Population for the specified Sample Size
     * 
     * @throws java.lang.Exception Thrown if the Expected Loss Upper Bound cannot be computed
     */

    public double lossExpectationUpperBound (
        final int iSampleSize)
        throws java.lang.Exception
    {
        if (0 >= iSampleSize)
            throw new java.lang.Exception
                ("MeasureConcentrationExpectationBound::lossExpectationUpperBound => Invalid Inputs");

        return _dblConstant * java.lang.Math.pow (iSampleSize, _dblExponent);
    }
}