Domain Adaptation with Factorizable Joint Shift

Existing domain adaptation (DA) usually assumes the domain shift comes from either the covariates or the labels. However, in real-world applications, samples selected from different domains could have biases in both the covariates and the labels. In this paper, we propose a new assumption, Factorizable Joint Shift (FJS), to handle the co-existence of sampling bias in covariates and labels. Although allowing for the shift from both sides, FJS assumes the independence of the bias between the two factors. We provide theoretical and empirical understandings about when FJS degenerates to prior assumptions and when it is necessary. We further propose Joint Importance Aligning (JIA), a discriminative learning objective to obtain joint importance estimators for both supervised and unsupervised domain adaptation. Our method can be seamlessly incorporated with existing domain adaptation algorithms for better importance estimation and weighting on the training data. Experiments on a synthetic dataset demonstrate the advantage of our method.