Adversarially robust change point detection

TL;DR

This paper introduces a new robust change point detection method resilient to adversarial contamination, demonstrating a phase transition boundary and optimal localization rates, with extensive experiments validating its effectiveness.

Contribution

It presents the first analysis of adversarial robustness in change point detection, including a phase transition boundary and minimax optimal localization error rates.

Findings

Identifies a phase transition boundary depending on contamination proportion.

Derives minimax-rate optimal localization error bounds.

Proposes a computationally feasible robust detection method.

Abstract

Change point detection is becoming increasingly popular in many application areas. On one hand, most of the theoretically-justified methods are investigated in an ideal setting without model violations, or merely robust against identical heavy-tailed noise distribution across time and/or against isolate outliers; on the other hand, we are aware that there have been exponentially growing attacks from adversaries, who may pose systematic contamination on data to purposely create spurious change points or disguise true change points. In light of the timely need for a change point detection method that is robust against adversaries, we start with, arguably, the simplest univariate mean change point detection problem. The adversarial attacks are formulated through the Huber $\varepsilon$-contamination framework, which in particular allows the contamination distributions to be different at each time point. In this paper, we demonstrate a phase transition phenomenon in change point detection. This detection boundary is a function of the contamination proportion $\varepsilon$ and is the first time shown in the literature. In addition, we derive the minimax-rate optimal localisation error rate, quantifying the cost of accuracy in terms of the contamination proportion. We propose a computationally feasible method, matching the minimax lower bound under certain conditions, saving for logarithmic factors. Extensive numerical experiments are conducted with comparisons to robust change point detection methods in the existing literature.