提出在线方法生成多水平嵌套预测集,实现全风险谱的稳定不确定性量化。
Online Conformal Prediction: Enforcing monotonicity via Online Optimization

- 基于在线优化框架,通过小遗憾保证控制分位数误差并强制预测集嵌套
- 在合成与真实数据上均实现所有覆盖水平的稳定覆盖率和严格嵌套结构
- 适合需多风险容忍度校准的场景,如气象、经济预测与风控
置信预测提供了一种具有有限样本覆盖保证的不确定性量化原理框架。尽管近期工作已将置信预测扩展至在线和序列设置,但现有方法通常仅关注单一覆盖水平,且无法保证多水平间的连续性。在天气预报、宏观经济预测和风险管理等实际应用中,不同用户具有异质的风险容忍度,需在多个覆盖水平下获得校准的不确定性估计。此时,生成对应于不同覆盖水平的嵌套且同时有效的预测集更为理想。本文提出两种新型在线置信预测方法,可输出跨多个覆盖水平的嵌套预测集,实现整个风险谱上的联合不确定性量化。除了可解释性外,联合估计多个覆盖水平已被证明可通过施加非交叉约束并共享分位数信息提升经典分位数回归的统计效率。我们的方法从在线优化视角出发,以小遗憾保证转化为分位数估计误差控制,并强制预测集嵌套。在合成与真实世界数据集上的实验结果表明,该方法在所有覆盖水平上实现了稳定的覆盖率、严格嵌套的预测集,且相比现有在线置信基线具有更高的效率。
原文摘要 · Abstract (English)
Conformal prediction provides a principled framework for uncertainty quantification with finite-sample coverage guarantees. While recent work has extended conformal prediction to online and sequential settings, existing methods typically focus on a single coverage level and do not ensure consistency across multiple confidence levels. In many real-world applications, such as weather forecasting, macroeconomic prediction, and risk management, different users operate under heterogeneous risk tolerances and require calibrated uncertainty estimates across a range of coverage levels. In such settings, it is desirable to produce prediction sets corresponding to different coverage levels that are nested and valid simultaneously. In this paper, we propose two novel online conformal prediction methods that output \emph{nested prediction sets} across a range of coverage levels, enabling simultaneous uncertainty quantification across the entire risk spectrum. Beyond interpretability, jointly estimating multiple coverage levels is known to improve statistical efficiency in classical quantile regression by enforcing non-crossing constraints and sharing information across quantiles. Our approaches leverage an online optimization perspective with small regret that translates to quantile estimation error control while enforcing nestedness of prediction sets. Empirical results on synthetic and real-world datasets, including applications in forecasting tasks with heterogeneous risk requirements, demonstrate that our method achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency compared to existing online conformal baselines.
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