Offline Change Detection under Contamination

TL;DR

This paper introduces a robust, non-parametric offline change detection algorithm capable of identifying multiple change points in contaminated time series data, with theoretical guarantees and empirical validation.

Contribution

It presents a novel robust change detection method that handles arbitrary contamination and weak moment assumptions, extending existing models like Huber contamination.

Findings

Algorithm is consistent as sample size grows.

Effective in detecting multiple change points.

Empirical results support theoretical guarantees.

Abstract

In this work, we propose a non-parametric and robust change detection algorithm to detect multiple change points in time series data under contamination. The contamination model is sufficiently general, in that, the most common model used in the context of change detection -- Huber contamination model -- is a special case. Also, the contamination model is oblivious and arbitrary. The change detection algorithm is designed for the offline setting, where the objective is to detect changes when all data are received. We only make weak moment assumptions on the inliers (uncorrupted data) to handle a large class of distributions. The robust scan statistic in the algorithm is fashioned using mean estimators based on influence functions. We establish the consistency of the estimated change point indexes as the number of samples increases, and provide empirical evidence to support the consistency results.