1|Functions on probabilistic graphical models

Probabilistic graphical models are tools that are used to represent the probability distribution of a vector of random variables X = (X₁, ..., X_N). In this paper we introduce functions f(x₁, ..., x_N) defined over the given vector. These functions also are random variables. The main result of the paper is an algorithm for finding the expected value and other moments for some classes of f(x₁, ..., x_N). The possible applications of that algorithm are discussed. Specifically, we use it to analyze the entropy of X and to compute the relative entropy of two probability distributions of the same vector X. Finally, open problems and possible topics of future researches are discussed.