Review for NeurIPS paper: Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift

This paper proposes a new approach to unsupervised domain adaptation (UDA) under label shift. The idea is a generalized label shift (GLS) assumption where conditional invariance is placed in representation rather than input space. The main contributions include 1) generalizing the information-theoretic lower bound of error to multiple classes; 2) devising generalization bounds in the target domain based on the balanced error rate and conditional error gap; 3) deriving necessary and sufficient conditions for GLS; 4) efficient importance reweighting algorithm for target/source label distributions using the integral probability metric. Overall, all reviewers including myself find the GLS framework interesting, providing an important new approach to UDA that can be flexibility embedded in existing methods. The theoretical foundation is also solid.