RegularizerR1ContinuousToR1Continuous.java
package org.drip.learning.regularization;
/*
* -*- 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>RegularizerR1ContinuousToR1Continuous</i> computes the Structural Loss and Risk for the specified
* Normed R<sup>1</sup> Continuous To Normed R<sup>1</sup> Continuous Learning Function.
*
* <br><br>
* <ul>
* <li>
* Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform
* Convergence, and Learnability <i>Journal of Association of Computational Machinery</i> <b>44
* (4)</b> 615-631
* </li>
* <li>
* Anthony, M., and P. L. Bartlett (1999): <i>Artificial Neural Network Learning - Theoretical
* Foundations</i> <b>Cambridge University Press</b> Cambridge, UK
* </li>
* <li>
* Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): <i>Towards Efficient Agnostic Learning</i>
* Machine Learning <b>17 (2)</b> 115-141
* </li>
* <li>
* Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with
* Squared Loss <i>IEEE Transactions on Information Theory</i> <b>44</b> 1974-1980
* </li>
* <li>
* Vapnik, V. N. (1998): <i>Statistical learning Theory</i> <b>Wiley</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/regularization">Statistical Learning Empirical Loss Regularizer</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class RegularizerR1ContinuousToR1Continuous extends
org.drip.spaces.rxtor1.NormedR1ContinuousToR1Continuous implements
org.drip.learning.regularization.RegularizerR1ToR1 {
private double _dblLambda = java.lang.Double.NaN;
/**
* RegularizerR1ContinuousToR1Continuous Function Space Constructor
*
* @param funcRegularizerR1ToR1 The R^1 To R^1 Regularizer Function
* @param r1ContinuousInput The Continuous R^1 Input Metric Vector Space
* @param r1ContinuousOutput The Continuous R^1 Output Metric Vector Space
* @param dblLambda The Regularization Lambda
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public RegularizerR1ContinuousToR1Continuous (
final org.drip.function.definition.R1ToR1 funcRegularizerR1ToR1,
final org.drip.spaces.metric.R1Continuous r1ContinuousInput,
final org.drip.spaces.metric.R1Continuous r1ContinuousOutput,
final double dblLambda)
throws java.lang.Exception
{
super (r1ContinuousInput, r1ContinuousOutput, funcRegularizerR1ToR1);
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLambda = dblLambda) || 0 > _dblLambda)
throw new java.lang.Exception
("RegularizerR1ContinuousToR1Continuous Constructor => Invalid Inputs");
}
@Override public double lambda()
{
return _dblLambda;
}
@Override public double structuralLoss (
final org.drip.function.definition.R1ToR1 funcR1ToR1,
final double[] adblX)
throws java.lang.Exception
{
if (null == funcR1ToR1 || null == adblX)
throw new java.lang.Exception
("RegularizerR1ContinuousToR1Continuous::structuralLoss => Invalid Inputs");
double dblLoss = 0.;
int iNumSample = adblX.length;
if (0 == iNumSample)
throw new java.lang.Exception
("RegularizerR1ContinuousToR1Continuous::structuralLoss => Invalid Inputs");
org.drip.function.definition.R1ToR1 funcRegularizerR1ToR1 = function();
int iPNorm = outputMetricVectorSpace().pNorm();
if (java.lang.Integer.MAX_VALUE == iPNorm) {
double dblSupremum = 0.;
for (int i = 0; i < iNumSample; ++i) {
double dblNodeValue = java.lang.Math.abs (funcRegularizerR1ToR1.evaluate (adblX[i]) *
funcR1ToR1.evaluate (adblX[i]));
if (dblSupremum < dblNodeValue) dblSupremum = dblNodeValue;
}
return dblSupremum;
}
for (int i = 0; i < iNumSample; ++i)
dblLoss += java.lang.Math.pow (java.lang.Math.abs (funcRegularizerR1ToR1.evaluate (adblX[i]) *
funcR1ToR1.evaluate (adblX[i])), iPNorm);
return dblLoss / iPNorm;
}
@Override public double structuralRisk (
final org.drip.measure.continuous.R1R1 distR1R1,
final org.drip.function.definition.R1ToR1 funcR1ToR1,
final double[] adblX,
final double[] adblY)
throws java.lang.Exception
{
if (null == funcR1ToR1 || null == adblX || null == adblY)
throw new java.lang.Exception
("RegularizerR1ContinuousToR1Continuous::structuralRisk => Invalid Inputs");
double dblLoss = 0.;
double dblNormalizer = 0.;
int iNumSample = adblX.length;
if (0 == iNumSample || iNumSample != adblY.length)
throw new java.lang.Exception
("RegularizerR1ContinuousToR1Continuous::structuralRisk => Invalid Inputs");
int iPNorm = outputMetricVectorSpace().pNorm();
org.drip.function.definition.R1ToR1 funcRegularizerR1ToR1 = function();
if (java.lang.Integer.MAX_VALUE == iPNorm) {
double dblWeightedSupremum = 0.;
double dblSupremumNodeValue = 0.;
for (int i = 0; i < iNumSample; ++i) {
double dblNodeValue = java.lang.Math.abs (funcRegularizerR1ToR1.evaluate (adblX[i]) *
funcR1ToR1.evaluate (adblX[i]));
double dblWeightedNodeValue = distR1R1.density (adblX[i], adblY[i]) * dblNodeValue;
if (dblWeightedNodeValue > dblWeightedSupremum) {
dblSupremumNodeValue = dblNodeValue;
dblWeightedSupremum = dblWeightedNodeValue;
}
}
return dblSupremumNodeValue;
}
for (int i = 0; i < iNumSample; ++i) {
double dblDensity = distR1R1.density (adblX[i], adblY[i]);
dblNormalizer += dblDensity;
dblLoss += dblDensity * java.lang.Math.pow (java.lang.Math.abs (funcRegularizerR1ToR1.evaluate
(adblX[i]) * funcR1ToR1.evaluate (adblX[i])), iPNorm);
}
return dblLoss / iPNorm / dblNormalizer;
}
}