Network Ranking With Bethe Pseudomarginals

Network structure often contains information that can be useful for ranking algorithms. We incorporate network structure by formulating ranking as marginal inference in a Markov random field (MRF). Though inference is generally NP-hard, we apply a recently-developed polynomial-time approximation scheme (PTAS) to infer Bethe pseudomarginals. As a case study, we investigate the problem of ranking failing transformers that are physically connected in a network. Compared to independent score-based ranking, the current state of the art, we show superior ranking results. We conclude by discussing an empirical phenomenon of critical parameter regions, with implications for new algorithms.