RegularizerRdContinuousToR1Continuous.java

  1. package org.drip.learning.regularization;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>RegularizerRdContinuousToR1Continuous</i> computes the Structural Loss and Risk for the specified
  83.  * Normed R<sup>d</sup> Continuous To Normed R<sup>1</sup> Continuous Learning Function.
  84.  *  
  85.  * <br><br>
  86.  * <ul>
  87.  *  <li>
  88.  *      Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform
  89.  *          Convergence, and Learnability <i>Journal of Association of Computational Machinery</i> <b>44
  90.  *          (4)</b> 615-631
  91.  *  </li>
  92.  *  <li>
  93.  *      Anthony, M., and P. L. Bartlett (1999): <i>Artificial Neural Network Learning - Theoretical
  94.  *          Foundations</i> <b>Cambridge University Press</b> Cambridge, UK
  95.  *  </li>
  96.  *  <li>
  97.  *      Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): <i>Towards Efficient Agnostic Learning</i>
  98.  *          Machine Learning <b>17 (2)</b> 115-141
  99.  *  </li>
  100.  *  <li>
  101.  *      Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with
  102.  *          Squared Loss <i>IEEE Transactions on Information Theory</i> <b>44</b> 1974-1980
  103.  *  </li>
  104.  *  <li>
  105.  *      Vapnik, V. N. (1998): <i>Statistical learning Theory</i> <b>Wiley</b> New York
  106.  *  </li>
  107.  * </ul>
  108.  *
  109.  *  <br><br>
  110.  *  <ul>
  111.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  112.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
  113.  *      <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>
  114.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning/regularization">Statistical Learning Empirical Loss Regularizer</a></li>
  115.  *  </ul>
  116.  *
  117.  * @author Lakshmi Krishnamurthy
  118.  */

  120. public class RegularizerRdContinuousToR1Continuous extends
  121.     org.drip.spaces.rxtor1.NormedRdContinuousToR1Continuous implements
  122.         org.drip.learning.regularization.RegularizerRdToR1 {
  123.     private double _dblLambda = java.lang.Double.NaN;

  125.     /**
  126.      * RegularizerRdContinuousToR1Continuous Function Space Constructor
  127.      * 
  128.      * @param funcRdToR1 The R^d To R^1 Function
  129.      * @param rdContinuousInput The Continuous R^d Input Metric Vector Space
  130.      * @param r1ContinuousOutput The Continuous R^1 Output Metric Vector Space
  131.      * @param dblLambda The Regularization Lambda
  132.      * 
  133.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  134.      */

  136.     public RegularizerRdContinuousToR1Continuous (
  137.         final org.drip.function.definition.RdToR1 funcRdToR1,
  138.         final org.drip.spaces.metric.RdContinuousBanach rdContinuousInput,
  139.         final org.drip.spaces.metric.R1Continuous r1ContinuousOutput,
  140.         final double dblLambda)
  141.         throws java.lang.Exception
  142.     {
  143.         super (rdContinuousInput, r1ContinuousOutput, funcRdToR1);

  145.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLambda = dblLambda) || 0 > _dblLambda)
  146.             throw new java.lang.Exception
  147.                 ("RegularizerRdContinuousToR1Continuous Constructor => Invalid Inputs");
  148.     }

  150.     @Override public double lambda()
  151.     {
  152.         return _dblLambda;
  153.     }

  155.     @Override public double structuralLoss (
  156.         final org.drip.function.definition.RdToR1 funcRdToR1,
  157.         final double[][] aadblX)
  158.         throws java.lang.Exception
  159.     {
  160.         if (null == funcRdToR1 || null == aadblX)
  161.             throw new java.lang.Exception
  162.                 ("RegularizerRdContinuousToR1Continuous::structuralLoss => Invalid Inputs");

  164.         double dblLoss = 0.;
  165.         int iNumSample = aadblX.length;

  167.         if (0 == iNumSample)
  168.             throw new java.lang.Exception
  169.                 ("RegularizerRdContinuousToR1Continuous::structuralLoss => Invalid Inputs");

  171.         int iPNorm = outputMetricVectorSpace().pNorm();

  173.         org.drip.function.definition.RdToR1 funcRegularizerRdToR1 = function();

  175.         if (java.lang.Integer.MAX_VALUE == iPNorm) {
  176.             double dblSupremum = 0.;

  178.             for (int i = 0; i < iNumSample; ++i) {
  179.                 double dblRegularizedValue = java.lang.Math.abs (funcRegularizerRdToR1.evaluate (aadblX[i]) *
  180.                     funcRdToR1.evaluate (aadblX[i]));

  182.                 if (dblSupremum < dblRegularizedValue) dblSupremum = dblRegularizedValue;
  183.             }

  185.             return dblSupremum;
  186.         }

  188.         for (int i = 0; i < iNumSample; ++i)
  189.             dblLoss += java.lang.Math.pow (java.lang.Math.abs (funcRegularizerRdToR1.evaluate (aadblX[i]) *
  190.                 funcRdToR1.evaluate (aadblX[i])), iPNorm);

  192.         return dblLoss / iPNorm;
  193.     }

  195.     @Override public double structuralRisk (
  196.         final org.drip.measure.continuous.RdR1 distRdR1,
  197.         final org.drip.function.definition.RdToR1 funcRdToR1,
  198.         final double[][] aadblX,
  199.         final double[] adblY)
  200.         throws java.lang.Exception
  201.     {
  202.         if (null == funcRdToR1 || null == aadblX || null == adblY)
  203.             throw new java.lang.Exception
  204.                 ("RegularizerRdContinuousToR1Continuous::structuralRisk => Invalid Inputs");

  206.         double dblLoss = 0.;
  207.         double dblNormalizer = 0.;
  208.         int iNumSample = aadblX.length;

  210.         if (0 == iNumSample || iNumSample != adblY.length)
  211.             throw new java.lang.Exception
  212.                 ("RegularizerRdContinuousToR1Continuous::structuralRisk => Invalid Inputs");

  214.         int iPNorm = outputMetricVectorSpace().pNorm();

  216.         org.drip.function.definition.RdToR1 funcRegularizerRdToR1 = function();

  218.         if (java.lang.Integer.MAX_VALUE == iPNorm) {
  219.             double dblSupremumDensity = 0.;
  220.             double dblSupremumNodeValue = 0.;

  222.             for (int i = 0; i < iNumSample; ++i) {
  223.                 double dblDensity = distRdR1.density (aadblX[i], adblY[i]);

  225.                 if (dblDensity > dblSupremumDensity) {
  226.                     dblSupremumDensity = dblDensity;

  228.                     dblSupremumNodeValue = java.lang.Math.abs (funcRegularizerRdToR1.evaluate (aadblX[i]) *
  229.                         funcRdToR1.evaluate (aadblX[i]));
  230.                 }
  231.             }

  233.             return dblSupremumNodeValue;
  234.         }

  236.         for (int i = 0; i < iNumSample; ++i) {
  237.             double dblDensity = distRdR1.density (aadblX[i], adblY[i]);

  239.             dblNormalizer += dblDensity;

  241.             dblLoss += dblDensity * java.lang.Math.pow (java.lang.Math.abs (funcRegularizerRdToR1.evaluate
  242.                 (aadblX[i]) * funcRdToR1.evaluate (aadblX[i])), iPNorm);
  243.         }

  245.         return dblLoss / iPNorm / dblNormalizer;
  246.     }
  247. }
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