Package org.drip.learning.kernel

Class EigenFunctionRdToR1

java.lang.Object

org.drip.spaces.rxtor1.NormedRxToNormedR1

org.drip.spaces.rxtor1.NormedRdToNormedR1

org.drip.learning.kernel.EigenFunctionRdToR1

public abstract class EigenFunctionRdToR1
extends NormedRdToNormedR1

EigenFunctionRdToR1 holds the Eigen-vector Function and its corresponding Space of the R^d To R¹ Kernel Linear Integral Operator defined by: T_k [f(.)] := Integral Over Input Space {k (., y) * f(y) * d[Prob(y)]}

The References are:

• Ash, R. (1965): Information Theory Inter-science New York
• Konig, H. (1986): Eigenvalue Distribution of Compact Operators Birkhauser Basel, Switzerland
• Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex Combinations and mlps, in: Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans - editors MIT Press Cambridge, MA

• Module = Computational Core Module
• Library = Statistical Learning
• Project = Agnostic Learning Bounds under Empirical Loss Minimization Schemes
• Package = Statistical Learning Banach Mercer Kernels

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	agnosticUpperBound()	Retrieve the Agnostic Upper Bound of the Eigen-Function

Methods inherited from class org.drip.spaces.rxtor1.NormedRdToNormedR1

function, inputMetricVectorSpace, outputMetricVectorSpace, populationESS, sampleMetricNorm, sampleSupremumNorm

Methods inherited from class org.drip.spaces.rxtor1.NormedRxToNormedR1

populationCoveringNumber, populationMetricNorm, populationSupremumCoveringNumber, populationSupremumMetricNorm, sampleCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

agnosticUpperBound

public double agnosticUpperBound()

Retrieve the Agnostic Upper Bound of the Eigen-Function

Returns:

The Agnostic Upper Bound of the Eigen-Function