A Theory of Label Propagation for Subpopulation Shift

The recent success of supervised deep learning is built upon two crucial cornerstones: That the training and test data are drawn from an identical distribution, and that representative labeled data are available for training. However, in real-world applications, labeled data drawn from the same distribution as test data are usually unavailable. Domain adaptation (Quionero-Candela et al., 2009; Saenko et al., 2010) suggests a way to overcome this challenge by transferring the knowledge of labeled data from a source domain to the target domain. Without further assumptions, the transferability of information is not possible. Existing theoretical works have investigated suitable assumptions that can provide learning guarantees. Many of the works are based on the covariate shift assumption (Heckman, 1979; Shimodaira, 2000), which states that the conditional distribution of the labels (given the input x) is invariant across domains, i.e., p