Detecting Abrupt Changes in High-Dimensional Self-Exciting Poisson Processes

TL;DR

This paper introduces a novel penalized dynamic programming method for detecting abrupt changes in the coefficient matrices of high-dimensional self-exciting Poisson processes, addressing key theoretical and computational challenges.

Contribution

It presents the first approach with theoretical guarantees for change detection in high-dimensional self-exciting Poisson processes.

Findings

The method effectively detects change points in simulated data.

Theoretical analysis provides convergence rates.

Numerical experiments validate the approach's accuracy.

Abstract

High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with detecting abrupt changes of the coefficient matrices in discrete-time high-dimensional self-exciting Poisson processes, which have yet to be studied in the existing literature due to both theoretical and computational challenges rooted in the non-stationary and high-dimensional nature of the underlying process. We propose a penalized dynamic programming approach which is supported by a theoretical rate analysis and numerical evidence.