Package org.drip.spaces.cover

Class L1R1CoveringBounds

java.lang.Object
org.drip.spaces.cover.L1R1CoveringBounds
All Implemented Interfaces:
FunctionClassCoveringBounds
public class L1R1CoveringBounds
extends java.lang.Object
implements FunctionClassCoveringBounds
L1R1CoveringBounds implements the Lower/Upper Bounds for the Class of Non-decreasing R1 to L1 R1 for Functions that are:

  • Absolutely Bounded
  • Have Bounded Variation
The References are:

  • 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
  • L. Birge (1987): Estimating a Density Under Order Restrictions: Non-asymptotic Minimax Risk Annals of Statistics 15 995-1012
It provides the following Functionality:
  • L1R1CoveringBounds Constructor
  • Retrieve the Ordinate Support
  • Retrieve the Function Variation
  • Retrieve the Function Bound

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

  • Constructor Summary

    Constructors
    Constructor Description
    L1R1CoveringBounds​(double support, double variation, double bound)
    L1R1CoveringBounds Constructor

  • Method Summary

    Modifier and Type Method Description
    double bound()
    Retrieve the Function Bound
    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
    double support()
    Retrieve the Ordinate Support
    double variation()
    Retrieve the Function Variation

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • L1R1CoveringBounds

      public L1R1CoveringBounds​(double support, double variation, double bound) throws java.lang.Exception
      L1R1CoveringBounds Constructor
      Parameters:
      support - The Ordinate Support
      variation - The Function Variation
      bound - The Function Bound
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • support

      public double support()
      Retrieve the Ordinate Support
      Returns:
      The Ordinate Support

    • variation

      public double variation()
      Retrieve the Function Variation
      Returns:
      The Function Variation

    • bound

      public double bound()
      Retrieve the Function Bound
      Returns:
      The Function Bound

    • logLowerBound

      public double logLowerBound​(double cover) throws java.lang.Exception
      Description copied from interface: FunctionClassCoveringBounds
      Log of the Lower Bound of the Function Covering Number
      Specified by:
      logLowerBound in interface FunctionClassCoveringBounds
      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

      public double logUpperBound​(double cover) throws java.lang.Exception
      Description copied from interface: FunctionClassCoveringBounds
      Log of the Upper Bound of the Function Covering Number
      Specified by:
      logUpperBound in interface FunctionClassCoveringBounds
      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