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An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

Published online by Cambridge University Press:  14 July 2016

Claudine Robert
Claudine Robert*
Affiliation:
Faculté de Médecine de Grenoble
*
∗Postal address: Laboratoire de Biostatistiques, Faculté de Médecine, Domaine de la Merci, 38700 La Tronche, France.
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Abstract

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

Keywords

KULLBACK ENTROPYLARGE DEVIATIONSMARKOV RANDOM FIELDSNEURAL NETWORKSMULTIVARIATE ANALYSIS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 303 - 313
Copyright
Copyright © Applied Probability Trust 1990 

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