D-Separation and computation of probability distributions in Bayesian networks
Consider a family (X(i))(i is an element of I) of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily (X(a))(a is an element of S) (respectively the probability distribution of (X(b))(b is an element of(S) over bar), where (S) over bar = I - S, conditional on (X(a))(a is an element of S)). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of (s) over bar); these partial results are then put together as a final product. In computing the probability distribution over (X(a))(a is an element of S), this procedure results in the production of a structure of level two Bayesian network structure for S.
d-separation bayesian networks level two bayesian networks close descendants