Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes

TL;DR

This paper introduces a neural network-based non-parametric method for estimating Hawkes process kernels, providing an efficient, interpretable, and flexible approach that performs well on synthetic and real data.

Contribution

It presents an unbiased likelihood estimator for Hawkes processes and a shallow neural network model for non-parametric kernel estimation, enhancing efficiency and flexibility.

Findings

Comparable or better performance than existing methods

Maintains interpretability of the Hawkes model

Effective on both synthetic and real datasets

Abstract

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.