|
|
Cross-entropy based combination of discrete probability distributions for distributed decision making
Sečkárová, Vladimíra ; Kárný, Miroslav (advisor) ; Jurečková, Jana (referee) ; Janžura, Martin (referee)
Dissertation abstract Title: Cross-entropy based combination of discrete probability distributions for distributed de- cision making Author: Vladimíra Sečkárová Author's email: seckarov@karlin.mff.cuni.cz Department: Department of Probability and Mathematical Statistics Faculty of Mathematics and Physics, Charles University in Prague Supervisor: Ing. Miroslav Kárný, DrSc., The Institute of Information Theory and Automation of the Czech Academy of Sciences Supervisor's email: school@utia.cas.cz Abstract: In this work we propose a systematic way to combine discrete probability distributions based on decision making theory and theory of information, namely the cross-entropy (also known as the Kullback-Leibler (KL) divergence). The optimal combination is a probability mass function minimizing the conditional expected KL-divergence. The ex- pectation is taken with respect to a probability density function also minimizing the KL divergence under problem-reflecting constraints. Although the combination is derived for the case when sources provided probabilistic type of information on the common support, it can applied to other types of given information by proposed transformation and/or extension. The discussion regarding proposed combining and sequential processing of available data, duplicate data, influence...
|
|
|
O významu entropie
Janžura, Martin
The aim of the paper consists in demonstrating the relevance of the fundamental information-theoretic concepts, namely the entropy and the I-divergence, for both the statistical inference and the limit theorems of probability theory.
|
|
|
O jednom přibližném řešení marginálního problému
Janžura, Martin
With the aid of the Maximum Entropy principle, a solution to the marginal problem is obtained in a form of parametric exponential (Gibbs-Markov) distribution. The unknown parameters can be calculated by an optimization procedure that agrees with the maximum likelihood estimate but it is numerically hardly feasible for highly dimensional systems. A numerically easily feasible solution can be obtained by the algebraic Möbius formula. The formula, unfortunately, involves terms that are not directly available but can be approximated. And the main aim of the present paper consists in this approximation.
|
|
| |
|
| |
|
|
Abstracts of the 24th European Meeting of Statisticians & 14th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes
Janžura, Martin ; Mikosch, T.
This issue contains short summariesof the contributed and invited papers, as well as posters, accepted for presentation at the 24th European Meeting of Statisticians, jointly held with the 14th Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Prague, 19-23 August, 2002.
|
|
| |
|
| |
|
| |
|
| |
guest ::
