org.drip.learning.regularization

Interface RegularizerRdToR1

All Known Implementing Classes:

RegularizerRdCombinatorialToR1Continuous, RegularizerRdContinuousToR1Continuous

public interface RegularizerRdToR1

RegularizerRdxToR1 exposes the Structural Loss and Risk Calculations for the specified Normed R^d To Normed R^1 Learning Function. The References are: 1) Alon, N., S. Ben-David, N. Cesa Bianchi, and D. Haussler (1997): Scale-sensitive Dimensions, Uniform Convergence, and Learnability, Journal of Association of Computational Machinery, 44 (4) 615-631. 2) Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations, Cambridge University Press, Cambridge, UK. 3) Kearns, M. J., R. E. Schapire, and L. M. Sellie (1994): Towards Efficient Agnostic Learning, Machine Learning, 17 (2) 115-141. 4) Lee, W. S., P. L. Bartlett, and R. C. Williamson (1998): The Importance of Convexity in Learning with Squared Loss, IEEE Transactions on Information Theory, 44 1974-1980. 5) Vapnik, V. N. (1998): Statistical Learning Theory, Wiley, New York.

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method and Description
double	lambda() Retrieve the Regularization Constant Lambda
double	structuralLoss(RdToR1 funcRdToR1, double[][] aadblX) Compute the Regularization Sample Structural Loss
double	structuralRisk(RdR1 distRdR1, RdToR1 funcRdToR1, double[][] aadblX, double[] adblY) Compute the Regularization Sample Structural Loss

Method Detail

lambda

double lambda()

Retrieve the Regularization Constant Lambda

Returns:

The Regularization Constant Lambda

structuralLoss

double structuralLoss(RdToR1 funcRdToR1,
                      double[][] aadblX)
               throws java.lang.Exception

Compute the Regularization Sample Structural Loss

Parameters:

funcRdToR1 - R^d To R^1 Function Instance

aadblX - The Sample Instance

Returns:

The Regularization Sample Structural Loss

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

structuralRisk

double structuralRisk(RdR1 distRdR1,
                      RdToR1 funcRdToR1,
                      double[][] aadblX,
                      double[] adblY)
               throws java.lang.Exception

Compute the Regularization Sample Structural Loss

Parameters:

distRdR1 - R^d R^1 Multivariate Measure

funcRdToR1 - R^d To R^1 Function Instance

aadblX - The Sample Instance

adblY - The Response Instance

Returns:

The Regularization Sample Structural Loss

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid