A Formalization of Generalized Probabilistic Reasoning and Its Procedure on Junction Trees

T. Matsushima and S. Hirasawa (Japan)

Keywords

Probabilistic reasoning, Distribution evidence, Junction Tree, KullbackLibler information, Posterior distribution.

Abstract

Many kinds of reasoning methods have been proposed for probabilistic reasoning given distribution evidence. Previ ous research only proposed methods of reasoning, but it did not prove the justification of the methods. The justification of the methods has only been given by qualitative and intu itive explanation in the previous research. We think the lack of mathematical justification is caused by a lack of math ematical definition of the distribution evidence reasoning problem. First, we define the distribution evidence reason ing by mathematical formulas. From the definition, we can show that the defined generalized probabilistic reasoning is solved by the minimization of Kullback-Leibler(K-L) in formation under marginal constraints. We also show that the Iterative Scaling Procedure(ISP) is applied to the rea soning, i.e., the minimization problem. We propose an ef ficient propagation algorithm, which is based on the pro cedure mentioned above, for the generalized probabilistic reasoning on Junction trees. Both the space and the time complexities of the proposed algorithms are lower than that of the previous research.

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