Uncovering Causality from Multivariate Hawkes Integrated Cumulants

TL;DR

This paper introduces a nonparametric method to estimate the influence and causality relationships in multivariate Hawkes processes using integrated cumulants, without requiring kernel shape estimation, demonstrated on social network data.

Contribution

It presents the first nonparametric approach to estimate the influence matrix and causality in multivariate Hawkes processes directly from activity timestamps.

Findings

Method accurately estimates influence matrices in simulations.

Robust to different kernel shapes in experiments.

Effective on MemeTracker social network data.

Abstract

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the third-order integrated cumulants of the process. We show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database.