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

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... ding 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.