Package org.drip.learning.bound

Class DiagonalOperatorCoveringBound

java.lang.Object
org.drip.learning.bound.DiagonalOperatorCoveringBound
public class DiagonalOperatorCoveringBound
extends java.lang.Object
DiagonalOperatorCoveringBound implements the Behavior of the Bound on the Covering Number of the Diagonal Scaling Operator. The Asymptote is set as either

log [e_n(A)] ~ O {(1/log n)^alpha}

- OR -

e_n(A) ~ O {(1/log n)^alpha}

The References are:
  • Ash, R. (1965): Information Theory Inter-science New York
  • Carl, B., and I. Stephani (1990): Entropy, Compactness, and Approximation of Operators Cambridge University Press Cambridge UK
  • Gordon, Y., H. Konig, and C. Schutt (1987): Geometric and Probabilistic Estimates of Entropy and Approximation Numbers of Operators Journal of Approximation Theory 49 219-237
  • Konig, H. (1986): Eigenvalue Distribution of Compact Operators Birkhauser Basel, Switzerland
  • Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex Combinations and mlps, in: Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans - editors MIT Press Cambridge, MA
  • Williamson, R. C., A. J. Smola, and B. Scholkopf (2001): Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators IEEE Transactions on Information Theory 47 (6) 2516-2532


Author:
Lakshmi Krishnamurthy

  • Field Summary

    Fields
    Modifier and Type Field Description
    static int BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
    Asymptote on the Base Diagonal Operator Entropy Number
    static int LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
    Asymptote on the Log of the Diagonal Operator Entropy Number

  • Constructor Summary

    Constructors
    Constructor Description
    DiagonalOperatorCoveringBound​(int iOperatorEntropyAsymptoteBase, double dblOperatorEntropyAsymptoteExponent)
    DiagonalOperatorCoveringBound Constructor

  • Method Summary

    Modifier and Type Method Description
    double entropyNumberAsymptoteExponent()
    Retrieve the Entropy Number Asymptote Exponent
    int entropyNumberAsymptoteType()
    Retrieve the Entropy Number Asymptote Type

    Methods inherited from class java.lang.Object

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

  • Field Details

    • BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

      public static final int BASE_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
      Asymptote on the Base Diagonal Operator Entropy Number
      See Also:
      Constant Field Values

    • LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT

      public static final int LOG_DIAGONAL_ENTROPY_ASYMPTOTE_EXPONENT
      Asymptote on the Log of the Diagonal Operator Entropy Number
      See Also:
      Constant Field Values

  • Constructor Details

    • DiagonalOperatorCoveringBound

      public DiagonalOperatorCoveringBound​(int iOperatorEntropyAsymptoteBase, double dblOperatorEntropyAsymptoteExponent) throws java.lang.Exception
      DiagonalOperatorCoveringBound Constructor
      Parameters:
      iOperatorEntropyAsymptoteBase - Indicate the Asymptote is on the Base Value or Log Value
      dblOperatorEntropyAsymptoteExponent - The Entropy Number Asymptote Exponent
      Throws:
      java.lang.Exception - Throws if the Inputs are Invalid

  • Method Details

    • entropyNumberAsymptoteType

      public int entropyNumberAsymptoteType()
      Retrieve the Entropy Number Asymptote Type
      Returns:
      The Entropy Number Asymptote Type

    • entropyNumberAsymptoteExponent

      public double entropyNumberAsymptoteExponent()
      Retrieve the Entropy Number Asymptote Exponent
      Returns:
      The Entropy Number Asymptote Exponent