Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process

We consider the task of learning the structure of the graph underlying a mutually-exciting multivariate Hawkes process in the high-dimensional setting. We propose a simple and computationally inexpensive edge screening approach. Under a subset of the assumptions required for penalized estimation approaches to recover the graph, this edge screening approach has the sure screening property: with high probability, the screened edge set is a superset of the true edge set. Furthermore, the screened edge set is relatively small. We illustrate the performance of this new edge screening approach in simulation studies.