Approximate inference of marginals using the IBIA framework
This work addresses the slow convergence of iterative message-passing methods in probabilistic graphical models, offering a faster alternative for researchers and practitioners in machine learning and AI.
The paper tackles the problem of approximate marginal inference in probabilistic graphical models, which is intractable for exact methods, by proposing a new algorithm based on the incremental build-infer-approximate (IBIA) framework. Results on benchmark sets show that the method achieves better or comparable accuracy than existing variational and sampling methods, with smaller runtimes.
Exact inference of marginals in probabilistic graphical models (PGM) is known to be intractable, necessitating the use of approximate methods. Most of the existing variational techniques perform iterative message passing in loopy graphs which is slow to converge for many benchmarks. In this paper, we propose a new algorithm for marginal inference that is based on the incremental build-infer-approximate (IBIA) paradigm. Our algorithm converts the PGM into a sequence of linked clique tree forests (SLCTF) with bounded clique sizes, and then uses a heuristic belief update algorithm to infer the marginals. For the special case of Bayesian networks, we show that if the incremental build step in IBIA uses the topological order of variables then (a) the prior marginals are consistent in all CTFs in the SLCTF and (b) the posterior marginals are consistent once all evidence variables are added to the SLCTF. In our approach, the belief propagation step is non-iterative and the accuracy-complexity trade-off is controlled using user-defined clique size bounds. Results for several benchmark sets from recent UAI competitions show that our method gives either better or comparable accuracy than existing variational and sampling based methods, with smaller runtimes.