RdDecisionFunction.java

  1. package org.drip.learning.svm;

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


  8. /*!
  9.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  15.  * 
  16.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  17.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  18.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  19.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  20.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  21.  *      and computational support.
  22.  *  
  23.  *      https://lakshmidrip.github.io/DROP/
  24.  *  
  25.  *  DROP is composed of three modules:
  26.  *  
  27.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  28.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  29.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  30.  * 
  31.  *  DROP Product Core implements libraries for the following:
  32.  *  - Fixed Income Analytics
  33.  *  - Loan Analytics
  34.  *  - Transaction Cost Analytics
  35.  * 
  36.  *  DROP Portfolio Core implements libraries for the following:
  37.  *  - Asset Allocation Analytics
  38.  *  - Asset Liability Management Analytics
  39.  *  - Capital Estimation Analytics
  40.  *  - Exposure Analytics
  41.  *  - Margin Analytics
  42.  *  - XVA Analytics
  43.  * 
  44.  *  DROP Computational Core implements libraries for the following:
  45.  *  - Algorithm Support
  46.  *  - Computation Support
  47.  *  - Function Analysis
  48.  *  - Model Validation
  49.  *  - Numerical Analysis
  50.  *  - Numerical Optimizer
  51.  *  - Spline Builder
  52.  *  - Statistical Learning
  53.  * 
  54.  *  Documentation for DROP is Spread Over:
  55.  * 
  56.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  57.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  58.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  59.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  60.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  61.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  62.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  63.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  64.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  65.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  66.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  67.  * 
  68.  *  Licensed under the Apache License, Version 2.0 (the "License");
  69.  *      you may not use this file except in compliance with the License.
  70.  *   
  71.  *  You may obtain a copy of the License at
  72.  *      http://www.apache.org/licenses/LICENSE-2.0
  73.  *  
  74.  *  Unless required by applicable law or agreed to in writing, software
  75.  *      distributed under the License is distributed on an "AS IS" BASIS,
  76.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  77.  *  
  78.  *  See the License for the specific language governing permissions and
  79.  *      limitations under the License.
  80.  */

  82. /**
  83.  * <i>RdDecisionFunction</i> exposes the R<sup>d</sup> Decision-Function Based SVM Functionality for
  84.  * Classification and Regression.
  85.  * 
  86.  * <br><br>
  87.  *  The References are:
  88.  * <br><br>
  89.  * <ul>
  90.  *  <li>
  91.  *      Shawe-Taylor, J., P. L. Bartlett, R. C. Williamson, and M. Anthony (1996): A Framework for Structural
  92.  *          Risk Minimization, in: <i>Proceedings of the 9th Annual Conference on Computational Learning
  93.  *          Theory</i> <b>ACM</b> New York 68-76
  94.  *  </li>
  95.  *  <li>
  96.  *      Vapnik, V., and A. Chervonenkis (1974): <i>Theory of Pattern Recognition (in Russian)</i>
  97.  *          <b>Nauka</b> Moscow USSR
  98.  *  </li>
  99.  *  <li>
  100.  *      Vapnik, V. (1995): <i>The Nature of Statistical Learning</i> <b>Springer-Verlag</b> New York
  101.  *  </li>
  102.  * </ul>
  103.  *
  104.  *  <br><br>
  105.  *  <ul>
  106.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  107.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
  108.  *      <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>
  109.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/learning/svm">Kernel SVM Decision Function Operator</a></li>
  110.  *  </ul>
  111.  *
  112.  * @author Lakshmi Krishnamurthy
  113.  */

  115. public abstract class RdDecisionFunction extends org.drip.function.definition.RdToR1 {
  116.     private double _dblB = java.lang.Double.NaN;
  117.     private double[] _adblInverseMarginWeight = null;
  118.     private org.drip.spaces.metric.RdNormed _rdInverseMargin = null;
  119.     private org.drip.spaces.tensor.RdGeneralizedVector _rdPredictor = null;

  121.     /**
  122.      * RdDecisionFunction Constructor
  123.      * 
  124.      * @param rdPredictor The R^d Metric Input Predictor Space
  125.      * @param rdInverseMargin The Inverse Margin Weights R^d Space
  126.      * @param adblInverseMarginWeight Array of Inverse Margin Weights
  127.      * @param dblB The Kernel Offset
  128.      * 
  129.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  130.      */

  132.     public RdDecisionFunction (
  133.         final org.drip.spaces.tensor.RdGeneralizedVector rdPredictor,
  134.         final org.drip.spaces.metric.RdNormed rdInverseMargin,
  135.         final double[] adblInverseMarginWeight,
  136.         final double dblB)
  137.         throws java.lang.Exception
  138.     {
  139.         super (null);

  141.         if (null == (_rdPredictor = rdPredictor) || null == (_rdInverseMargin = rdInverseMargin) || null ==
  142.             (_adblInverseMarginWeight = adblInverseMarginWeight) || !org.drip.numerical.common.NumberUtil.IsValid
  143.                 (_dblB = dblB))
  144.             throw new java.lang.Exception ("RdDecisionFunction ctr: Invalid Inputs");

  146.         int iNumMarginWeight = _adblInverseMarginWeight.length;

  148.         if (0 == iNumMarginWeight || iNumMarginWeight != _rdPredictor.dimension())
  149.             throw new java.lang.Exception ("RdDecisionFunction ctr: Invalid Inputs");
  150.     }

  152.     /**
  153.      * Retrieve the Input Predictor Metric Vector Space
  154.      * 
  155.      * @return The Input Predictor Metric Vector Space
  156.      */

  158.     public org.drip.spaces.tensor.RdGeneralizedVector predictorSpace()
  159.     {
  160.         return _rdPredictor;
  161.     }

  163.     /**
  164.      * Retrieve the Inverse Margin Weight Metric Vector Space
  165.      * 
  166.      * @return The Inverse Margin Weight Metric Vector Space
  167.      */

  169.     public org.drip.spaces.metric.RdNormed inverseMarginSpace()
  170.     {
  171.         return _rdInverseMargin;
  172.     }

  174.     /**
  175.      * Retrieve the Decision Kernel Weights
  176.      * 
  177.      * @return The Decision Kernel Weights
  178.      */

  180.     public double[] inverseMarginWeights()
  181.     {
  182.         return _adblInverseMarginWeight;
  183.     }

  185.     /**
  186.      * Retrieve the Offset
  187.      * 
  188.      * @return The Offset
  189.      */

  191.     public double offset()
  192.     {
  193.         return _dblB;
  194.     }

  196.     /**
  197.      * Classify the Specified Multi-dimensional Point
  198.      * 
  199.      * @param adblX The Multi-dimensional Input Point
  200.      * 
  201.      * @return +1/-1 Boolean Space Output Equivalents
  202.      * 
  203.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  204.      */

  206.     public short classify (
  207.         final double[] adblX)
  208.         throws java.lang.Exception
  209.     {
  210.         return evaluate (adblX) > 0. ? org.drip.spaces.tensor.BinaryBooleanVector.BBV_UP :
  211.             org.drip.spaces.tensor.BinaryBooleanVector.BBV_DOWN;
  212.     }

  214.     /**
  215.      * Regress on the Specified Multi-dimensional Point
  216.      * 
  217.      * @param adblX The Multi-dimensional Input Point
  218.      * 
  219.      * @return The Regression Output
  220.      * 
  221.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  222.      */

  224.     public double regress (
  225.         final double[] adblX)
  226.         throws java.lang.Exception
  227.     {
  228.         return evaluate (adblX);
  229.     }

  231.     /**
  232.      * Compute the Entropy Number Upper Bounds Instance for the Specified Inputs
  233.      * 
  234.      * @param dsoFactorizer The Factorizing Diagonal Scaling Operator
  235.      * @param dblFeatureSpaceMaureyConstant The Feature Space Maurey Constant
  236.      * 
  237.      * @return The Entropy Number Upper Bounds Instance
  238.      */

  240.     public org.drip.learning.svm.DecisionFunctionOperatorBounds entropyNumberUpperBounds (
  241.         final org.drip.learning.kernel.DiagonalScalingOperator dsoFactorizer,
  242.         final double dblFeatureSpaceMaureyConstant)
  243.     {
  244.         try {
  245.             return new org.drip.learning.svm.DecisionFunctionOperatorBounds (dsoFactorizer,
  246.                 inverseMarginSpace().populationMetricNorm(), dblFeatureSpaceMaureyConstant,
  247.                     predictorSpace().dimension());
  248.         } catch (java.lang.Exception e) {
  249.             e.printStackTrace();
  250.         }

  252.         return null;
  253.     }

  255.     /**
  256.      * Compute the Decision Function's Asymptotic Exponent for the Entropy Number
  257.      * 
  258.      * @param dsoFactorizer The Factorizing Diagonal Scaling Operator
  259.      * 
  260.      * @return The Decision Function's Asymptotic Exponent for the Entropy Number
  261.      * 
  262.      * @throws java.lang.Exception Thrown if the Asymptotoc Exponent cannot be computed
  263.      */

  265.     public double logEntropyNumberAsymptote (
  266.         final org.drip.learning.kernel.DiagonalScalingOperator dsoFactorizer)
  267.         throws java.lang.Exception
  268.     {
  269.         if (null == dsoFactorizer)
  270.             throw new java.lang.Exception
  271.                 ("RdDecisionFunction::logEntropyNumberAsymptote => Invalid Inputs");

  273.         org.drip.learning.bound.DiagonalOperatorCoveringBound docb = dsoFactorizer.entropyNumberAsymptote();

  275.         if (null == docb)
  276.             throw new java.lang.Exception
  277.                 ("RdDecisionFunction::logEntropyNumberAsymptote => Cannot get Diagonal Operator Covering Bounds");

  279.         return org.drip.learning.bound.DiagonalOperatorCoveringBound.BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
  280.             == docb.entropyNumberAsymptoteType() ? -1. * docb.entropyNumberAsymptoteExponent() - 0.5 :
  281.                 -1. * docb.entropyNumberAsymptoteExponent();
  282.     }

  284.     /**
  285.      * Optimize the Hyper-plane for the Purposes of Regression
  286.      * 
  287.      * @param adblEmpirical The Empirical Observation Array
  288.      * @param dblMargin The Optimization Margin
  289.      * @param dblInverseWidthNormConstraint The Inverse Width Norm Constraint
  290.      * 
  291.      * @return TRUE - The Hyper-plane has been successfully Optimized for Regression
  292.      */

  294.     public abstract boolean optimizeRegressionHyperplane (
  295.         final double[] adblEmpirical,
  296.         final double dblMargin,
  297.         final double dblInverseWidthNormConstraint
  298.     );

  300.     /**
  301.      * Optimize the Hyper-plane for the Purposes of Classification
  302.      * 
  303.      * @param asEmpirical The Empirical Observation Array
  304.      * @param dblMargin The Optimization Margin
  305.      * @param dblInverseWidthNormConstraint The Inverse Width Norm Constraint
  306.      * 
  307.      * @return TRUE - The Hyper-plane has been successfully Optimized for Classification
  308.      */

  310.     public abstract boolean optimizeClassificationHyperplane (
  311.         final short[] asEmpirical,
  312.         final double dblMargin,
  313.         final double dblInverseWidthNormConstraint
  314.     );
  315. }
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