  As a crucial step toward real-world learning scenarios with changing
environments, dataset shift theory and invariant representation learning
algorithm have been extensively studied to relax the identical distribution
assumption in classical learning setting. Among the different assumptions on
the essential of shifting distributions, generalized label shift (GLS) is the
latest developed one which shows great potential to deal with the complex
factors within the shift. In this paper, we aim to explore the limitations of
current dataset shift theory and algorithm, and further provide new insights by
presenting a comprehensive understanding of GLS. From theoretical aspect, two
informative generalization bounds are derived, and the GLS learner is proved to
be sufficiently close to optimal target model from the Bayesian perspective.
The main results show the insufficiency of invariant representation learning,
and prove the sufficiency and necessity of GLS correction for generalization,
which provide theoretical supports and innovations for exploring generalizable
model under dataset shift. From methodological aspect, we provide a unified
view of existing shift correction frameworks, and propose a kernel
embedding-based correction algorithm (KECA) to minimize the generalization
error and achieve successful knowledge transfer. Both theoretical results and
extensive experiment evaluations demonstrate the sufficiency and necessity of
GLS correction for addressing dataset shift and the superiority of proposed
algorithm.
