Credal Networks under Maximum Entropy

We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution of a Bayesian tree coincides with the maximum entropy model of its conditional distributions. This result, however, does not hold anymore for general Bayesian networks. We thus present a new kind of maximum entropy models, which are computed sequentially. We then show that for all general Bayesian networks, the sequential maximum entropy model coincides with the unique joint distribution. Moreover, we apply the new principle of sequential maximum entropy to interval Bayesian networks and more generally to credal networks. We especially show that this application is equivalent to a number of small local entropy maximizations. 1Institut und Ludwig Wittgenstein Labor für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, A-1040 Vienna, Austria. E-mail: [email protected]. Acknowledgements: I am very grateful to Fabio Gagliardi Cozman, Gabriele Kern-Isberner, and Richard Neapolitan for their useful comments on an earlier version of this paper. This work has been partially supported by a DFG grant and the Austrian Science Fund Project N Z29-INF. Copyright c 2000 by the authors 2 INFSYS RR 1843-00-03