Conditionally Partially Exchangeable Partitions for Dynamic Networks

In network analysis, understanding the dynamics of evolving networks is often of paramount importance. We introduce and study a novel class of models to detect evolving communities underlying dynamic network data. The methods build upon the established literature on stochastic block models and extend it to accommodate temporal evolution. The cornerstone of our approach is the interplay of random partitions induced by hierarchical normalized completely random measures and the assumption of conditional partial exchangeability, a recently introduced modeling principle for capturing the dynamic of evolving partitions within a Bayesian framework. Our methodology effectively addresses the limitations inherent in traditional static community detection methods, and in contrast with other dynamic extensions of the classical stochastic block models, provides flexibility and built-in uncertainty quantification, while inducing a form of distributional invariance coherent with a time-evolving clustering scheme.