## Sparse and low-rank multivariate Hawkes processes

**E. Bacry, M. Bompaire, S. Gaïffas and J-F. Muzy**

*Journal of Machine Learning Research*, 2020

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by $\ell_1$ and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. ** Read more**