发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出预测秩鞅（PRM）方法，解决序贯分布漂移检测中参考集污染及依赖问题，可实现任意时刻有效I类错误控制，在合成与真实数据上性能优于CCTM。
AI 中文摘要
许多序贯分布漂移检测器会用传入的观测值更新不断增长的参考集。发生变化后，这种更新会用变化后的观测值污染参考集，削弱后续证据。保持校准样本固定可减轻这种污染，但重复复用会导致固定参考秩之间产生依赖，因此基于独立共形p值的论证不适用。我们推导了给定前序秩的下一个秩的精确条件零分布，并用其构建预测秩鞅（PRM）。对PRM设置阈值可得到与分布无关、有限样本的任意时刻边际I类错误控制。为针对特定偏差，我们对每个秩应用预先指定的特征，在预测零律下对所得收益进行中心化，并使用在线牛顿步（ONS）调整投注。顺序特征和离散特征分别针对方向变化和中心与尾部变化。对于任何在备择假设下具有非零诱导对比的Lipschitz特征，我们建立了有限窗口检测保证，并表明当初始校准规模增大时，该检验是一致的。然而，在固定校准规模下，我们推导了每个与分布无关的检测程序的功效上限。在合成数据和真实数据上，我们的PRM方法比条件共形检验鞅（CCTM）实现了更好的检测性能。
英文摘要
Many sequential distribution shift detectors update a growing reference set with incoming observations. After a change, this update contaminates the reference set with post-change observations and can weaken subsequent evidence. Keeping the calibration sample fixed mitigates this contamination, but repeated reuse induces dependence among fixed-reference ranks, so arguments based on independent conformal \(p\)-values do not apply. We derive the exact conditional null distribution of the next rank given the preceding ranks and use it to construct a predictive rank martingale (PRM). Thresholding a PRM gives distribution-free, finite-sample anytime marginal type I error control. To target specific departures, we apply a pre-specified feature to each rank, center the resulting payoff under the predictive null law, and use Online Newton Step (ONS) to adapt the bet. Order and dispersion features target directional and center-versus-tail changes, respectively. For any Lipschitz feature with nonzero induced contrast under the alternative, we establish a finite-window detection guarantee and show that the test is consistent as the initial calibration size increases. At a fixed calibration size, however, we derive a power ceiling for every distribution-free detection procedure. Across synthetic and real data, our PRM methods achieve better detection performance than conditional conformal test martingale (CCTM).
