Identifying Latent Causal Content for Multi-Source Domain Adaptation

Multi-source domain adaptation (MSDA) learns to predict the labels in target domain data, under the setting that data from multiple source domains are labelled and data from the target domain are unlabelled. Most methods for this task focus on learning invariant representations across domains. However, their success relies heavily on the assumption that the label distribution remains consistent across domains, which may not hold in general real-world problems. In this paper, we propose a new and more flexible assumption, termed \textit{latent covariate shift}, where a latent content variable $\mathbf{z}_c$ and a latent style variable $\mathbf{z}_s$ are introduced in the generative process, with the marginal distribution of $\mathbf{z}_c$ changing across domains and the conditional distribution of the label given $\mathbf{z}_c$ remaining invariant across domains. We show that although (completely) identifying the proposed latent causal model is challenging, the latent content variable can be identified up to scaling by using its dependence with labels from source domains, together with the identifiability conditions of nonlinear ICA. This motivates us to propose a novel method for MSDA, which learns the invariant label distribution conditional on the latent content variable, instead of learning invariant representations. Empirical evaluation on simulation and real data demonstrates the effectiveness of the proposed method.