Making Maximum Entropy Computations Easier

This paper presents a new way to compute the probability distribution with maximum entropy satisfying a set of constraints. Unlike previous approaches , our method is integrated with the planning of data collection and tabulation. We show how adding constraints and performing the associated additional tabulations can substantially speed up computation by replacing the usual iterative techniques with a straightforward computation. These extra constraints are shown to correspond to the intermediate tables used in Cheeseman's method. We also show that the class of constraint graphs that our method handles is a proper generalization of Pearl's singly-connected networks. An open problem is to determine a minimal set of constraints necessary to make a hypergraph acyclic. We conjecture that this problem is NP-complete, and discuss heuristics to approximate the optimal solution.