Package org.drip.learning.svm

Class DecisionFunctionOperatorBounds

java.lang.Object
org.drip.learning.svm.DecisionFunctionOperatorBounds
public class DecisionFunctionOperatorBounds
extends java.lang.Object
DecisionFunctionOperatorBounds implements the Dot Product Entropy Number Upper Bounds for the Product of Kernel Feature Map Function and the Scaling Diagonal Operator.

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


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    DecisionFunctionOperatorBounds​(DiagonalScalingOperator dsoFactorizer, double dblInverseMarginNormBound, double dblFeatureSpaceMaureyConstant, int iFeatureSpaceDimension)
    DecisionFunctionOperatorBounds Constructor

  • Method Summary

    Modifier and Type Method Description
    DiagonalScalingOperator factorizingOperator()
    Retrieve the Factorizing Diagonal Scaling Operator Instance
    double featureMaureyOperatorEntropy​(int iFeatureSpaceEntropyNumber)
    Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Entropy Number Upper Bound
    double featureMaureyOperatorNorm​(int iFeatureSpaceEntropyNumber)
    Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Norm
    double featureNormOperatorEntropy()
    Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Entropy Number Upper Bound
    double featureSpaceDimension()
    Retrieve the Feature Space Dimension
    double featureSpaceMaureyBound​(int iFeatureSpaceEntropyNumber)
    Compute the Feature Space's Maurey Bound for the Entropy Number given the specified Entropy Number
    double featureSpaceMaureyConstant()
    Retrieve the Feature Space Maurey Constant
    double infimumUpperBound​(int iFeatureSpaceEntropyNumber)
    Compute the Infimum of the Decision Function Operator Upper Bound across all the Product Bounds for the specified Feature Space Entropy Number
    double inverseMarginNormBound()
    Retrieve the Norm Upper Bound of the Inverse Margin
    double productFeatureOperatorNorm()
    Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Norm

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • DecisionFunctionOperatorBounds

      public DecisionFunctionOperatorBounds​(DiagonalScalingOperator dsoFactorizer, double dblInverseMarginNormBound, double dblFeatureSpaceMaureyConstant, int iFeatureSpaceDimension) throws java.lang.Exception
      DecisionFunctionOperatorBounds Constructor
      Parameters:
      dsoFactorizer - The Factorizing Diagonal Scaling Operator
      dblInverseMarginNormBound - The Decision Function Inverse Margin Norm Bound
      dblFeatureSpaceMaureyConstant - The Kernel Feature Space Function Maurey Constant
      iFeatureSpaceDimension - The Kernel Feature Space Dimension
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • factorizingOperator

      public DiagonalScalingOperator factorizingOperator()
      Retrieve the Factorizing Diagonal Scaling Operator Instance
      Returns:
      The Factorizing Diagonal Scaling Operator Instance

    • inverseMarginNormBound

      public double inverseMarginNormBound()
      Retrieve the Norm Upper Bound of the Inverse Margin
      Returns:
      The Norm Upper Bound of the Inverse Margin

    • featureSpaceMaureyConstant

      public double featureSpaceMaureyConstant()
      Retrieve the Feature Space Maurey Constant
      Returns:
      The Feature Space Maurey Constant

    • featureSpaceDimension

      public double featureSpaceDimension()
      Retrieve the Feature Space Dimension
      Returns:
      The Feature Space Dimension

    • featureSpaceMaureyBound

      public double featureSpaceMaureyBound​(int iFeatureSpaceEntropyNumber) throws java.lang.Exception
      Compute the Feature Space's Maurey Bound for the Entropy Number given the specified Entropy Number
      Parameters:
      iFeatureSpaceEntropyNumber - The Feature Space Entropy Number
      Returns:
      The Feature Space's Maurey Bound for the specified Entropy Number
      Throws:
      java.lang.Exception - The Feature Space's Maurey Bound cannot be computed

    • featureMaureyOperatorEntropy

      public double featureMaureyOperatorEntropy​(int iFeatureSpaceEntropyNumber) throws java.lang.Exception
      Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Entropy Number Upper Bound
      Parameters:
      iFeatureSpaceEntropyNumber - The Feature Space Entropy Number
      Returns:
      The Feature Space's Operator Entropy for the specified Entropy Number
      Throws:
      java.lang.Exception - The Feature Space's Operator Entropy cannot be computed

    • featureMaureyOperatorNorm

      public double featureMaureyOperatorNorm​(int iFeatureSpaceEntropyNumber) throws java.lang.Exception
      Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Maurey Upper Bound for the Entropy for the specified Entropy Number and the Scaling Operator Norm
      Parameters:
      iFeatureSpaceEntropyNumber - The Feature Space Entropy Number
      Returns:
      The Feature Space's Operator Norm for the specified Entropy Number
      Throws:
      java.lang.Exception - The Feature Space's Operator Norm cannot be computed

    • productFeatureOperatorNorm

      public double productFeatureOperatorNorm() throws java.lang.Exception
      Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Norm
      Returns:
      The Entropy Number Upper Bound using the Product Norm
      Throws:
      java.lang.Exception - The Entropy Number Upper Bound cannot be computed

    • featureNormOperatorEntropy

      public double featureNormOperatorEntropy() throws java.lang.Exception
      Compute the Decision Function Entropy Number Upper Bound using the Product of the Feature Space's Norm for the Upper Bound of the Entropy Number and the Scaling Operator Entropy Number Upper Bound
      Returns:
      The Entropy Number Upper Bound using the Product Norm
      Throws:
      java.lang.Exception - The Entropy Number Upper Bound cannot be computed

    • infimumUpperBound

      public double infimumUpperBound​(int iFeatureSpaceEntropyNumber) throws java.lang.Exception
      Compute the Infimum of the Decision Function Operator Upper Bound across all the Product Bounds for the specified Feature Space Entropy Number
      Parameters:
      iFeatureSpaceEntropyNumber - The specified Feature Space Entropy Number
      Returns:
      Infimum of the Decision Function Operator Upper Bound
      Throws:
      java.lang.Exception - Thrown if the Infimum of the Decision Function Operator Upper Bound cannot be calculated