Offline Change Detection under Contamination

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.