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。

当不变表示学习遇到标签漂移：不充分性和理论洞察

When Invariant Representation Learning Meets Label Shift: Insufficiency  and Theoretical Insights

An open scientific challenge is how to classify events with reliable measures
of uncertainty, when we have a mechanistic model of the data-generating process
but the distribution over both labels and latent nuisance parameters is
different between train and target data. We refer to this type of
distributional shift as generalized label shift (GLS). Direct classification
using observed data $\mathbf{X}$ as covariates leads to biased predictions and
invalid uncertainty estimates of labels $Y$. We overcome these biases by
proposing a new method for robust uncertainty quantification that casts
classification as a hypothesis testing problem under nuisance parameters. The
key idea is to estimate the classifier's receiver operating characteristic
(ROC) across the entire nuisance parameter space, which allows us to devise
cutoffs that are invariant under GLS. Our method effectively endows a
pre-trained classifier with domain adaptation capabilities and returns valid
prediction sets while maintaining high power. We demonstrate its performance on
two challenging scientific problems in biology and astroparticle physics with
data from realistic mechanistic models.

我们提出了一种新的方法用于稳健的不确定性量化，将分类问题视为在干扰参数下的假设检验问题，通过估计分类器在整个干扰参数空间上的接收器操作特性（ROC），我们能够设计在广义标签偏移下不变的截断点，从而有效赋予预训练分类器领域适应能力，并返回有效的预测集合同时保持高度的分类性能。