Changepoint detection on a graph of time series

TL;DR

This paper introduces a graph-informed Bayesian model for detecting changepoints in multiple time series, leveraging network structure to improve detection of weak signals and reduce false alarms.

Contribution

It proposes a novel prior and a reversible jump MCMC algorithm for changepoint detection that incorporates graph-based dependencies among time series.

Findings

Enhanced detection of weak signals in network intrusion data

Reduced false alarms in changepoint detection

Demonstrated improvement over traditional methods

Abstract

When analysing multiple time series that may be subject to changepoints, it is sometimes possible to specify a priori, by means of a graph, which pairs of time series are likely to be impacted by simultaneous changepoints. This article proposes an informative prior for changepoints which encodes the information contained in the graph, inducing a changepoint model for multiple time series that borrows strength across clusters of connected time series to detect weak signals for synchronous changepoints. The graphical model for changepoints is further extended to allow dependence between nearby but not necessarily synchronous changepoints across neighbouring time series in the graph. A novel reversible jump Markov chain Monte Carlo (MCMC) algorithm making use of auxiliary variables is proposed to sample from the graphical changepoint model. The merit of the proposed approach is demonstrated through a changepoint analysis of computer network authentication logs from Los Alamos National Laboratory (LANL), demonstrating an improvement at detecting weak signals for network intrusions across users linked by network connectivity, whilst limiting the number of false alerts.