Exploiting independencies to compute semigraphoid and graphoid structures

Authors:
Marco Baioletti;Giuseppe Busanello;Barbara Vantaggi
Affiliations:
Dip. Matematica e Informatica, Università di Perugia, Italy;Dip. Scienze di Base e Applicate per l'Ingegneria, Università “La Sapienza”, Roma, Italy;Dip. Scienze di Base e Applicate per l'Ingegneria, Università “La Sapienza”, Roma, Italy
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

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.