DecisionFunctionOperatorBounds.java

  1. package org.drip.learning.svm;

  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>DecisionFunctionOperatorBounds</i> implements the Dot Product Entropy Number Upper Bounds for the
  83.  * Product of Kernel Feature Map Function and the Scaling Diagonal Operator.
  84.  *  
  85.  * <br><br>
  86.  *  The References are:
  87.  * <br><br>
  88.  * <ul>
  89.  *  <li>
  90.  *      Ash, R. (1965): <i>Information Theory</i> <b>Inter-science</b> New York
  91.  *  </li>
  92.  *  <li>
  93.  *      Carl, B., and I. Stephani (1990): <i>Entropy, Compactness, and Approximation of Operators</i>
  94.  *          <b>Cambridge University Press</b> Cambridge UK
  95.  *  </li>
  96.  *  <li>
  97.  *      Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and
  98.  *          Approximation Numbers of Operators <i>Journal of Approximation Theory</i> <b>49</b> 219-237
  99.  *  </li>
  100.  *  <li>
  101.  *      Konig, H. (1986): <i>Eigenvalue Distribution of Compact Operators</i> <b>Birkhauser</b> Basel,
  102.  *          Switzerland
  103.  *  </li>
  104.  *  <li>
  105.  *      Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex
  106.  *          Combinations and mlps, in: <i>Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B.
  107.  *          Scholkopf, and D. Schuurmans - editors</i> <b>MIT Press</b> Cambridge, MA
  108.  *  </li>
  109.  * </ul>
  110.  *
  111.  *  <br><br>
  112.  *  <ul>
  113.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  114.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
  115.  *      <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>
  116.  *      <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>
  117.  *  </ul>
  118.  *
  119.  * @author Lakshmi Krishnamurthy
  120.  */

  122. public class DecisionFunctionOperatorBounds {
  123.     private int _iFeatureSpaceDimension = -1;
  124.     private double _dblInverseMarginNormBound = java.lang.Double.NaN;
  125.     private double _dblFeatureSpaceMaureyConstant = java.lang.Double.NaN;
  126.     private org.drip.learning.kernel.DiagonalScalingOperator _dsoFactorizer = null;

  128.     /**
  129.      * DecisionFunctionOperatorBounds Constructor
  130.      * 
  131.      * @param dsoFactorizer The Factorizing Diagonal Scaling Operator
  132.      * @param dblInverseMarginNormBound The Decision Function Inverse Margin Norm Bound
  133.      * @param dblFeatureSpaceMaureyConstant The Kernel Feature Space Function Maurey Constant
  134.      * @param iFeatureSpaceDimension The Kernel Feature Space Dimension
  135.      * 
  136.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  137.      */

  139.     public DecisionFunctionOperatorBounds (
  140.         final org.drip.learning.kernel.DiagonalScalingOperator dsoFactorizer,
  141.         final double dblInverseMarginNormBound,
  142.         final double dblFeatureSpaceMaureyConstant,
  143.         final int iFeatureSpaceDimension)
  144.         throws java.lang.Exception
  145.     {
  146.         if (null == (_dsoFactorizer = dsoFactorizer) || !org.drip.numerical.common.NumberUtil.IsValid
  147.             (_dblInverseMarginNormBound = dblInverseMarginNormBound) ||
  148.                 !org.drip.numerical.common.NumberUtil.IsValid (_dblFeatureSpaceMaureyConstant =
  149.                     dblFeatureSpaceMaureyConstant) || 0 >= (_iFeatureSpaceDimension =
  150.                         iFeatureSpaceDimension))
  151.             throw new java.lang.Exception ("DecisionFunctionOperatorBounds ctr => Invalid Inputs");
  152.     }

  154.     /**
  155.      * Retrieve the Factorizing Diagonal Scaling Operator Instance
  156.      * 
  157.      * @return The Factorizing Diagonal Scaling Operator Instance
  158.      */

  160.     public org.drip.learning.kernel.DiagonalScalingOperator factorizingOperator()
  161.     {
  162.         return _dsoFactorizer;
  163.     }

  165.     /**
  166.      * Retrieve the Norm Upper Bound of the Inverse Margin
  167.      * 
  168.      * @return The Norm Upper Bound of the Inverse Margin
  169.      */

  171.     public double inverseMarginNormBound()
  172.     {
  173.         return _dblInverseMarginNormBound;
  174.     }

  176.     /**
  177.      * Retrieve the Feature Space Maurey Constant
  178.      * 
  179.      * @return The Feature Space Maurey Constant
  180.      */

  182.     public double featureSpaceMaureyConstant()
  183.     {
  184.         return _dblFeatureSpaceMaureyConstant;
  185.     }

  187.     /**
  188.      * Retrieve the Feature Space Dimension
  189.      * 
  190.      * @return The Feature Space Dimension
  191.      */

  193.     public double featureSpaceDimension()
  194.     {
  195.         return _iFeatureSpaceDimension;
  196.     }

  198.     /**
  199.      * Compute the Feature Space's Maurey Bound for the Entropy Number given the specified Entropy Number
  200.      * 
  201.      * @param iFeatureSpaceEntropyNumber The Feature Space Entropy Number
  202.      * 
  203.      * @return The Feature Space's Maurey Bound for the specified Entropy Number
  204.      * 
  205.      * @throws java.lang.Exception The Feature Space's Maurey Bound cannot be computed
  206.      */

  208.     public double featureSpaceMaureyBound (
  209.         final int iFeatureSpaceEntropyNumber)
  210.         throws java.lang.Exception
  211.     {
  212.         if (0 >= iFeatureSpaceEntropyNumber)
  213.             throw new java.lang.Exception
  214.                 ("DecisionFunctionOperatorBounds::featureSpaceMaureyBound => Invalid Inputs");

  216.         return java.lang.Math.sqrt (1. / (iFeatureSpaceEntropyNumber * java.lang.Math.sqrt
  217.             (java.lang.Math.log (1. + (((double) _iFeatureSpaceDimension) / java.lang.Math.log
  218.                 (iFeatureSpaceEntropyNumber))))));
  219.     }

  221.     /**
  222.      * Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's
  223.      *  Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Entropy
  224.      *  Number Upper Bound
  225.      * 
  226.      * @param iFeatureSpaceEntropyNumber The Feature Space Entropy Number
  227.      * 
  228.      * @return The Feature Space's Operator Entropy for the specified Entropy Number
  229.      * 
  230.      * @throws java.lang.Exception The Feature Space's Operator Entropy cannot be computed
  231.      */

  233.     public double featureMaureyOperatorEntropy (
  234.         final int iFeatureSpaceEntropyNumber)
  235.         throws java.lang.Exception
  236.     {
  237.         return _dblInverseMarginNormBound * _dsoFactorizer.entropyNumberUpperBound() *
  238.             featureSpaceMaureyBound (iFeatureSpaceEntropyNumber);
  239.     }

  241.     /**
  242.      * Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's
  243.      *  Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Norm
  244.      * 
  245.      * @param iFeatureSpaceEntropyNumber The Feature Space Entropy Number
  246.      * 
  247.      * @return The Feature Space's Operator Norm for the specified Entropy Number
  248.      * 
  249.      * @throws java.lang.Exception The Feature Space's Operator Norm cannot be computed
  250.      */

  252.     public double featureMaureyOperatorNorm (
  253.         final int iFeatureSpaceEntropyNumber)
  254.         throws java.lang.Exception
  255.     {
  256.         return _dblInverseMarginNormBound * _dsoFactorizer.norm() * featureSpaceMaureyBound
  257.             (iFeatureSpaceEntropyNumber);
  258.     }

  260.     /**
  261.      * Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's
  262.      *  Norm for the Upper Bound of the Entropy Number and the Scaling Operator Norm
  263.      * 
  264.      * @return The Entropy Number Upper Bound using the Product Norm
  265.      * 
  266.      * @throws java.lang.Exception The Entropy Number Upper Bound cannot be computed
  267.      */

  269.     public double productFeatureOperatorNorm()
  270.         throws java.lang.Exception
  271.     {
  272.         return _dblInverseMarginNormBound * _dsoFactorizer.norm();
  273.     }

  275.     /**
  276.      * Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's
  277.      *  Norm for the Upper Bound of the Entropy Number and the Scaling Operator Entropy Number Upper Bound
  278.      * 
  279.      * @return The Entropy Number Upper Bound using the Product Norm
  280.      * 
  281.      * @throws java.lang.Exception The Entropy Number Upper Bound cannot be computed
  282.      */

  284.     public double featureNormOperatorEntropy()
  285.         throws java.lang.Exception
  286.     {
  287.         return _dblInverseMarginNormBound * _dsoFactorizer.entropyNumberUpperBound();
  288.     }

  290.     /**
  291.      * Compute the Infimum of the Decision Function Operator Upper Bound across all the Product Bounds for
  292.      *  the specified Feature Space Entropy Number
  293.      * 
  294.      * @param iFeatureSpaceEntropyNumber The specified Feature Space Entropy Number
  295.      * 
  296.      * @return Infimum of the Decision Function Operator Upper Bound
  297.      * 
  298.      * @throws java.lang.Exception Thrown if the Infimum of the Decision Function Operator Upper Bound cannot
  299.      *  be calculated
  300.      */

  302.     public double infimumUpperBound (
  303.         final int iFeatureSpaceEntropyNumber)
  304.         throws java.lang.Exception
  305.     {
  306.         double dblFactorizerNorm = _dsoFactorizer.norm();

  308.         double dblFactorizerEntropyUpperBound = _dsoFactorizer.entropyNumberUpperBound();

  310.         double dblFeatureSpaceMaureyBound = featureSpaceMaureyBound (iFeatureSpaceEntropyNumber);

  312.         double dblProductFeatureOperatorNorm = _dblInverseMarginNormBound * dblFactorizerNorm;
  313.         double dblFeatureMaureyOperatorNorm = dblProductFeatureOperatorNorm * dblFeatureSpaceMaureyBound;
  314.         double dblFeatureNormOperatorEntropy = _dblInverseMarginNormBound * dblFactorizerEntropyUpperBound;
  315.         double dblInfimumUpperBound = dblFeatureNormOperatorEntropy * dblFeatureSpaceMaureyBound;

  317.         if (dblInfimumUpperBound > dblFeatureMaureyOperatorNorm)
  318.             dblInfimumUpperBound = dblFeatureMaureyOperatorNorm;

  320.         if (dblInfimumUpperBound > dblProductFeatureOperatorNorm)
  321.             dblInfimumUpperBound = dblProductFeatureOperatorNorm;

  323.         return dblInfimumUpperBound > dblFeatureNormOperatorEntropy ? dblInfimumUpperBound :
  324.             dblFeatureNormOperatorEntropy;
  325.     }
  326. }
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