Hawkes Processes Modeling, Inference and Control: An Overview

Rafael Lima

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Abstract
Hawkes processes are a type of point process that models self-excitement among time events. They have been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis. Recently, a variety of different tools and algorithms have been presented at top-tier machine learning conferences. This work aims to give a broad view of recent advances in Hawkes process modeling and inference suitable for a newcomer to the field. The parametric, nonparametric, deep learning, and reinforcement learning approaches are broadly discussed, along with the current research challenges for the topic and the real-world limitations of each approach. Illustrative application examples in the modeling of retweeting behavior, earthquake aftershock occurrence, and malaria outbreak modeling are also briefly discussed.