KernelDensityL1Bound.java

package org.drip.sample.efronstein;

import org.drip.function.r1tor1.FlatUnivariate;
import org.drip.numerical.common.FormatUtil;
import org.drip.sequence.custom.KernelDensityEstimationL1;
import org.drip.sequence.functional.*;
import org.drip.sequence.metrics.SingleSequenceAgnosticMetrics;
import org.drip.sequence.random.*;
import org.drip.service.env.EnvManager;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * 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 risk, transaction costs, exposure, margin
 *      calculations, valuation adjustment, and portfolio construction within and across fixed income,
 *      credit, commodity, equity, FX, and structured products.
 *  
 *      https://lakshmidrip.github.io/DROP/
 *  
 *  DROP is composed of three modules:
 *  
 *  - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
 *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
 *  - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
 * 
 *  DROP Analytics Core implements libraries for the following:
 *  - Fixed Income Analytics
 *  - Asset Backed Analytics
 *  - XVA Analytics
 *  - Exposure and Margin Analytics
 * 
 *  DROP Portfolio Core implements libraries for the following:
 *  - Asset Allocation Analytics
 *  - Transaction Cost Analytics
 * 
 *  DROP Numerical Core implements libraries for the following:
 *  - Statistical Learning
 *  - Numerical Optimizer
 *  - Spline Builder
 *  - Algorithm Support
 * 
 *  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>KernelDensityL1Bound</i> demonstrates the Computation of the Probabilistic Bounds for the L<sub>1</sub>
 * Errors of Kernel Density Estimation using Variants of the Efron-Stein Methodology.
 *  
 * <br><br>
 *  <ul>
 *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
 *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/README.md">Sample</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sample/efronstein/README.md">Efron-Stein Semi-Agnostic Sequence Bounds</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class KernelDensityL1Bound {

    private static final SingleSequenceAgnosticMetrics[] IIDDraw (
        final UnivariateSequenceGenerator rsg,
        final int iNumSample)
        throws Exception
    {
        SingleSequenceAgnosticMetrics[] aSSAM = new SingleSequenceAgnosticMetrics[iNumSample];

        for (int i = 0; i < iNumSample; ++i)
            aSSAM[i] = rsg.sequence (
                iNumSample,
                null
            );

        return aSSAM;
    }

    private static final KernelDensityEstimationL1 KernelDensityL1Function (
        final int iNumVariate)
        throws Exception
    {
        return new KernelDensityEstimationL1 (
            new FlatUnivariate (0.),
            1.,
            iNumVariate,
            new FlatUnivariate (-2.)
        );
    }

    private static final void MartingaleDifferencesRun (
        final Binary bsg,
        final int iNumSample,
        final int iNumSet)
        throws Exception
    {
        String strDump = "\t| " + FormatUtil.FormatDouble (iNumSample, 2, 0, 1.) + " => ";

        for (int j = 0; j < iNumSet; ++j) {
            SingleSequenceAgnosticMetrics[] aSSAM = IIDDraw (
                bsg,
                iNumSample
            );

            EfronSteinMetrics esam = new EfronSteinMetrics (
                KernelDensityL1Function (iNumSample),
                aSSAM
            );

            if (0 != j) strDump += " |";

            strDump += FormatUtil.FormatDouble (esam.martingaleVarianceUpperBound(), 1, 3, 1.);
        }

        System.out.println (strDump + " |");
    }

    private static final void GhostVariateVarianceRun (
        final Binary bsg,
        final int iNumSample,
        final int iNumSet)
        throws Exception
    {
        String strDump = "\t| " + FormatUtil.FormatDouble (iNumSample, 2, 0, 1.) + " => ";

        for (int j = 0; j < iNumSet; ++j) {
            SingleSequenceAgnosticMetrics[] aSSAM = IIDDraw (
                bsg,
                iNumSample
            );

            EfronSteinMetrics esam = new EfronSteinMetrics (
                KernelDensityL1Function (iNumSample),
                aSSAM
            );

            SingleSequenceAgnosticMetrics[] aSSAMGhost = IIDDraw (
                bsg,
                iNumSample
            );

            if (0 != j) strDump += " |";

            strDump += FormatUtil.FormatDouble (esam.ghostVarianceUpperBound (aSSAMGhost), 1, 3, 1.);
        }

        System.out.println (strDump + " |");
    }

    private static final void EfronSteinSteeleRun (
        final Binary bsg,
        final int iNumSample,
        final int iNumSet)
        throws Exception
    {
        String strDump = "\t| " + FormatUtil.FormatDouble (iNumSample, 2, 0, 1.) + " => ";

        for (int j = 0; j < iNumSet; ++j) {
            SingleSequenceAgnosticMetrics[] aSSAM = IIDDraw (
                bsg,
                iNumSample
            );

            EfronSteinMetrics esam = new EfronSteinMetrics (
                KernelDensityL1Function (iNumSample),
                aSSAM
            );

            SingleSequenceAgnosticMetrics[] aSSAMGhost = IIDDraw (
                bsg,
                iNumSample
            );

            if (0 != j) strDump += " |";

            strDump += FormatUtil.FormatDouble (esam.efronSteinSteeleBound (aSSAMGhost), 1, 3, 1.);
        }

        System.out.println (strDump + " |");
    }

    private static final void PivotDifferencesRun (
        final Binary bsg,
        final int iNumSample,
        final int iNumSet)
        throws Exception
    {
        String strDump = "\t| " + FormatUtil.FormatDouble (iNumSample, 2, 0, 1.) + " => ";

        for (int j = 0; j < iNumSet; ++j) {
            SingleSequenceAgnosticMetrics[] aSSAM = IIDDraw (
                bsg,
                iNumSample
            );

            EfronSteinMetrics esam = new EfronSteinMetrics (
                KernelDensityL1Function (iNumSample),
                aSSAM
            );

            if (0 != j) strDump += " |";

            strDump += FormatUtil.FormatDouble (esam.pivotVarianceUpperBound (new FlatMultivariateRandom (0.)), 1, 3, 1.);
        }

        System.out.println (strDump + " |");
    }

    public static final void main (
        final String[] astrArgs)
        throws Exception
    {
        EnvManager.InitEnv ("");

        int iNumSet = 5;

        int[] aiSampleSize = new int[] {
            3, 10, 25, 50
        };

        Binary bin = new Binary (0.7);

        System.out.println ("\n\t|-----------------------------------------------|");

        System.out.println ("\t|  Martingale Differences Variance Upper Bound  |");

        System.out.println ("\t|-----------------------------------------------|");

        for (int iSampleSize : aiSampleSize)
            MartingaleDifferencesRun (
                bin,
                iSampleSize,
                iNumSet
            );

        System.out.println ("\t|-----------------------------------------------|");

        System.out.println ("\n\t|-----------------------------------------------|");

        System.out.println ("\t|   Symmetrized Variate Variance Upper Bound    |");

        System.out.println ("\t|-----------------------------------------------|");

        for (int iSampleSize : aiSampleSize)
            GhostVariateVarianceRun (
                bin,
                iSampleSize,
                iNumSet
            );

        System.out.println ("\t|-----------------------------------------------|");

        aiSampleSize = new int[] {
            3, 10, 25, 50, 75, 99
        };

        System.out.println ("\n\t|-----------------------------------------------|");

        System.out.println ("\t|    Efron-Stein-Steele Variance Upper Bound    |");

        System.out.println ("\t|-----------------------------------------------|");

        for (int iSampleSize : aiSampleSize)
            EfronSteinSteeleRun (
                bin,
                iSampleSize,
                iNumSet
            );

        System.out.println ("\t|-----------------------------------------------|");

        System.out.println ("\n\t|-----------------------------------------------|");

        System.out.println ("\t|    Pivoted Differences Variance Upper Bound   |");

        System.out.println ("\t|-----------------------------------------------|");

        for (int iSampleSize : aiSampleSize)
            PivotDifferencesRun (
                bin,
                iSampleSize,
                iNumSet
            );

        System.out.println ("\t|-----------------------------------------------|");

        EnvManager.TerminateEnv();
    }
}