Previous studies have shown that leveraging domain index can significantly boost domain adaptation performance (arXiv:2007.01807, arXiv:2202.03628). However, such domain indices are not always available. To address this challenge, we first provide a formal definition of domain index from the probabilistic perspective, and then propose an adversarial variational Bayesian framework that infers domain indices from multi-domain data, thereby providing additional insight on domain relations and improving domain adaptation performance. Our theoretical analysis shows that our adversarial variational Bayesian framework finds the optimal domain index at equilibrium. Empirical results on both synthetic and real data verify that our model can produce interpretable domain indices which enable us to achieve superior performance compared to state-of-the-art domain adaptation methods. Code is available at https://github.com/Wang-ML-Lab/VDI.

翻译：先前研究表明，利用域索引可显著提升领域自适应性能（arXiv:2007.01807, arXiv:2202.03628）。然而，此类域索引并非总是可用。针对这一挑战，我们首先从概率视角给出域索引的形式化定义，进而提出一种对抗变分贝叶斯框架，该框架能够从多领域数据中推断域索引，从而提供对领域关系的额外洞察并改进领域自适应性能。理论分析表明，我们的对抗变分贝叶斯框架可在均衡状态下获得最优域索引。在合成数据与真实数据上的实验结果均验证了，该模型能生成可解释的域索引，并据此实现优于现有主流领域自适应方法的性能。代码已开源至https://github.com/Wang-ML-Lab/VDI。