Exploiting Independencies to Compute Semigraphoid and Graphoid Structures

We deal with conditional independencies, which have a fundamental role in probability and multivariate statistics. The structure of probabilistic independencies is described by semigraphoids or, for strictly positive probabilities, by graphoids. In this paper, given a set of independencies compatible with a probability, the attention is focused toward the problem of computing efficiently the closure with respect to the semigraphoid and graphoid structures. We introduce a suitable notion of projection in order to provide a new method which properly uses conditional independence statements.