Auditing Bayesian Graph Alignment: Diagnostic Comparisons and Reference Failure

Melika Gorgi, Kourosh Mirsohi

Bayesian graph alignment estimates correspondence probabilities, but convergence of an alignment-score trace need not imply accurate correspondence marginals. We audit this gap on 240 new exact graph pairs from four source families, 240 larger pairs with 20-100 vertices, and a separate 60-case exact implementation check. Under an explicit edge-flip likelihood, we compare three samplers and score, marginal, indicator, categorical, and classifier-based diagnostics. Marginal disagreement improves error discrimination over score R-hat for the exact informed sampler, but its improvement for vanilla local sampling is uncertain. Assignment-based R* and short indicator panels are competitive; no diagnostic dominates across samplers and endpoints. At larger sizes, diagnostics predict subsequent marginal changes, not posterior error, and classification performance depends on the drift threshold. Disjoint-window and held-out-chain checks attenuate but preserve positive associations. Only 22 of 240 original reference sets pass an agreement screen. On forty failure-selected cases, eightfold SMC particle escalation does not resolve disagreement, whereas additional rejuvenation helps. Longer…