Package org.drip.spaces.cover

Interface FunctionClassCoveringBounds

All Known Implementing Classes:
L1R1CoveringBounds, ScaleSensitiveCoveringBounds
public interface FunctionClassCoveringBounds
FunctionClassCoveringBounds implements the estimate Lower/Upper Bounds and/or Absolute Values of the Covering Number for the Function Class. The Main References are:

  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK
  • P. L. Bartlett, S. R. Kulkarni, and S. E. Posner (1997): Covering Numbers for Real-valued Function Classes IEEE Transactions on Information Theory 45 (5) 1721-1724
It provides the following Functionality:
  • Log of the Lower Bound of the Function Covering Number
  • Log of the Upper Bound of the Function Covering Number

Module Computational Core Module
Library Statistical Learning Library
Project R1 and Rd Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package Vector Spaces Covering Number Estimator
Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    double logLowerBound​(double cover)
    Log of the Lower Bound of the Function Covering Number
    double logUpperBound​(double cover)
    Log of the Upper Bound of the Function Covering Number

  • Method Details

    • logLowerBound

      double logLowerBound​(double cover) throws java.lang.Exception
      Log of the Lower Bound of the Function Covering Number
      Parameters:
      cover - The Size of the Cover
      Returns:
      Log of the Lower Bound of the Function Covering Number
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • logUpperBound

      double logUpperBound​(double cover) throws java.lang.Exception
      Log of the Upper Bound of the Function Covering Number
      Parameters:
      cover - The Size of the Cover
      Returns:
      Log of the Upper Bound of the Function Covering Number
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid