On the Approximation of a Discrete Multivariate Probability Distribution Using the New Concept of t-Cherry Junction Tree

Abstract

Most everyday reasoning and decision making is based on uncertain premises. The premises or attributes, which we must take into consideration, are random variables, so that we often have to deal with a high dimensional discrete multivariate random vector. We are going to construct an approximation of a high dimensional probability distribution that is based on the dependence structure between the random variables and on a special clustering of the graph describing this structure. Our method uses just one-, two- and three-dimensional marginal probability distributions. We give a formula that expresses how well the constructed approximation fits to the real probability distribution. We then prove that every time there exists a probability distribution constructed this way, that fits to reality at least as well as the approximation constructed from the Chow–Liu dependence tree. In the last part we give some examples that show how efficient is our approximation in application areas like pattern recognition and feature selection.