  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 floating point number. In this paper, we present three key
extensions of RC. First, we modify the algorithm so it applies to more general
factorization 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
requirmenets 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 first MAP algorithm allowing a smooth time-space
tradeoff. A key advantage of 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 significant savings in
ceratain cases.
