<gh_stars>0

package org.drip.learning.regularization;

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

/*!
 * Copyright (C) 2017 <NAME>
 * Copyright (C) 2016 <NAME>
 * Copyright (C) 2015 <NAME>
 * 
 *  This file is part of DRIP, a free-software/open-source library for buy/side financial/trading model
 *  	libraries targeting analysts and developers
 *  	https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *  	Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *  	Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *  	Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *  	Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *  	Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * RegularizerRdxToR1 exposes the Structural Loss and Risk Calculations for the specified Normed R^d To Normed
 *  R^1 Learning Function.
 *  
 * The References are:
 *  
 *  1) <NAME>., <NAME>, <NAME>, and <NAME> (1997): Scale-sensitive Dimensions, Uniform
 *  	Convergence, and Learnability, Journal of Association of Computational Machinery, 44 (4) 615-631.
 * 
 *  2) <NAME>., and <NAME> (1999): Artificial Neural Network Learning - Theoretical Foundations,
 *  	Cambridge University Press, Cambridge, UK.
 *  
 *  3) <NAME>., <NAME>, and <NAME> (1994): Towards Efficient Agnostic Learning, Machine
 *  	Learning, 17 (2) 115-141.
 *  
 *  4) <NAME>., <NAME>, and <NAME> (1998): The Importance of Convexity in Learning with
 *  	Squared Loss, IEEE Transactions on Information Theory, 44 1974-1980.
 * 
 *  5) <NAME>. (1998): Statistical Learning Theory, Wiley, New York.
 *
 * @author <NAME>
 */

public interface RegularizerRdToR1 {

	/**
	 * Retrieve the Regularization Constant Lambda
	 * 
	 * @return The Regularization Constant Lambda
	 */

	public abstract double lambda();

	/**
	 * Compute the Regularization Sample Structural Loss
	 * 
	 * @param funcRdToR1 R^d To R^1 Function Instance
	 * @param aadblX The Sample Instance
	 * 
	 * @return The Regularization Sample Structural Loss
	 * 
	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
	 */

	public abstract double structuralLoss (
		final org.drip.function.definition.RdToR1 funcRdToR1,
		final double[][] aadblX)
		throws java.lang.Exception;

	/**
	 * Compute the Regularization Sample Structural Loss
	 * 
	 * @param distRdR1 R^d R^1 Multivariate Measure
	 * @param funcRdToR1 R^d To R^1 Function Instance
	 * @param aadblX The Sample Instance
	 * @param adblY The Response Instance
	 * 
	 * @return The Regularization Sample Structural Loss
	 * 
	 * @throws java.lang.Exception Thrown if the Inputs are Invalid
	 */

	public abstract double structuralRisk (
		final org.drip.measure.continuousjoint.RdR1 distRdR1,
		final org.drip.function.definition.RdToR1 funcRdToR1,
		final double[][] aadblX,
		final double[] adblY)
		throws java.lang.Exception;
}
