Conference Agenda

Multivariate Hawkes processes form a class of point processes describing self and inter exciting/inhibiting processes. There is now a renewed interest of such processes in applied domains and in machine learning, but there exists only limited theory about inference in such models, in particular in high dimensions. To be more precise, the intensity function of a linear Hawkes process has the following form: for each dimension $k \leq K$ $$\lambda_k(t) = \nu_k + \sum_{l=1}^K\int_{t-A}^{t^-} h_{lk}(t-s) dN^l_s ,$$ for t in [0,T] and $k \leq K$ and where $(N^l , l \leq K)$ is the multivariate Hawkes process and $\nu_k>0$.

There have been some recent theoretical results on Bayesian estimation in the context of linear and nonlinear multivariate Hawkes processes, but these results assumed that the dimension K was fixed. Convergence rates were studied assuming that the observation window T goes to infinity. In this work we consider the case where K is allowed to go to infinity with T. We consider generic conditions to obtain posterior convergence rates and we derive, under sparsity assumptions, convergence rates in L1 norm and consistent estimation of the graph of interactions.