Inducing Triplet Regions for Amortized Kikuchi Learning in Discrete Bayesian Network Models

Learning parameters in large discrete Bayesian networks (BNs) from massive incomplete data is challenging due to the high computational cost of repeatedly estimating joint marginals. Standard ELBO-based amortization, such as amortized variational inference (VI), scales well but suffers from restrictive posterior factorization assumptions. To overcome this, we introduce $\underline{T}$riplet $\underline{R}$egion Induction-Constrained $\underline{N}$eural $\underline{K}$ikuchi Learning (TRNK), a non-ELBO framework grounded in Kikuchi free energy and region graph approximations. TRNK captures higher-order variable interactions for improved accuracy and scalable amortized learning. By leveraging BN structural and factor information, it identifies effective triplet base regions and induces higher-order regions to enhance approximation fidelity and provide orthogonality regularized region interactions. Under these region constraints, TRNK trains an evidence-conditioned deep neural network to produce overlap-consistent region beliefs for each partially observed instance, amortizing inference overhead across the entire dataset. Empirical results show that TRNK significantly outperforms amortized VI and approximate EM baselines in accuracy and efficiency. Furthermore, our region induction algorithm surpasses Bethe and other well-established region-graph alternatives on most benchmarks.