Package 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 References are:

  • Anthony, M., and P. L. Bartlett (1999): Artificial Neural Network Learning - Theoretical Foundations Cambridge University Press Cambridge, UK
  • 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


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    LipschitzCoveringNumberBound​(double dblSupremumUpperBound, double dblLpUpperBound)
    LipschitzCoveringNumberBound Constructor

  • Method Summary

    Modifier and Type Method 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 Details

    • 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 Details

    • 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