改进交叉预测的统计效率，让预测区间更小更准。
Improving the statistical efficiency of cross-conformal prediction
- 利用交换性与随机化优化p值组合，提升方法效率。
- 在保证覆盖率达1-2α的前提下，显著缩小预测集范围。
- 适合关注预测精度与可靠性平衡的研究者。
Vovk（2015）提出了交叉共形预测，是对分拆共形预测的改进，旨在减小预测集宽度。当以α为误覆盖率训练且n ≫ K时，该方法可保证边际覆盖概率至少为1 - 2α - 2(1-α)(K-1)/(n+K)，其中n为样本数，K为折数。对方法进行简单修改后，可实现至少1-2α的覆盖概率。本文提出两种新变体，在不牺牲上述理论保证的前提下，进一步缩小预测集。新方法基于近期关于利用交换性与随机化实现更高效p值合并的研究成果。模拟实验验证了理论结果，并揭示了一些关键权衡关系。
原文摘要 · Abstract (English)
Vovk (2015) introduced cross-conformal prediction, a modification of split conformal designed to improve the width of prediction sets. The method, when trained with a miscoverage rate equal to $α$ and $n \gg K$, ensures a marginal coverage of at least $1 - 2α- 2(1-α)(K-1)/(n+K)$, where $n$ is the number of observations and $K$ denotes the number of folds. A simple modification of the method achieves coverage of at least $1-2α$. In this work, we propose new variants of both methods that yield smaller prediction sets without compromising the latter theoretical guarantees. The proposed methods are based on recent results deriving more statistically efficient combination of p-values that leverage exchangeability and randomization. Simulations confirm the theoretical findings and bring out some important tradeoffs.
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