Conformal prediction (CP) is an emerging uncertainty quantification framework
that allows us to construct a prediction set to cover the true label with a
pre-specified marginal or conditional probability. Although the valid coverage
guarantee has been extensively studied for classification problems, CP often
produces large prediction sets which may not be practically useful. This issue
is exacerbated for the setting of class-conditional coverage on imbalanced
classification tasks. This paper proposes the Rank Calibrated Class-conditional
CP (RC3P) algorithm to reduce the prediction set sizes to achieve
class-conditional coverage, where the valid coverage holds for each class. In
contrast to the standard class-conditional CP (CCP) method that uniformly
thresholds the class-wise conformity score for each class, the augmented label
rank calibration step allows RC3P to selectively iterate this class-wise
thresholding subroutine only for a subset of classes whose class-wise top-k
error is small. We prove that agnostic to the classifier and data distribution,
RC3P achieves class-wise coverage. We also show that RC3P reduces the size of
prediction sets compared to the CCP method. Comprehensive experiments on
multiple real-world datasets demonstrate that RC3P achieves class-wise coverage
and 26.25% reduction in prediction set sizes on average.

针对不平衡分类任务的一种新的不确定性量化框架，Rank Calibrated Class-conditional CP (RC3P) 算法，通过降低预测集大小以实现类条件覆盖，对于每个类别都具有有效的覆盖保证。

增强标签排序校准的适用于每类覆盖的合拢预测

Conformal Prediction for Class-wise Coverage via Augmented Label Rank  Calibration

While conformal predictors reap the benefits of rigorous statistical
guarantees for their error frequency, the size of their corresponding
prediction sets is critical to their practical utility. Unfortunately, there is
currently a lack of finite-sample analysis and guarantees for their prediction
set sizes. To address this shortfall, we theoretically quantify the expected
size of the prediction set under the split conformal prediction framework. As
this precise formulation cannot usually be calculated directly, we further
derive point estimates and high probability intervals that can be easily
computed, providing a practical method for characterizing the expected
prediction set size across different possible realizations of the test and
calibration data. Additionally, we corroborate the efficacy of our results with
experiments on real-world datasets, for both regression and classification
problems.

本文旨在解决当前对于确保错误频率的合规性统计保证，且相应预测集的大小对其实用性至关重要，但预测集大小缺乏有限样本分析和保证的问题，通过量化拆分一致性预测框架下预测集的期望大小来解决此不足，并提供一种实用的方法来表示测试和校准数据的不同可能实现的预期预测集大小。实验结果表明，对于回归和分类问题的现实世界数据集，本文的结果的功效得到了验证。