Package org.drip.learning.kernel

Class DiagonalScalingOperator

java.lang.Object

org.drip.learning.kernel.DiagonalScalingOperator

All Implemented Interfaces:

OperatorClassCoveringBounds

public abstract class DiagonalScalingOperator
extends java.lang.Object
implements OperatorClassCoveringBounds

DiagonalScalingOperator implements the Scaling Operator that is used to determine the Bounds of the R^x L₂ To R^x L₂ 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
• Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators Cambridge University Press Cambridge UK
• Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and Approximation Numbers of Operators Journal of Approximation Theory 49 219-237
• 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

Constructor Summary

Constructors

Constructor	Description
DiagonalScalingOperator(double[] adblDiagonalScaler)	DiagonalScalingOperator Constructor

Method Summary

Modifier and Type	Method	Description
int	entropyNumberIndex()	Compute the Entropy Number Index of the Operator
double	entropyNumberLowerBound()	Lower Bound of the Operator Entropy Number
double	entropyNumberUpperBound()	Upper Bound of the Operator Entropy Number
double[]	scaler()	Retrieve the Diagonal Scaling Multiplier Array

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.drip.spaces.cover.OperatorClassCoveringBounds

entropyNumberAsymptote, norm

Constructor Details

DiagonalScalingOperator

public DiagonalScalingOperator(double[] adblDiagonalScaler)
                        throws java.lang.Exception

DiagonalScalingOperator Constructor

Parameters:

adblDiagonalScaler - The Diagonal Scaling Multiplier Array

Throws:

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

Method Details

scaler

public double[] scaler()

Retrieve the Diagonal Scaling Multiplier Array

Returns:

The Diagonal Scaling Multiplier Array

entropyNumberIndex

public int entropyNumberIndex()

Description copied from interface: OperatorClassCoveringBounds

Compute the Entropy Number Index of the Operator

Specified by:

entropyNumberIndex in interface OperatorClassCoveringBounds

Returns:

The Entropy Number Index of the Operator

entropyNumberLowerBound

public double entropyNumberLowerBound()

Description copied from interface: OperatorClassCoveringBounds

Lower Bound of the Operator Entropy Number

Specified by:

entropyNumberLowerBound in interface OperatorClassCoveringBounds

Returns:

Lower Bound of the Operator Entropy Number

entropyNumberUpperBound

public double entropyNumberUpperBound()

Description copied from interface: OperatorClassCoveringBounds

Upper Bound of the Operator Entropy Number

Specified by:

entropyNumberUpperBound in interface OperatorClassCoveringBounds

Returns:

Upper Bound of the Operator Entropy Number