  Multi-Source Domain Adaptation (MSDA) focuses on transferring the knowledge
from multiple source domains to the target domain, which is a more practical
and challenging problem compared to the conventional single-source domain
adaptation. In this problem, it is essential to utilize the labeled source data
and the unlabeled target data to approach the conditional distribution of
semantic label on target domain, which requires the joint modeling across
different domains and also an effective domain combination scheme. The
graphical structure among different domains is useful to tackle these
challenges, in which the interdependency among various instances/categories can
be effectively modeled. In this work, we propose two types of graphical
models,i.e. Conditional Random Field for MSDA (CRF-MSDA) and Markov Random
Field for MSDA (MRF-MSDA), for cross-domain joint modeling and learnable domain
combination. In a nutshell, given an observation set composed of a query sample
and the semantic prototypes i.e. representative category embeddings) on various
domains, the CRF-MSDA model seeks to learn the joint distribution of labels
conditioned on the observations. We attain this goal by constructing a
relational graph over all observations and conducting local message passing on
it. By comparison, MRF-MSDA aims to model the joint distribution of
observations over different Markov networks via an energy-based formulation,
and it can naturally perform label prediction by summing the joint likelihoods
over several specific networks. Compared to the CRF-MSDA counterpart, the
MRF-MSDA model is more expressive and possesses lower computational cost. We
evaluate these two models on four standard benchmark data sets of MSDA with
distinct domain shift and data complexity, and both models achieve superior
performance over existing methods on all benchmarks.
