Reducing sequential change detection to sequential estimation

TL;DR

This paper introduces a simple method to convert the problem of sequential change detection into a sequential estimation task using confidence sequences, enabling robust detection with minimal assumptions.

Contribution

It presents a novel reduction from change detection to estimation via confidence sequences, allowing for dependent and nonparametric data.

Findings

Average run length at least 1/α

Works with dependent data and nonparametric distributions

Strong guarantees on false alarm control

Abstract

We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).