提出统一校准框架，实现有限样本下可靠预测与不确定性建模。
Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction
- 基于泛化维恩校准，将任意完美校准模型转为集值预测器。
- 有限样本保证至少一个边际校准点，渐进收敛到条件校准结果。
- 适用于子群体校准和分位数损失，适合需可信预测的场景。
确保模型校准对可靠预测至关重要，但流行无分布方法如直方图分箱和等式回归仅提供渐近保证。本文提出一种统一的维恩与维恩-阿伯斯校准框架，将沃夫克的方法从二分类扩展至由通用损失函数定义的广泛预测问题。该方法可将任意完全样本内校准的预测器转化为集值预测器，在有限样本下输出至少一个边际校准的点预测。这些集合预测随样本量增加而收缩，渐进收敛至单一条件校准预测，有效捕捉认知不确定性。我们进一步提出维恩多校准，实现子群体层面的有限样本校准。针对分位数损失，本框架恢复了组条件与多校准的合流预测作为特例，并生成具有分位数条件覆盖性的新预测区间。
原文摘要 · Abstract (English)
Ensuring model calibration is critical for reliable prediction, yet popular distribution-free methods such as histogram binning and isotonic regression offer only asymptotic guarantees. We introduce a unified framework for Venn and Venn-Abers calibration that extends Vovk's approach beyond binary classification to a broad class of prediction problems defined by generic loss functions. Our method transforms any perfectly in-sample calibrated predictor into a set-valued predictor that, in finite samples, outputs at least one marginally calibrated point prediction. These set predictions shrink asymptotically and converge to a single conditionally calibrated prediction, capturing epistemic uncertainty. We further propose Venn multicalibration, a new approach for achieving finite-sample calibration across subpopulations. For quantile loss, our framework recovers group-conditional and multicalibrated conformal prediction as special cases and yields novel prediction intervals with quantile-conditional coverage.
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