Detecting Abrupt Changes in Point Processes: Fundamental Limits and Applications

TL;DR

This paper establishes fundamental limits and proposes methods for detecting abrupt changes in the rate function of point processes, applicable to various real-world scenarios including epidemic modeling.

Contribution

It introduces a theoretical framework for detecting sharp changes in unknown, non-stationary point process rate functions, with necessary conditions and practical applications.

Findings

Abrupt changes can be detected if sharper than the pre-change smoothness.

Detection is possible under necessary information-theoretic conditions.

Methods are validated on synthetic and real datasets.

Abstract

We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that depends on the history of event times. We show that abrupt changes can be accurately identified from observations of the point process, provided the changes are sharper than the "smoothness'' of the rate function before the abrupt change. This condition is also shown to be necessary from an information-theoretic point of view. We then apply our theory to several special cases of interest, including the detection of significant changes in piecewise smooth rate functions and detecting super-spreading events in epidemic models on graphs. Finally, we confirm the effectiveness of our methods through a detailed empirical analysis of both synthetic and real datasets.