Bayesian Domain Adaptation with Gaussian Mixture Domain-Indexing

Recent methods are proposed to improve performance of domain adaptation by inferring domain index under an adversarial variational bayesian framework, where domain index is unavailable. However, existing methods typically assume that the global domain indices are sampled from a vanilla gaussian prior, overlooking the inherent structures among different domains.To address this challenge, we propose a Bayesian Domain Adaptation with Gaussian Mixture Domain-Indexing(GMDI) algorithm. GMDI employs a Gaussian Mixture Model for domain indices, with the number of component distributions in the "domain-themes'' space adaptively determined by a Chinese Restaurant Process. By dynamically adjusting the mixtures at the domain indices level, GMDI significantly improves domain adaptation performance. Our theoretical analysis demonstrates that GMDI achieves a more stringent evidence lower bound, closer to the log-likelihood. For classification, GMDI outperforms all approaches, and surpasses the state-of-the-art method, VDI, by up to 3.4%, reaching 99.3%. For regression, GMDI reduces MSE by up to 21% (from 3.160 to 2.493), achieving the lowest errors among all methods.