org.drip.learning.bound

Class DiagonalOperatorCoveringBound

java.lang.Object

org.drip.learning.bound.DiagonalOperatorCoveringBound

public class DiagonalOperatorCoveringBound
extends java.lang.Object

DiagonalOperatorCoveringBound implements the Behavior of the Bound on the Covering Number of the Diagonal Scaling Operator. The Asymptote is set as either log [e_n(A)] ~ O {(1/log n)^alpha} - OR - e_n(A) ~ O {(1/log n)^alpha} 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. 6) Williamson, R. C., A. J. Smola, and B. Scholkopf (2001): Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators, IEEE Transactions on Information Theory 47 (6) 2516-2532.

Author:

Lakshmi Krishnamurthy

Field Summary

Fields

Modifier and Type	Field and Description
static int	BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT Asymptote on the Base Diagonal Operator Entropy Number
static int	LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT Asymptote on the Log of the Diagonal Operator Entropy Number

Constructor Summary

Constructors

Constructor and Description
DiagonalOperatorCoveringBound(int iOperatorEntropyAsymptoteBase, double dblOperatorEntropyAsymptoteExponent) DiagonalOperatorCoveringBound Constructor

Method Summary

Modifier and Type	Method and Description
double	entropyNumberAsymptoteExponent() Retrieve the Entropy Number Asymptote Exponent
int	entropyNumberAsymptoteType() Retrieve the Entropy Number Asymptote Type

Methods inherited from class java.lang.Object

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

Field Detail

BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

public static final int BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

Asymptote on the Base Diagonal Operator Entropy Number

See Also:

Constant Field Values

LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

public static final int LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

Asymptote on the Log of the Diagonal Operator Entropy Number

See Also:

Constant Field Values

Constructor Detail

DiagonalOperatorCoveringBound

public DiagonalOperatorCoveringBound(int iOperatorEntropyAsymptoteBase,
                                     double dblOperatorEntropyAsymptoteExponent)
                              throws java.lang.Exception

DiagonalOperatorCoveringBound Constructor

Parameters:

iOperatorEntropyAsymptoteBase - Indicate the Asymptote is on the Base Value or Log Value

dblOperatorEntropyAsymptoteExponent - The Entropy Number Asymptote Exponent

Throws:

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

Method Detail

entropyNumberAsymptoteType

public int entropyNumberAsymptoteType()

Retrieve the Entropy Number Asymptote Type

Returns:

The Entropy Number Asymptote Type

entropyNumberAsymptoteExponent

public double entropyNumberAsymptoteExponent()

Retrieve the Entropy Number Asymptote Exponent

Returns:

The Entropy Number Asymptote Exponent