This paper introduces a distribution-free framework for constructing post-detection confidence sets for changepoints after stopping a sequential change detection procedure. It is well known that conformal test martingales can be used to sequentially detect changes in distribution, but by themselves provide no inference for the time at which a proclaimed change occurred. Past work on post-detection inference requires pre- and post-change classes of distributions to be known, but this paper accomplishes localization of the changepoint without any distributional assumptions. We establish finite-sample coverage guarantees (conditional on correct detection). We provide non-asymptotic bounds on the conditional expected size of the confidence sets. Under suitable asymptotic regimes, we proved that the conditional expected size of the confidence set remains uniformly bounded. and demonstrate strong empirical performance on simulated and real data. To the best of our knowledge, this is the first general distribution-free framework for sequential changepoint localization with a valid post-detection coverage guarantee.

翻译：本文提出了一种无分布假设框架，用于在终止序贯变化检测程序后构建变点的后检测置信集。已知共形检验鞅可序贯检测分布变化，但其本身无法为声称变化发生的时间提供推断。以往的后检测推断工作需要已知变化前后的分布类别，而本文无需任何分布假设即可实现变点定位。我们建立了有限样本覆盖保证（条件于正确检测），给出了置信集条件期望大小的非渐近界，并在合适的渐近体系下证明了置信集条件期望大小的一致有界性。通过在模拟数据和真实数据上的实证，该方法展现出强性能。据我们所知，这是首个具有有效后检测覆盖保证的通用无分布序贯变点定位框架。