Performing Bayesian Network Inference Using Amortized Region Approximation with Graph Factorization

Exact inference for large, directed graphical models, also known as Bayesian networks (BNs), can be intractable the space complexity grows exponentially in tree-width of model. Approximate inference, such generalized belief propagation (GBP), is used instead. GBP treats Bethe/Kikuchi energy function optimization problem. The solution found using iterative message passing, which inefficient and convergent problematic. Recent progress on amortized technique an attractive alternative that optimize (deep) neural networks, requiring no passing. Despite being efficient, applied to undirected models with specific structures factors, guarantee approximation quality. This because defined by a region (or factor) graph ad hoc difficult construct ensure sensible approximations. paper proposes new algorithm BN efficient inference. proposed composed following: (i) pairwise conversion (PWC) converts all conditional probability distributions into factors facilitate constructions; (ii) following PWC, improved loop structured (LSRG) was derived generate valid satisfying desired regional properties; (iii) PWC-LSRG directly Empirical studies show practical use significantly improves convergence efficiency compared conventional algorithms.