Exploiting Uniform Assignments in First-Order MPE

The MPE (Most Probable Explanation) query plays an important role in probabilistic inference. MPE solution algorithms for probabilistic relational models essentially adapt existing belief assessment method, replacing summation with maximization. But the rich structure and symmetries captured by relational models together with the properties of the maximization operator offer an opportunity for additional simplification with potentially significant computational ramifications. Specifically, these models often have groups of variables that define symmetric distributions over some population of formulas. The maximizing choice for different elements of this group is the same. If we can realize this ahead of time, we can significantly reduce the size of the model by eliminating a potentially significant portion of random variables. This paper defines the notion of uniformly assigned and partially uniformly assigned sets of variables, shows how one can recognize these sets efficiently, and how the model can be greatly simplified once we recognize them, with little computational effort. We demonstrate the effectiveness of these ideas empirically on a number of models.