Package org.drip.spaces.cover

Interface OperatorClassCoveringBounds

All Known Implementing Classes:
DiagonalScalingOperator
public interface OperatorClassCoveringBounds
OperatorClassCoveringBounds implements the estimate Lower/Upper Bounds and/or Absolute Values of the Covering Number for the Operator Class. The Main References are:

  • Guo, Y., P. L. Bartlett, J. Shawe-Taylor, and R. C. Williamson (1999): Covering Numbers for Support Vector Machines, in: Proceedings of the 12th Annual Conference of Computational Learning Theory ACM New York 267-277
It provides the following Functionality:
  • Lower Bound of the Operator Entropy Number
  • Upper Bound of the Operator Entropy Number
  • Compute the Entropy Number Index of the Operator
  • Compute the Metric Norm of the Operator
  • Compute the Entropy Number Asymptotic Behavior

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 Details

    • entropyNumberLowerBound

      double entropyNumberLowerBound() throws java.lang.Exception
      Lower Bound of the Operator Entropy Number
      Returns:
      Lower Bound of the Operator Entropy Number
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • entropyNumberUpperBound

      double entropyNumberUpperBound() throws java.lang.Exception
      Upper Bound of the Operator Entropy Number
      Returns:
      Upper Bound of the Operator Entropy Number
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

    • entropyNumberIndex

      int entropyNumberIndex()
      Compute the Entropy Number Index of the Operator
      Returns:
      The Entropy Number Index of the Operator

    • norm

      double norm() throws java.lang.Exception
      Compute the Metric Norm of the Operator
      Returns:
      The Metric Norm of the Operator
      Throws:
      java.lang.Exception - Thrown if the Metric Norm cannot be computed

    • entropyNumberAsymptote

      DiagonalOperatorCoveringBound entropyNumberAsymptote()
      Compute the Entropy Number Asymptotic Behavior
      Returns:
      the Entropy Number Asymptote Instance