Parameter Estimation for Anonymous Hawkes Processes

Abstract

Hawkes Processes are self-exciting point processes used to model many real-life networks in which an event from one agent causes the rate at which events occur from related agents to increase, such as in earthquake networks or social media. This project investigates the question of finding the underlying structure of the Hawkes Processes given a history of when events occurred. This problem has been studied extensively in the regime where the event labels are known, and the bulk of the literature involves parameterizing the model and passing it through statistical learning tools. Our proposed work focuses on the the same question in “anonymous" case where labels are not given. In this regime, the lack of information makes many previous approaches intractable and we develop novel non-parametric approaches for solving cases of the structure learning problem in algorithmic and information theoretic settings. Our results show the ability to learn the entire model under mild assumptions in the information theoretic regime, where we have access to an arbitrarily long Anonymous Hawkes Process transcript, whereas when we’re confined to a polynomially lengthed transcript, the situation is considerably more difficult.