Hypergraphs as a mean of discovering the dependence structure of a discrete multivariate probability distribution

摘要: Most everyday reasoning and decision making is based on uncertain premises. The premises or attributes, which we must take into consideration, are random variables, therefore often have to deal with a high dimensional multivariate vector. A vector can be represented graphically as Markov network. Usually the structure of network unknown. In this paper construct special type junction trees, in order obtain good approximations real probability distribution. These trees capable revealing some conditional independences We already introduced concept t-cherry tree (E. Kovacs T. Szantai Proceedings IFIP/IIASA//GAMM Workshop Coping Uncertainty, 2010), graph structure. This approximation uses only two three marginal distributions. Now use k-th also called simplex multitrees introduce tree. prove that gives best among family k-width trees. Then give method starting from constructs (k+1)-th at least approximation. last part present numerical results possible applications.