IBIA: Bayesian Inference via Incremental Build-Infer-Approximate operations on Clique Trees

Abstract

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.

MPE inference using an Incremental Build-Infer-Approximate Paradigm

“…The IBIA framework has been used to infer the partition function and the prior and posterior marginal probabilities of non-evidence variables in Bathla and Vasudevan [2022].…”

“…Step 1: Incremental Build: The CTF can be built incrementally using either of the algorithms detailed in Flores, Gámez, and Olesen [2002], Bathla and Vasudevan [2022]. We use the approach described in Bathla and Vasudevan [2022] since it works directly with the clique tree model and eliminates the need for computation of any other intermediate representation. Typically, it chooses a smaller graph chosen for re-triangulation than Flores et al [2002].…”

“…Therefore, these are required for building the next partition. We adopt a similar approximation methodology as suggested in Bathla and Vasudevan [2022] to reduce the clique sizes. We also denote the calibrated tree obtained after BP as CT F in and the approximated CTF as CT F a .…”

“…The connection between the solutions obtained using two methods is explored in Bauer et al [2019] In this work, we propose a different approach for MPE inference. Our method is based on an Incremental Build-Infer-Approximate paradigm (IBIA) that returns a set of bounded clique size partitions of the BN along with the calibrated forest of of clique trees (CTFs) corresponding to each partition [Bathla and Vasudevan, 2022]. Instead of the sum-product calibration used in Bathla and Vasudevan [2022], we use a max-product calibration along with suitable modifications to the Approximate step.…”

“…Our method is based on an Incremental Build-Infer-Approximate paradigm (IBIA) that returns a set of bounded clique size partitions of the BN along with the calibrated forest of of clique trees (CTFs) corresponding to each partition [Bathla and Vasudevan, 2022]. Instead of the sum-product calibration used in Bathla and Vasudevan [2022], we use a max-product calibration along with suitable modifications to the Approximate step. Based on this, we propose a single search algorithm for MPE inference with the following features.…”