ABC Learning of Hawkes Processes with Missing or Noisy Event Times

TL;DR

This paper introduces ABC-Hawkes, a novel estimation method for Hawkes processes that explicitly models data distortion, enabling accurate parameter learning even with missing or noisy event times.

Contribution

It develops the ABC-Hawkes algorithm combining ABC and MCMC to address data distortion in Hawkes process modeling, improving estimation accuracy.

Findings

Performs well on real data

Handles missing and noisy event times effectively

Reduces bias in parameter estimation

Abstract

The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such distortion can severely bias the learning of the Hawkes process parameters. To circumvent this, we propose modeling the distortion function explicitly. This leads to a model with an intractable likelihood function which makes it difficult to deploy standard parameter estimation techniques. As such, we develop the ABC-Hawkes algorithm which is a novel approach to estimation based on Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo. This allows the parameters of the Hawkes process to be learned in settings where conventional methods induce substantial bias or are inapplicable. The proposed approach is shown to perform well on both real and simulated data.