A Note on Online Change Point Detection

TL;DR

This paper introduces a simple CUSUM-based method for online change point detection in univariate nonparametric data streams, effectively controlling false alarms and minimizing detection delay across various scenarios.

Contribution

It develops a new CUSUM-based approach that provably controls false alarms and adapts to multiple change points in a broad nonparametric setting.

Findings

Method effectively controls false alarm probability.

Minimizes detection delay in minimax sense.

Applicable to multiple change point estimation.

Abstract

We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but otherwise unknown means are collected. We develop a simple CUSUM-based methodology that provably control the probability of false alarms or the average run length while minimizing, in a minimax sense, the detection delay. We allow for all the model parameters to vary in order to capture a broad range of levels of statistical hardness for the problem at hand. We further show how our methodology is applicable to the case in which multiple change points are to be estimated sequentially.