Neural network-based CUSUM for online change-point detection

TL;DR

This paper introduces NN-CUSUM, a neural network-based method for online change-point detection that addresses the limitations of classic CUSUM in high-dimensional and unknown post-change scenarios, with theoretical guarantees and strong empirical results.

Contribution

It proposes a neural network CUSUM method with theoretical conditions and guarantees, extending change-point detection to high-dimensional data.

Findings

Effective detection in high-dimensional data

Theoretical conditions for neural network performance

Strong empirical results on synthetic and real data

Abstract

Change-point detection, detecting an abrupt change in the data distribution from sequential data, is a fundamental problem in statistics and machine learning. CUSUM is a popular statistical method for online change-point detection due to its efficiency from recursive computation and constant memory requirement, and it enjoys statistical optimality. CUSUM requires knowing the precise pre- and post-change distribution. However, post-change distribution is usually unknown a priori since it represents anomaly and novelty. Classic CUSUM can perform poorly when there is a model mismatch with actual data. While likelihood ratio-based methods encounter challenges facing high dimensional data, neural networks have become an emerging tool for change-point detection with computational efficiency and scalability. In this paper, we introduce a neural network CUSUM (NN-CUSUM) for online change-point detection. We also present a general theoretical condition when the trained neural networks can perform change-point detection and what losses can achieve our goal. We further extend our analysis by combining it with the Neural Tangent Kernel theory to establish learning guarantees for the standard performance metrics, including the average run length (ARL) and expected detection delay (EDD). The strong performance of NN-CUSUM is demonstrated in detecting change-point in high-dimensional data using both synthetic and real-world data.