Uncertainty Quantification for Inferring Hawkes Networks

TL;DR

This paper introduces a new statistical inference framework for multivariate Hawkes processes that provides reliable uncertainty quantification, enabling better causal inference in networked event data with applications to neuronal connectivity.

Contribution

It develops a non-asymptotic confidence set for Hawkes process parameters using martingale concentration inequalities, improving inference reliability over existing asymptotic methods.

Findings

The proposed method offers more accurate uncertainty quantification.

It outperforms previous asymptotic confidence intervals in simulations.

Application to neuronal data demonstrates practical effectiveness.

Abstract

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.