  This paper is concerned with data-driven unsupervised domain adaptation,
where it is unknown in advance how the joint distribution changes across
domains, i.e., what factors or modules of the data distribution remain
invariant or change across domains. To develop an automated way of domain
adaptation with multiple source domains, we propose to use a graphical model as
a compact way to encode the change property of the joint distribution, which
can be learned from data, and then view domain adaptation as a problem of
Bayesian inference on the graphical models. Such a graphical model
distinguishes between constant and varied modules of the distribution and
specifies the properties of the changes across domains, which serves as prior
knowledge of the changing modules for the purpose of deriving the posterior of
the target variable $Y$ in the target domain. This provides an end-to-end
framework of domain adaptation, in which additional knowledge about how the
joint distribution changes, if available, can be directly incorporated to
improve the graphical representation. We discuss how causality-based domain
adaptation can be put under this umbrella. Experimental results on both
synthetic and real data demonstrate the efficacy of the proposed framework for
domain adaptation. The code is available at https://github.com/mgong2/DA_Infer .
