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.
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