Unsupervised Change Detection using DRE-CUSUM

TL;DR

This paper introduces DRE-CUSUM, an unsupervised method for detecting statistical changes in time-series data using density ratio estimation and CUSUM, with theoretical guarantees and superior performance demonstrated on synthetic and real datasets.

Contribution

It is the first unsupervised change detection method with theoretical justification and accuracy guarantees based on density ratio estimation.

Findings

DRE-CUSUM reliably detects changes regardless of split point.

The method outperforms existing unsupervised algorithms on synthetic and real data.

The approach is applicable to high-dimensional and online time-series data.

Abstract

This paper presents DRE-CUSUM, an unsupervised density-ratio estimation (DRE) based approach to determine statistical changes in time-series data when no knowledge of the pre-and post-change distributions are available. The core idea behind the proposed approach is to split the time-series at an arbitrary point and estimate the ratio of densities of distribution (using a parametric model such as a neural network) before and after the split point. The DRE-CUSUM change detection statistic is then derived from the cumulative sum (CUSUM) of the logarithm of the estimated density ratio. We present a theoretical justification as well as accuracy guarantees which show that the proposed statistic can reliably detect statistical changes, irrespective of the split point. While there have been prior works on using density ratio based methods for change detection, to the best of our knowledge, this is the first unsupervised change detection approach with a theoretical justification and accuracy guarantees. The simplicity of the proposed framework makes it readily applicable in various practical settings (including high-dimensional time-series data); we also discuss generalizations for online change detection. We experimentally show the superiority of DRE-CUSUM using both synthetic and real-world datasets over existing state-of-the-art unsupervised algorithms (such as Bayesian online change detection, its variants as well as several other heuristic methods).