Uncertainty Quantification for Inferring Hawkes Networks
This work addresses the problem of uncertainty quantification in inferring causal networks from streaming event data, which is incremental as it builds on existing Hawkes process methods.
The authors tackled the challenge of extracting reliable inference with uncertainty quantification from complex networked event data modeled by multivariate Hawkes processes, by developing a statistical inference framework that provides non-asymptotic confidence sets for network estimates, demonstrating its strengths in neuronal connectivity reconstruction.
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.