org.drip.learning.bound

Class LipschitzCoveringNumberBound

java.lang.Object

org.drip.learning.bound.LipschitzCoveringNumberBound

public class LipschitzCoveringNumberBound
extends java.lang.Object

LipschitzCoveringNumberBound contains the Upper Bounds of the Covering Numbers induced by Lipschitz and approximate Lipschitz Loss Function Class. The Reference are: 1) Bartlett, P. L., P. Long, and R. C. Williamson (1996): Fat-shattering and the Learnability of Real- Valued Functions, Journal of Computational System Science, 52 (3) 434-452. 2) Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations, Cambridge University Press, Cambridge, UK.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
LipschitzCoveringNumberBound(double dblSupremumUpperBound, double dblLpUpperBound) LipschitzCoveringNumberBound Constructor

Method Summary

Modifier and Type	Method and Description
double	leastUpperBound() Retrieve the Least Covering Number Upper Bound
double	lpUpperBound() Retrieve the Lp-based Covering Number Upper Bound
double	supremumUpperBound() Retrieve the Supremum-based Covering Number Upper Bound

Methods inherited from class java.lang.Object

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

Constructor Detail

LipschitzCoveringNumberBound

public LipschitzCoveringNumberBound(double dblSupremumUpperBound,
                                    double dblLpUpperBound)
                             throws java.lang.Exception

LipschitzCoveringNumberBound Constructor

Parameters:

dblSupremumUpperBound - Supremum Upper Bound for the Covering Number

dblLpUpperBound - The Lp Upper Bound for the Covering Number

Throws:

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

Method Detail

supremumUpperBound

public double supremumUpperBound()

Retrieve the Supremum-based Covering Number Upper Bound

Returns:

The Supremum-based Covering Number Upper Bound

lpUpperBound

public double lpUpperBound()

Retrieve the Lp-based Covering Number Upper Bound

Returns:

The Lp-based Covering Number Upper Bound

leastUpperBound

public double leastUpperBound()

Retrieve the Least Covering Number Upper Bound

Returns:

The Least Covering Number Upper Bound