Multi-Source Domain Adaptation: A Causal View

Abstract

This paper is concerned with the problem of domain adaptation with multiple sources from a causal point of view. In particular, we use causal models to represent the relationship between the features X and class label Y , and consider possible situations where different modules of the causal model change with the domain. In each situation, we investigate what knowledge is appropriate to transfer and find the optimal target-domain hypothesis. This gives an intuitive interpretation of the assumptions underlying certain previous methods and motivates new ones. We finally focus on the case where Y is the cause for X with changing PY and PX|Y , that is, PY and PX|Y change independently across domains. Under appropriate assumptions, the availability of multiple source domains allows a natural way to reconstruct the conditional distribution on the target domain; we propose to model PX|Y (the process to generate effect X from cause Y ) on the target domain as a linear mixture of those on source domains, and estimate all involved parameters by matching the target-domain feature distribution. Experimental results on both synthetic and real-world data verify our theoretical results.