GNN-Guided Block Selection in Gibbs MCMC

Exact inference in large Bayesian Networks (BNs) is computationally intractable, limiting its practical application.Markov Chain Monte Carlo (MCMC) methods like Gibbs sampling offer a scalable alternative but can be arbitrarily slowed by highly coupled variables--- addressable by jointly sampling some variables as a block. We propose an automated block detection method to amortise inference time: training a Graph Neural Network (GNN) to propose blocks directly from the BN structure.We further introduce a novel coupling heuristic based on the Markov chain's spectral gap, which we show can be more robust than existing heuristics.Our GNN, trained on a dataset of small, randomly generated BNs, generalizes well to larger networks, accelerating MCMC sample efficiency in our experiments.