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.

该论文研究了数据集转移理论和不变表示学习算法，提出了广义标签转移（GLS）理论，并通过推导信息量化的一般化界限和基于贝叶斯观点证明了 GLS 学习器与最优目标模型的足够接近性；同时提出了基于内核嵌入的校正算法（KECA），通过最小化泛化误差和成功的知识转移实现了对数据集转移的校正，证明了 GLS 校正处理数据集转移的充分性和必要性。