Exact inference in Bayesian networks is intractable and has an exponential dependence on the size of the largest clique in the corresponding clique tree, necessitating approximations. Techniques for approximate inference typically use iterative BP in graphs with bounded cluster sizes. We propose an alternative approach for approximate inference based on an incremental build-infer-approximate (IBIA) paradigm. In the build stage of this approach, bounded-clique size partitions are obtained by building the clique tree (CT) incrementally. Nodes are added to the CT as long as the sizes are within a user-specified clique size constraint. Once the clique size constraint is reached, the infer and approximate part of the algorithm finds an approximate CT with lower clique sizes to which new nodes can be added. This step involves exact inference to calibrate the CT and a combination of exact and approximate marginalization for approximation. The approximate CT serves as a starting point for the construction of CT for the next partition. The algorithm returns a forest of calibrated clique trees corresponding to all partitions. We show that our algorithm for incremental construction of clique trees always generates a valid CT and our approximation technique automatically maintains consistency of within-clique beliefs. The queries of interest are prior and posterior singleton marginals and the partition function. More than 500 benchmarks were used to test the method and the results show a significant reduction in error when compared to other approximate methods, with competitive runtimes.

Exact inference of the most probable explanation (MPE) in Bayesian networks is known to be NPcomplete. In this paper, we propose an algorithm for approximate MPE inference that is based on the incremental build-infer-approximate (IBIA) framework. We use this framework to obtain an ordered set of partitions of the Bayesian network and the corresponding max-calibrated clique trees. We show that the maximum belief in the last partition gives an estimate of the probability of the MPE assignment. We propose an iterative algorithm for decoding, in which the subset of variables for which an assignment is obtained is guaranteed to increase in every iteration. There are no issues of convergence, and we do not perform a search for solutions. Even though it is a single shot algorithm, we obtain valid assignments in 100 out of the 117 benchmarks used for testing. The accuracy of our solution is comparable to a branch and bound search in majority of the benchmarks, with competitive run times.To be used for reviewing only.