RdDecisionFunction.java
package org.drip.learning.svm;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* 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 analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* 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>RdDecisionFunction</i> exposes the R<sup>d</sup> Decision-Function Based SVM Functionality for
* Classification and Regression.
*
* <br><br>
* The References are:
* <br><br>
* <ul>
* <li>
* Shawe-Taylor, J., P. L. Bartlett, R. C. Williamson, and M. Anthony (1996): A Framework for Structural
* Risk Minimization, in: <i>Proceedings of the 9th Annual Conference on Computational Learning
* Theory</i> <b>ACM</b> New York 68-76
* </li>
* <li>
* Vapnik, V., and A. Chervonenkis (1974): <i>Theory of Pattern Recognition (in Russian)</i>
* <b>Nauka</b> Moscow USSR
* </li>
* <li>
* Vapnik, V. (1995): <i>The Nature of Statistical Learning</i> <b>Springer-Verlag</b> New York
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning</a></li>
* <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>
* <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>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class RdDecisionFunction extends org.drip.function.definition.RdToR1 {
private double _dblB = java.lang.Double.NaN;
private double[] _adblInverseMarginWeight = null;
private org.drip.spaces.metric.RdNormed _rdInverseMargin = null;
private org.drip.spaces.tensor.RdGeneralizedVector _rdPredictor = null;
/**
* RdDecisionFunction Constructor
*
* @param rdPredictor The R^d Metric Input Predictor Space
* @param rdInverseMargin The Inverse Margin Weights R^d Space
* @param adblInverseMarginWeight Array of Inverse Margin Weights
* @param dblB The Kernel Offset
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RdDecisionFunction (
final org.drip.spaces.tensor.RdGeneralizedVector rdPredictor,
final org.drip.spaces.metric.RdNormed rdInverseMargin,
final double[] adblInverseMarginWeight,
final double dblB)
throws java.lang.Exception
{
super (null);
if (null == (_rdPredictor = rdPredictor) || null == (_rdInverseMargin = rdInverseMargin) || null ==
(_adblInverseMarginWeight = adblInverseMarginWeight) || !org.drip.numerical.common.NumberUtil.IsValid
(_dblB = dblB))
throw new java.lang.Exception ("RdDecisionFunction ctr: Invalid Inputs");
int iNumMarginWeight = _adblInverseMarginWeight.length;
if (0 == iNumMarginWeight || iNumMarginWeight != _rdPredictor.dimension())
throw new java.lang.Exception ("RdDecisionFunction ctr: Invalid Inputs");
}
/**
* Retrieve the Input Predictor Metric Vector Space
*
* @return The Input Predictor Metric Vector Space
*/
public org.drip.spaces.tensor.RdGeneralizedVector predictorSpace()
{
return _rdPredictor;
}
/**
* Retrieve the Inverse Margin Weight Metric Vector Space
*
* @return The Inverse Margin Weight Metric Vector Space
*/
public org.drip.spaces.metric.RdNormed inverseMarginSpace()
{
return _rdInverseMargin;
}
/**
* Retrieve the Decision Kernel Weights
*
* @return The Decision Kernel Weights
*/
public double[] inverseMarginWeights()
{
return _adblInverseMarginWeight;
}
/**
* Retrieve the Offset
*
* @return The Offset
*/
public double offset()
{
return _dblB;
}
/**
* Classify the Specified Multi-dimensional Point
*
* @param adblX The Multi-dimensional Input Point
*
* @return +1/-1 Boolean Space Output Equivalents
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public short classify (
final double[] adblX)
throws java.lang.Exception
{
return evaluate (adblX) > 0. ? org.drip.spaces.tensor.BinaryBooleanVector.BBV_UP :
org.drip.spaces.tensor.BinaryBooleanVector.BBV_DOWN;
}
/**
* Regress on the Specified Multi-dimensional Point
*
* @param adblX The Multi-dimensional Input Point
*
* @return The Regression Output
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double regress (
final double[] adblX)
throws java.lang.Exception
{
return evaluate (adblX);
}
/**
* Compute the Entropy Number Upper Bounds Instance for the Specified Inputs
*
* @param dsoFactorizer The Factorizing Diagonal Scaling Operator
* @param dblFeatureSpaceMaureyConstant The Feature Space Maurey Constant
*
* @return The Entropy Number Upper Bounds Instance
*/
public org.drip.learning.svm.DecisionFunctionOperatorBounds entropyNumberUpperBounds (
final org.drip.learning.kernel.DiagonalScalingOperator dsoFactorizer,
final double dblFeatureSpaceMaureyConstant)
{
try {
return new org.drip.learning.svm.DecisionFunctionOperatorBounds (dsoFactorizer,
inverseMarginSpace().populationMetricNorm(), dblFeatureSpaceMaureyConstant,
predictorSpace().dimension());
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Compute the Decision Function's Asymptotic Exponent for the Entropy Number
*
* @param dsoFactorizer The Factorizing Diagonal Scaling Operator
*
* @return The Decision Function's Asymptotic Exponent for the Entropy Number
*
* @throws java.lang.Exception Thrown if the Asymptotoc Exponent cannot be computed
*/
public double logEntropyNumberAsymptote (
final org.drip.learning.kernel.DiagonalScalingOperator dsoFactorizer)
throws java.lang.Exception
{
if (null == dsoFactorizer)
throw new java.lang.Exception
("RdDecisionFunction::logEntropyNumberAsymptote => Invalid Inputs");
org.drip.learning.bound.DiagonalOperatorCoveringBound docb = dsoFactorizer.entropyNumberAsymptote();
if (null == docb)
throw new java.lang.Exception
("RdDecisionFunction::logEntropyNumberAsymptote => Cannot get Diagonal Operator Covering Bounds");
return org.drip.learning.bound.DiagonalOperatorCoveringBound.BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
== docb.entropyNumberAsymptoteType() ? -1. * docb.entropyNumberAsymptoteExponent() - 0.5 :
-1. * docb.entropyNumberAsymptoteExponent();
}
/**
* Optimize the Hyper-plane for the Purposes of Regression
*
* @param adblEmpirical The Empirical Observation Array
* @param dblMargin The Optimization Margin
* @param dblInverseWidthNormConstraint The Inverse Width Norm Constraint
*
* @return TRUE - The Hyper-plane has been successfully Optimized for Regression
*/
public abstract boolean optimizeRegressionHyperplane (
final double[] adblEmpirical,
final double dblMargin,
final double dblInverseWidthNormConstraint
);
/**
* Optimize the Hyper-plane for the Purposes of Classification
*
* @param asEmpirical The Empirical Observation Array
* @param dblMargin The Optimization Margin
* @param dblInverseWidthNormConstraint The Inverse Width Norm Constraint
*
* @return TRUE - The Hyper-plane has been successfully Optimized for Classification
*/
public abstract boolean optimizeClassificationHyperplane (
final short[] asEmpirical,
final double dblMargin,
final double dblInverseWidthNormConstraint
);
}