CoveringNumberBoundBuilder.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>CoveringNumberBoundBuilder</i> constructs the CoveringNumberProbabilityBound Instances for specific
 * Learning Situations. The References are:
 * <br><br>
 * <ul>
 *  <li>
 *      Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform
 *          Convergence, and Learnability <i>Journal of Association of Computational Machinery</i> <b>44
 *          (4)</b> 615-631
 *  </li>
 *  <li>
 *      Anthony, M., and P. L. Bartlett (1999): <i>Artificial Neural Network Learning - Theoretical
 *          Foundations</i> <b>Cambridge University Press</b> Cambridge, UK
 *  </li>
 *  <li>
 *      Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): <i>Towards Efficient Agnostic Learning</i>
 *          Machine Learning <b>17 (2)</b> 115-141
 *  </li>
 *  <li>
 *      Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with
 *          Squared Loss <i>IEEE Transactions on Information Theory</i> <b>44</b> 1974-1980
 *  </li>
 *  <li>
 *      Vapnik, V. N. (1998): <i>Statistical learning Theory</i> <b>Wiley</b> New York
 *  </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 CoveringNumberBoundBuilder {

    /**
     * Epsilon Exponent for Regression Learning
     */

    public static final double EPSILON_EXPONENT_REGRESSION_LEARNING = 1.;

    /**
     * Epsilon Exponent for Agnostic Learning
     */

    public static final double EPSILON_EXPONENT_AGNOSTIC_LEARNING = 2.;

    /**
     * Epsilon Exponent for Agnostic Learning with Convex Functions
     */

    public static final double EPSILON_EXPONENT_AGNOSTIC_CONVEX_LEARNING = 1.;

    /**
     * Construct the Regression Learning CoveringNumberProbabilityBound Instance
     * 
     * @param funcSampleCoefficient The Sample Coefficient Function
     * @param dblExponentScaler The Exponent Scaler
     * 
     * @return The Regression Learning CoveringNumberProbabilityBound Instance
     */

    public static final org.drip.learning.bound.CoveringNumberLossBound
        RegressionLearning (
            final org.drip.function.definition.R1ToR1 funcSampleCoefficient,
            final double dblExponentScaler)
    {
        try {
            return new org.drip.learning.bound.CoveringNumberLossBound (funcSampleCoefficient,
                EPSILON_EXPONENT_REGRESSION_LEARNING, dblExponentScaler);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct the Agnostic Learning CoveringNumberProbabilityBound Instance
     * 
     * @param funcSampleCoefficient The Sample Coefficient Function
     * @param dblExponentScaler The Exponent Scaler
     * 
     * @return The Agnostic Learning CoveringNumberProbabilityBound Instance
     */

    public static final org.drip.learning.bound.CoveringNumberLossBound
        AgnosticLearning (
            final org.drip.function.definition.R1ToR1 funcSampleCoefficient,
            final double dblExponentScaler)
    {
        try {
            return new org.drip.learning.bound.CoveringNumberLossBound (funcSampleCoefficient,
                EPSILON_EXPONENT_AGNOSTIC_LEARNING, dblExponentScaler);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * Construct the Agnostic Convex Learning CoveringNumberProbabilityBound Instance
     * 
     * @param funcSampleCoefficient The Sample Coefficient Function
     * @param dblExponentScaler The Exponent Scaler
     * 
     * @return The Agnostic Convex Learning CoveringNumberProbabilityBound Instance
     */

    public static final org.drip.learning.bound.CoveringNumberLossBound
        AgnosticConvexLearning (
            final org.drip.function.definition.R1ToR1 funcSampleCoefficient,
            final double dblExponentScaler)
    {
        try {
            return new org.drip.learning.bound.CoveringNumberLossBound (funcSampleCoefficient,
                EPSILON_EXPONENT_AGNOSTIC_CONVEX_LEARNING, dblExponentScaler);
        } catch (java.lang.Exception e) {
            e.printStackTrace();
        }

        return null;
    }
}