Package org.drip.learning.bound

Class MeasureConcentrationExpectationBound

java.lang.Object
org.drip.learning.bound.MeasureConcentrationExpectationBound
public class MeasureConcentrationExpectationBound
extends java.lang.Object
MeasureConcentrationExpectationBound provides the Upper Bound of the Expected Loss between Empirical Outcome and the Prediction of the given Learner Class using the Concentration of Measure Inequalities. This is expressed as C na, where n is the Size of the Sample, and 'C' and 'a' are Constants specific to the Learning Class. The References are:

  • Boucheron, S., G. Lugosi, and P. Massart (2003): Concentration Inequalities Using the Entropy Method Annals of Probability 31 1583-1614
  • Lugosi, G. (2002): Pattern Classification and Learning Theory, in: L. Györ, editor, Principles of Non-parametric Learning Springer Wien 5-62


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    MeasureConcentrationExpectationBound​(double dblConstant, double dblExponent)
    MeasureConcentrationExpectationBound Constructor

  • Method Summary

    Modifier and Type Method Description
    double constant()
    Retrieve the Asymptote Constant
    double exponent()
    Retrieve the Asymptote Exponent
    double lossExpectationUpperBound​(int iSampleSize)
    Compute the Expected Loss Upper Bound between the Sample and the Population for the specified Sample Size

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • MeasureConcentrationExpectationBound

      public MeasureConcentrationExpectationBound​(double dblConstant, double dblExponent) throws java.lang.Exception
      MeasureConcentrationExpectationBound Constructor
      Parameters:
      dblConstant - Asymptote Constant
      dblExponent - Asymptote Exponent
      Throws:
      java.lang.Exception - Thrown if the Constant and/or Exponent is Invalid

  • Method Details

    • constant

      public double constant()
      Retrieve the Asymptote Constant
      Returns:
      The Asymptote Constant

    • exponent

      public double exponent()
      Retrieve the Asymptote Exponent
      Returns:
      The Asymptote Exponent

    • lossExpectationUpperBound

      public double lossExpectationUpperBound​(int iSampleSize) throws java.lang.Exception
      Compute the Expected Loss Upper Bound between the Sample and the Population for the specified Sample Size
      Parameters:
      iSampleSize - The Sample Size
      Returns:
      The Expected Loss Upper Bound the Sample and the Population for the specified Sample Size
      Throws:
      java.lang.Exception - Thrown if the Expected Loss Upper Bound cannot be computed