Any-Space Probabilistic Inference

We have recently introduced an any{space algorithm for exact inference in Bayesian networks, called Recursive Conditioning, rc, which allows one to trade space with time at increments of X-bytes, where X is the number of bytes needed to cache a oating point number. In this paper, we present three key extensions of rc. First, we modify the algorithm so it applies to more general factorizations of probability distributions, including (but not limited to) Bayesian network factorizations. Second, we present a forgetting mechanism which reduces the space requirements of rc considerably and then compare such requirements with those of variable elimination on a number of realistic networks, showing orders of magnitude improvements in certain cases. Third, we present a version of rc for computing maximum a posteriori hypotheses (MAP), which turns out to be the rst MAP algorithm allowing a smooth time-space tradeo. A key advantage of the presented MAP algorithm is that it does not have to start from scratch each time a new query is presented, but can reuse some of its computations across multiple queries, leading to signicant savings in certain cases.