Belief Updating by Enumerating High-Probability Independence-based Assignments

Independence-based (IB) assignments to Bayesian belief networks were originally pro­ posed as abductive explanations. IB as­ signments assign fewer variables in abduc­ tive explanations than do schemes assign­ ing values to all evidentially supported vari­ ables. We use IB assignments to approxi­ mate marginal probabilities in Bayesian be­ lief networks. Recent work in belief up­ dating for Bayes networks attempts to ap­ proximate posterior probabilities by finding a small number of the highest probability com­ plete (or perhaps evidentially supported) as­ signments. Under certain assumptions, the probability mass in the union of these assign­ ments is sufficient to obtain a good approx­ imation. Such methods are especially use­ ful for highly-connected networks, where the maximum clique size or the cutset size make the standard algorithms intractable. Since IB assignments contain fewer assigned variables, the probability mass in each as­ signment is greater than in the respective complete assignment. Thus, fewer IB assign­ ments are sufficient, and a good approxima­ tion can be obtained more efficiently. IB as­ signments can be used for efficiently approxi­ mating posterior node probabilities even in cases which do not obey the rather strict skewness assumptions used in previous re­ search. Two algorithms for finding the high probability IB assignments are suggested: one by doing a best-first heuristic search, and another by special-purpose integer linear pro­ gramming. Experimental results show that this approach is feasible for highly connected belief networks.