Uncovering Causality from Multivariate Hawkes Integrated Cumulants
This provides a way to infer causality from activity timestamps in domains like social networks, but it is incremental as it builds on existing nonparametric approaches.
The authors tackled the problem of estimating causality relationships between nodes in a multivariate Hawkes process without parametric modeling of kernels, and their method achieved robust results on the MemeTracker database.
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.