A Hierarchical Bayesian Approach for Non-Markovian Evolving Domain Generalization

Evolving Domain Generalization (EDG) considers learning from a sequence of domains whose underlying distributions change over time, reflecting the non-stationary nature of many real-world learning environments. Recent structure-aware methods model this evolution by separating static task factors from dynamic domain factors that evolve across domains. However, their autoregressive latents impose a first-order Markov assumption, tying the current domain state to its immediate predecessor, which is restrictive when the dynamics have persistent temporal structure or abrupt transitions. We propose a hierarchical state-space model (SSM) formulation that introduces regime latents governed by change-point variables. Moreover, the formulation naturally casts EDG as a sequential Bayesian inference problem, which we leverage Rao-Blackwellized particle filter (RBPF) to approximate the posterior over the latents. Experiments on synthetic benchmarks containing both gradual and abrupt distribution shifts and real-world evolving domain benchmarks show that the proposed approach improves mean target-domain accuracy by 17.06 points over the strongest baseline on the original streams and by 15.74 points on the abrupt variants. An ablation shows that the change-point latent contributes 12.47 points of abrupt-stream accuracy. These results highlight the value of hierarchical sequential Bayesian inference for modeling complex dynamics in evolving domains.