Bayesian inference for multivariate event data with dependence

par Deborah Sulem (Barcelona School of Economics)

mardi 16 janv. 2024, 11:15 → 12:15 Europe/Paris

Salle K. Johnson, 1er étage (1R3)

Multivariate sequences of events’ such as earthquakes, financial transactions, crimes, and neurons’ activations, can be modelled by temporal point processes.  In the Hawkes process model, the probability of occurrences of future events depend on the past of the process and allows to account for dependencies in the data . This model is particularly popular for modelling interactive phenomena such as disease propagation and brain functional connectivity. In this presentation we consider the nonlinear multivariate Hawkes model, which allows to account for excitation and inhibition between interacting entities, estimated with Bayesian nonparametric methods. We will first show that we can provide asymptotic guarantees on such methods, under mild assumptions on the prior distribution and the model. Then, we proposed a variational framework to compute approximations of the posterior distribution, for moderately large to large dimensional data.  We also derived similar asymptotic  guarantees for such class of approximations, and designed an efficient parallelised variational inference algorithm that leverages sparsity patterns in the dependency structure. Our algorithm is organised in two steps where in the first one,  we infer a dependency graph that allows us to reduce the dimensionality of the problem.