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Domain invariant learning aims to learn models that extract invariantfeatures over various training domains, resulting in better generalization tounseen target domains. Recently, Bayesian Neural Networks have achievedpromising results in domain invariant learning, but most works concentrate onaligning features distributions rather than parameter distributions. Inspiredby the principle of Bayesian Neural Network, we attempt to directly learn thedomain invariant posterior distribution of network parameters. We first proposea theorem to show that the invariant posterior of parameters can be implicitlyinferred by aggregating posteriors on different training domains. Ourassumption is more relaxed and allows us to extract more domain invariantinformation. We also propose a simple yet effective method, named PosTeriorGeneralization (PTG), that can be used to estimate the invariant parameterdistribution. PTG fully exploits variational inference to approximate parameterdistributions, including the invariant posterior and the posteriors on trainingdomains. Furthermore, we develop a lite version of PTG for widespreadapplications. PTG shows competitive performance on various domaingeneralization benchmarks on DomainBed. Additionally, PTG can use any existingdomain generalization methods as its prior, and combined with previousstate-of-the-art method the performance can be further improved. Code will bemade public.

Bayesian Domain Invariant Learning via Posterior Generalization of Parameter Distributions