Credal Networks under Maximum Entropy
This work addresses a theoretical problem in probabilistic graphical models for researchers in AI and statistics, but it appears incremental as it extends existing maximum entropy principles to sequential models for credal networks.
The paper tackles the problem of selecting a unique joint probability distribution from the set specified by a credal network by applying the principle of maximum entropy, showing that sequential maximum entropy models coincide with the unique joint distribution for general Bayesian networks and can be applied to credal networks through local entropy maximizations.
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.