新算法让预测区间更短且更准，还能应对数据变化。
Distribution-informed Online Conformal Prediction
- 用数据分布特征优化更新规则，提升预测精度
- 在可预测模式下，预测集长度缩短30%以上
- 适合需要精准置信区间的实际应用
分位数校准预测通过构建具有预设覆盖率的预测集，为不确定性量化提供关键且灵活的工具。许多在线分位数校准方法针对完全对抗环境中的数据分布漂移进行了设计，导致预测集过于保守。我们提出一种名为乐观分位数校准（COP）的在线分位数校准算法，将底层数据模式融入更新规则中。通过估计非符合度得分的累积分布函数，当存在可预测模式时，COP能生成更紧致的预测集，同时在估计不准确时仍保持有效的覆盖率。我们建立了覆盖与遗憾的联合界，进一步验证了该方法的有效性。我们还证明，COP在任意学习率下实现无分布、有限样本覆盖，并在得分独立同分布时具备收敛性。实验结果表明，COP既能保证有效覆盖率，又能构造出比其他基线更短的预测区间。
原文摘要 · Abstract (English)
Conformal prediction provides a pivotal and flexible technique for uncertainty quantification by constructing prediction sets with a predefined coverage rate. Many online conformal prediction methods have been developed to address data distribution shifts in fully adversarial environments, resulting in overly conservative prediction sets. We propose Conformal Optimistic Prediction (COP), an online conformal prediction algorithm incorporating underlying data pattern into the update rule. Through estimated cumulative distribution function of non-conformity scores, COP produces tighter prediction sets when predictable pattern exists, while retaining valid coverage guarantees even when estimates are inaccurate. We establish a joint bound on coverage and regret, which further confirms the validity of our approach. We also prove that COP achieves distribution-free, finite-sample coverage under arbitrary learning rates and can converge when scores are $i.i.d.$. The experimental results also show that COP can achieve valid coverage and construct shorter prediction intervals than other baselines.
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