Hawkes Processes Modeling, Inference and Control: An Overview

Abstract

Hawkes Processes are a type of point process which model self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis. Recently, a surge of different tools and algorithms have showed their way up to top-tier Machine Learning conferences. This work aims to give a broad view of the recent advances on the Hawkes Processes modeling and inference to a newcomer to the field. The parametric, nonparametric, Deep Learning and Reinforcement Learning approaches are broadly discussed, along with the current research challenges on the topic and the real-world limitations of each approach. Illustrative application examples in the modeling of Retweeting behaviour, Earthquake aftershock occurence and COVID-19 spreading are also briefly discussed.