Bayesian Inference from Hans Bathe

3 function files for Bethe, Variational Bayes and Gibb's Sampling and a demo

The Matlab package contains three inference routines for the Bayesian overlapping graph clustering model described in the paper, together with one demo script that generates synthetic data and runs all methods. The file bethe_hurdle_overlap.m implements a practical Bethe-style solver for the diagonal hurdle model. It uses binary message passing for each cluster, updates singleton inclusion probabilities, and alternates these updates with simple parameter refinement for the cluster weights, prevalence terms, and global bias. This is the main deterministic method.

The file vb_hurdle_overlap.m implements a mean-field variational Bayes baseline. It maintains Bernoulli membership probabilities for every node-cluster pair, updates Beta-type prevalence parameters, and refines the continuous parameters through a bounded surrogate objective. This version is faster and simpler, but less expressive than Bethe.

The file gs_hurdle_overlap.m provides a stochastic reference method. For simplicity and portability, it is implemented as a self-contained Metropolis-within-Gibbs sampler rather than relying on an external Pólya–Gamma package. It samples latent memberships and updates model parameters iteratively to approximate posterior inclusion probabilities.

Finally, demo_bayesian_overlap.m creates a small synthetic weighted graph with overlapping memberships, runs Bethe, VB, and GS, reports runtimes and summary statistics, and produces a quick side-by-side comparison of the inferred posterior membership probabilities.