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。