HOP-MAP: Efficient Message Passing with High Order Potentials

There is a growing interest in building probabilistic models with high order potentials (HOPs), or interactions, among discrete variables. Message passing inference in such models generally takes time exponential in the size of the interaction, but in some cases maximum a posteriori (MAP) inference can be carried out efficiently. We build upon such results, introducing two new classes, including composite HOPs that allow us to flexibly combine tractable HOPs using simple logical switching rules. We present efficient message update algorithms for the new HOPs, and we improve upon the efficiency of message updates for a general class of existing HOPs. Importantly, we present both new and existing HOPs in a common representation; performing inference with any combination of these HOPs requires no change of representations or new derivations.