org.drip.learning.svm

Class DecisionFunctionOperatorBounds

java.lang.Object

org.drip.learning.svm.DecisionFunctionOperatorBounds

public class DecisionFunctionOperatorBounds
extends java.lang.Object

DecisionFunctionOperatorBounds implements the Dot Product Entropy Number Upper Bounds for the Product of Kernel Feature Map Function and the Scaling Diagonal Operator. 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) 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. 4) Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators, Cambridge University Press, Cambridge UK. 5) 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

Constructor Summary

Constructors

Constructor and Description
DecisionFunctionOperatorBounds(DiagonalScalingOperator dsoFactorizer, double dblInverseMarginNormBound, double dblFeatureSpaceMaureyConstant, int iFeatureSpaceDimension) DecisionFunctionOperatorBounds Constructor

Method Summary

Modifier and Type	Method and Description
DiagonalScalingOperator	factorizingOperator() Retrieve the Factorizing Diagonal Scaling Operator Instance
double	featureMaureyOperatorEntropy(int iFeatureSpaceEntropyNumber) Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Entropy Number Upper Bound
double	featureMaureyOperatorNorm(int iFeatureSpaceEntropyNumber) Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Norm
double	featureNormOperatorEntropy() Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Entropy Number Upper Bound
double	featureSpaceDimension() Retrieve the Feature Space Dimension
double	featureSpaceMaureyBound(int iFeatureSpaceEntropyNumber) Compute the Feature Space's Maurey Bound for the Entropy Number given the specified Entropy Number
double	featureSpaceMaureyConstant() Retrieve the Feature Space Maurey Constant
double	infimumUpperBound(int iFeatureSpaceEntropyNumber) Compute the Infimum of the Decision Function Operator Upper Bound across all the Product Bounds for the specified Feature Space Entropy Number
double	inverseMarginNormBound() Retrieve the Norm Upper Bound of the Inverse Margin
double	productFeatureOperatorNorm() Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Norm

Methods inherited from class java.lang.Object

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

Constructor Detail

DecisionFunctionOperatorBounds

public DecisionFunctionOperatorBounds(DiagonalScalingOperator dsoFactorizer,
                                      double dblInverseMarginNormBound,
                                      double dblFeatureSpaceMaureyConstant,
                                      int iFeatureSpaceDimension)
                               throws java.lang.Exception

DecisionFunctionOperatorBounds Constructor

Parameters:

dsoFactorizer - The Factorizing Diagonal Scaling Operator

dblInverseMarginNormBound - The Decision Function Inverse Margin Norm Bound

dblFeatureSpaceMaureyConstant - The Kernel Feature Space Function Maurey Constant

iFeatureSpaceDimension - The Kernel Feature Space Dimension

Throws:

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

Method Detail

factorizingOperator

public DiagonalScalingOperator factorizingOperator()

Retrieve the Factorizing Diagonal Scaling Operator Instance

Returns:

The Factorizing Diagonal Scaling Operator Instance

inverseMarginNormBound

public double inverseMarginNormBound()

Retrieve the Norm Upper Bound of the Inverse Margin

Returns:

The Norm Upper Bound of the Inverse Margin

featureSpaceMaureyConstant

public double featureSpaceMaureyConstant()

Retrieve the Feature Space Maurey Constant

Returns:

The Feature Space Maurey Constant

featureSpaceDimension

public double featureSpaceDimension()

Retrieve the Feature Space Dimension

Returns:

The Feature Space Dimension

featureSpaceMaureyBound

public double featureSpaceMaureyBound(int iFeatureSpaceEntropyNumber)
                               throws java.lang.Exception

Compute the Feature Space's Maurey Bound for the Entropy Number given the specified Entropy Number

Parameters:

iFeatureSpaceEntropyNumber - The Feature Space Entropy Number

Returns:

The Feature Space's Maurey Bound for the specified Entropy Number

Throws:

java.lang.Exception - The Feature Space's Maurey Bound cannot be computed

featureMaureyOperatorEntropy

public double featureMaureyOperatorEntropy(int iFeatureSpaceEntropyNumber)
                                    throws java.lang.Exception

Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Entropy Number Upper Bound

Parameters:

iFeatureSpaceEntropyNumber - The Feature Space Entropy Number

Returns:

The Feature Space's Operator Entropy for the specified Entropy Number

Throws:

java.lang.Exception - The Feature Space's Operator Entropy cannot be computed

featureMaureyOperatorNorm

public double featureMaureyOperatorNorm(int iFeatureSpaceEntropyNumber)
                                 throws java.lang.Exception

Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Norm

Parameters:

iFeatureSpaceEntropyNumber - The Feature Space Entropy Number

Returns:

The Feature Space's Operator Norm for the specified Entropy Number

Throws:

java.lang.Exception - The Feature Space's Operator Norm cannot be computed

productFeatureOperatorNorm

public double productFeatureOperatorNorm()
                                  throws java.lang.Exception

Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Norm

Returns:

The Entropy Number Upper Bound using the Product Norm

Throws:

java.lang.Exception - The Entropy Number Upper Bound cannot be computed

featureNormOperatorEntropy

public double featureNormOperatorEntropy()
                                  throws java.lang.Exception

Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Entropy Number Upper Bound

Returns:

The Entropy Number Upper Bound using the Product Norm

Throws:

java.lang.Exception - The Entropy Number Upper Bound cannot be computed

infimumUpperBound

public double infimumUpperBound(int iFeatureSpaceEntropyNumber)
                         throws java.lang.Exception

Compute the Infimum of the Decision Function Operator Upper Bound across all the Product Bounds for the specified Feature Space Entropy Number

Parameters:

iFeatureSpaceEntropyNumber - The specified Feature Space Entropy Number

Returns:

Infimum of the Decision Function Operator Upper Bound

Throws:

java.lang.Exception - Thrown if the Infimum of the Decision Function Operator Upper Bound cannot be calculated