Post-detection inference for sequential changepoint localization

TL;DR

This paper introduces a universal, nonparametric framework for constructing confidence sets for changepoints after detection, valid at data-dependent stopping times, with theoretical guarantees and practical effectiveness.

Contribution

It presents the first general, non-asymptotic method for sequential changepoint localization applicable across various detection algorithms and settings.

Findings

Confidence sets have reasonable size and coverage.

Method is nonparametric and broadly applicable.

Theoretical guarantees on confidence set width.

Abstract

This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite post-change class, the observation space, or the sequential detection procedure used, and is non-asymptotically valid. We also extend it to handle composite pre-change classes under a suitable assumption, and also derive confidence sets for the change magnitude in parametric settings. We provide theoretical guarantees on the width of our confidence intervals. Extensive simulations demonstrate that the produced sets have reasonable size, and slightly conservative coverage. In summary, we present the first general method for sequential changepoint localization, which is theoretically sound and broadly applicable in practice.