Adaptive Tree CPDs in Max-Product Belief Propagation

In general, the problem of computing the maximum a posteriori (MAP) assignment in a Bayesian network is computationally intractable. In some cases, such as in tree-structured networks, inference can be done efficiently and exactly. However, there are still practical challenges when trying to do inference in networks containing variables with large cardinalities. In this case, representing and manipulating the local conditional probability densities (CPDs) may be cumbersome with standard techniques. Since one is then typically forced to resort to approximations in the CPD representation, exact inference becomes intractable even in networks with otherwise tractable structure. I present an adaptive CPD representation suitable for max-product inference that is able to adjust its complexity as inference progresses, offering a means of performing exact inference in networks with tractable structure but prohibitively large variable cardinalities. I show results for a series of experiments on Hidden Markov Models, showing that my technique gives a speed improvement over standard Viterbi decoding on networks with large state spaces, then I show that my method is able to successfully perform inference on problems where inference would otherwise be intractable.