Distribution-free changepoint localization after sequential change detection

2026-05-31

AI Summary

This study addresses the problem of constructing confidence intervals for change-point locations in sequential data without imposing distributional assumptions, while guaranteeing finite-sample coverage. The work proposes the first general distribution-free framework for change-point localization that does not require prior knowledge of pre- or post-change distributions. It leverages conformal test martingales to construct confidence sets and integrates conditional coverage analysis with non-asymptotic theoretical guarantees. The resulting method ensures valid conditional coverage in finite samples and achieves asymptotically bounded expected confidence set size. Empirical evaluations on both simulated and real-world datasets demonstrate its superior performance compared to existing approaches.

Abstract

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.

Problem

• changepoint localization
• distribution-free
• sequential change detection
• post-detection inference
• confidence sets

Innovation

• distribution-free
• changepoint localization
• conformal test martingales
• post-detection inference
• finite-sample coverage