用黎曼-普罗霍罗夫距离建模分布偏移，让预测区间在数据变化时依然可靠。
Conformal Prediction under Levy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations
- 用黎曼-普罗霍罗夫模糊集建模局部和全局数据分布偏移
- 将高维分布偏移转化为一维问题，精确计算最坏情况下的置信区间
- 实验验证了方法在真实数据集上的鲁棒性，适合对可靠性要求高的场景
共形预测提供了一种具有有限样本保证的预测区间构建框架，但在分布偏移下的鲁棒性仍是重大挑战。本文通过使用黎曼-普罗霍罗夫（Levy-Prokhorov, LP）模糊集来建模分布偏移，该集合能够捕捉局部与全局扰动。我们系统地介绍了LP模糊集及其与Wasserstein和总变差等常见度量的联系。研究表明，共形预测与LP模糊集之间存在自然关联：通过将LP模糊集传递至评分函数，可将复杂的高维分布偏移简化为可管理的一维分布偏移，从而实现最坏情况分位数与覆盖率的精确量化。基于此分析，我们构建了在分布偏移下仍保持有效的鲁棒共形预测区间，并明确揭示了LP参数与区间宽度、置信水平之间的关系。在真实数据集上的实验结果验证了所提方法的有效性。
原文摘要 · Abstract (English)
Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using Levy-Prokhorov (LP) ambiguity sets, which capture both local and global perturbations. We provide a self-contained overview of LP ambiguity sets and their connections to popular metrics such as Wasserstein and Total Variation. We show that the link between conformal prediction and LP ambiguity sets is a natural one: by propagating the LP ambiguity set through the scoring function, we reduce complex high-dimensional distribution shifts to manageable one-dimensional distribution shifts, enabling exact quantification of worst-case quantiles and coverage. Building on this analysis, we construct robust conformal prediction intervals that remain valid under distribution shifts, explicitly linking LP parameters to interval width and confidence levels. Experimental results on real-world datasets demonstrate the effectiveness of the proposed approach.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。