Combining marginal probability distributions via minimization of weighted sum of Kullback--Leibler divergences

Authors:
Jan Kracík
Affiliations:
Department of Adaptive Systems, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

This paper deals with the problem of combining marginal probability distributions as a means for aggregating pieces of expert information. A novel approach, which takes the combining problem as an analogy of statistical estimation, is proposed and discussed. The combined distribution is then searched as a minimizer of a weighted sum of Kullback-Leibler divergences of the given marginal distributions and corresponding marginals of the searched one. Necessary and sufficient conditions for a distribution to be a minimizer are stated. For discrete random variables an iterative algorithm for approximate solution of the minimization problem is proposed and its convergence is proved.