Multivariate nonlinear Hawkes processes are powerful models for multi-
variate point processes with excitation and inhibation phenomenon. Bayesian
nonparametric methods have been proposed and studied theoretically, showing good properties. However their implementation remain a challenge due to the complexity of the likelihood and the potentially high dimensional
space. In this work we propose a two step variational Bayes approach to
estimate both the graph of interaction and the functions of interactions. We
give theoretical guarantees to the procedure and show that it scales well for
moderately high dimensional Hawkes processes.
This is a joint work with Deborah Sulem and Vincent Rivoirard.