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

EigEigenFunctionRdToR1enFunction holds the Eigen-vector Function and its corresponding Space of the R^d To R^1 Kernel Linear Integral Operator defined by: T_k [f(.)] := Integral Over Input Space {k (., y) * f(y) * d[Prob(y)]} The References are: 1) Ash, R. (1965): Information Theory, Inter-science New York. 2) Konig, H. (1986): Eigenvalue Distribution of Compact Operators, Birkhauser, Basel, Switzerland. 3) 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.

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method and 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 Detail

agnosticUpperBound

public double agnosticUpperBound()

Retrieve the Agnostic Upper Bound of the Eigen-Function

Returns:

The Agnostic Upper Bound of the Eigen-Function