Domain invariant learning aims to learn models that extract invariant features over various training domains, resulting in better generalization to unseen target domains. Recently, Bayesian Neural Networks have achieved promising results in domain invariant learning, but most works concentrate on aligning features distributions rather than parameter distributions. Inspired by the principle of Bayesian Neural Network, we attempt to directly learn the domain invariant posterior distribution of network parameters. We first propose a theorem to show that the invariant posterior of parameters can be implicitly inferred by aggregating posteriors on different training domains. Our assumption is more relaxed and allows us to extract more domain invariant information. We also propose a simple yet effective method, named PosTerior Generalization (PTG), that can be used to estimate the invariant parameter distribution. PTG fully exploits variational inference to approximate parameter distributions, including the invariant posterior and the posteriors on training domains. Furthermore, we develop a lite version of PTG for widespread applications. PTG shows competitive performance on various domain generalization benchmarks on DomainBed. Additionally, PTG can use any existing domain generalization methods as its prior, and combined with previous state-of-the-art method the performance can be further improved. Code will be made public.

通过聚合不同训练领域上的后验，本研究提出了一个引理来隐式推断参数的不变后验分布，并使用 Posterior Generalization (PTG) 方法来估计不变参数分布，该方法基于变分推断近似参数分布，包括不变后验和训练领域的后验。研究结果表明，PTG 在 DomainBed 上的各种领域泛化基准测试上表现出竞争性能，且可与现有的领域泛化方法相结合以进一步提高性能。

基于贝叶斯的领域不变学习通过参数分布的后验概括