LipschitzLossLearner.java

  1. package org.drip.learning.rxtor1;

  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>LipschitzLossLearner</i> implements the Learner Class that holds the Space of Normed R<sup>1</sup> To
  83.  * Normed R<sup>1</sup> Learning Functions for the Family of Loss Functions that are Lipschitz, i.e.,
  84.  * 
  85.  *              loss (ep) - loss (ep') Less Than C * |ep-ep'|
  86.  *  
  87.  * <br><br>
  88.  * The References are:
  89.  *  
  90.  * <br><br>
  91.  * <ul>
  92.  *  <li>
  93.  *      Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform
  94.  *          Convergence, and Learnability <i>Journal of Association of Computational Machinery</i> <b>44
  95.  *          (4)</b> 615-631
  96.  *  </li>
  97.  *  <li>
  98.  *      Anthony, M., and P. L. Bartlett (1999): <i>Artificial Neural Network Learning - Theoretical
  99.  *          Foundations</i> <b>Cambridge University Press</b> Cambridge, UK
  100.  *  </li>
  101.  *  <li>
  102.  *      Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): <i>Towards Efficient Agnostic Learning</i>
  103.  *          Machine Learning <b>17 (2)</b> 115-141
  104.  *  </li>
  105.  *  <li>
  106.  *      Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with
  107.  *          Squared Loss <i>IEEE Transactions on Information Theory</i> <b>44</b> 1974-1980
  108.  *  </li>
  109.  *  <li>
  110.  *      Vapnik, V. N. (1998): <i>Statistical learning Theory</i> <b>Wiley</b> New York
  111.  *  </li>
  112.  * </ul>
  113.  *
  114.  *  <br><br>
  115.  *  <ul>
  116.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  117.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
  118.  *      <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>
  119.  *      <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>
  120.  *  </ul>
  121.  *
  122.  * @author Lakshmi Krishnamurthy
  123.  */

  125. public class LipschitzLossLearner extends org.drip.learning.rxtor1.GeneralizedLearner {
  126.     private double _dblLipschitzSlope = java.lang.Double.NaN;

  128.     /**
  129.      * LipschitzLossLearner Constructor
  130.      * 
  131.      * @param funcClassRxToR1 R^x To R^1 Function Class
  132.      * @param cdpb The Covering Number based Deviation Upper Probability Bound Generator
  133.      * @param regularizerFunc The Regularizer Function
  134.      * @param dblLipschitzSlope The Lipschitz Slope Bound
  135.      * 
  136.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  137.      */

  139.     public LipschitzLossLearner (
  140.         final org.drip.spaces.functionclass.NormedRxToNormedR1Finite funcClassRxToR1,
  141.         final org.drip.learning.bound.CoveringNumberLossBound cdpb,
  142.         final org.drip.learning.regularization.RegularizationFunction regularizerFunc,
  143.         final double dblLipschitzSlope)
  144.         throws java.lang.Exception
  145.     {
  146.         super (funcClassRxToR1, cdpb, regularizerFunc);

  148.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLipschitzSlope = dblLipschitzSlope))
  149.             throw new java.lang.Exception ("LipschitzLossLearner ctr: Invalid Inputs");
  150.     }

  152.     /**
  153.      * Retrieve the Lipschitz Slope Bound
  154.      * 
  155.      * @return The Lipschitz Slope Bound
  156.      */

  158.     public double lipschitzSlope()
  159.     {
  160.         return _dblLipschitzSlope;
  161.     }

  163.     @Override public double lossSampleCoveringNumber (
  164.         final org.drip.spaces.instance.GeneralizedValidatedVector gvvi,
  165.         final double dblEpsilon,
  166.         final boolean bSupremum)
  167.         throws java.lang.Exception
  168.     {
  169.         if (null == gvvi || !org.drip.numerical.common.NumberUtil.IsValid (dblEpsilon) || 0. >= dblEpsilon)
  170.             throw new java.lang.Exception
  171.                 ("LipschitzLossLearner::lossSampleCoveringNumber => Invalid Inputs");

  173.         double dblLipschitzCover = dblEpsilon / _dblLipschitzSlope;

  175.         org.drip.spaces.functionclass.NormedRxToNormedR1Finite funcClassRxToR1 = functionClass();

  177.         org.drip.learning.bound.LipschitzCoveringNumberBound llcn = new
  178.             org.drip.learning.bound.LipschitzCoveringNumberBound (funcClassRxToR1.sampleSupremumCoveringNumber
  179.                 (gvvi, dblLipschitzCover), funcClassRxToR1.sampleCoveringNumber (gvvi, gvvi.sampleSize() *
  180.                     dblLipschitzCover));

  182.         return bSupremum ? llcn.supremumUpperBound() : llcn.lpUpperBound();
  183.     }

  185.     @Override public double empiricalLoss (
  186.         final org.drip.function.definition.R1ToR1 funcLearnerR1ToR1,
  187.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviX,
  188.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviY)
  189.         throws java.lang.Exception
  190.     {
  191.         throw new java.lang.Exception ("LipschitzLossLearner::empiricalLoss => No Generic Implementation");
  192.     }

  194.     @Override public double empiricalLoss (
  195.         final org.drip.function.definition.RdToR1 funcLearnerRdToR1,
  196.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviX,
  197.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviY)
  198.         throws java.lang.Exception
  199.     {
  200.         throw new java.lang.Exception ("LipschitzLossLearner::empiricalLoss => No Generic Implementation");
  201.     }

  203.     @Override public double empiricalRisk (
  204.         final org.drip.measure.continuous.R1R1 distR1R1,
  205.         final org.drip.function.definition.R1ToR1 funcLearnerR1ToR1,
  206.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviX,
  207.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviY)
  208.         throws java.lang.Exception
  209.     {
  210.         throw new java.lang.Exception ("LipschitzLossLearner::empiricalRisk => No Generic Implementation");
  211.     }

  213.     @Override public double empiricalRisk (
  214.         final org.drip.measure.continuous.RdR1 distRdR1,
  215.         final org.drip.function.definition.RdToR1 funcLearnerRdToR1,
  216.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviX,
  217.         final org.drip.spaces.instance.GeneralizedValidatedVector gvviY)
  218.         throws java.lang.Exception
  219.     {
  220.         throw new java.lang.Exception ("LipschitzLossLearner::empiricalRisk => No Generic Implementation");
  221.     }
  222. }
Created with JaCoCo 0.7.9.201702052155