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 * n^a, where n is the Size of the Sample, and 'C' and 'a' are Constants specific to the Learning Class. The References are: 1) Lugosi, G. (2002): Pattern Classification and Learning Theory, in: L. Györ, editor, Principles of Non-parametric Learning, 5-62, Springer, Wien. 2) Boucheron, S., G. Lugosi, and P. Massart (2003): Concentration Inequalities Using the Entropy Method, Annals of Probability, 31, 1583-1614.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
MeasureConcentrationExpectationBound(double dblConstant, double dblExponent) MeasureConcentrationExpectationBound Constructor

Method Summary

Modifier and Type	Method and 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 Detail

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 Detail

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