Self-exciting point process modeling of conversation event sequences

Self-exciting processes of Hawkes type have been used to model various phenomena including earthquakes, neural activities, and views of online videos. Studies of temporal networks have revealed that sequences of social interevent times for individuals are highly bursty. We examine some basic properties of event sequences generated by the Hawkes self-exciting process to show that it generates bursty interevent times for a wide parameter range. Then, we fit the model to the data of conversation sequences recorded in company offices in Japan. In this way, we can estimate relative magnitudes of the self excitement, its temporal decay, and the base event rate independent of the self excitation. These variables highly depend on individuals. We also point out that the Hawkes model has an important limitation that the correlation in the interevent times and the burstiness cannot be independently modulated.

💡 Research Summary

The paper investigates the applicability of Hawkes self‑exciting point processes to model the timing of conversational events in a corporate environment. After a brief review of previous applications of Hawkes processes to phenomena such as earthquakes, neuronal spikes, and online video views, the authors focus on a well‑documented property of human activity: inter‑event times are highly bursty and often exhibit long‑range correlations. They first explore, through extensive simulations, whether the simple exponential‑kernel Hawkes model (λ(t)=μ+∑_{ti<t}α e^{−β(t−ti)}) can generate bursty inter‑event intervals across a realistic range of parameters. By varying the excitation strength α and decay rate β while keeping the branching ratio n=α/β<1 (the stationarity condition), they find that even modest excitation (α/β≈0.3–0.6) produces coefficient‑of‑variation (CV) and burstiness (B) values well above those of a Poisson process, confirming that the model naturally yields heavy‑tailed waiting‑time distributions.

The empirical part of the study uses a dataset collected from several Japanese companies, where the start times of face‑to‑face conversations among employees were recorded over three months. For each individual, the authors fit the Hawkes model by maximizing the log‑likelihood L=∑_{i}