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...
