Scalable and adaptive variational inference for multivariate Hawkes processes
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: "bayesian, "variational", graphs, hawkes, point processes;
Session: IPS 793 - Network Stochastic Processes and Time Series
Thursday 9 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is generally a computationally expensive task, all the more with Bayesian estimation methods. Recently, efficient algorithms targeting a mean-field variational approximation of the posterior distribution have been proposed, however, these methods do not allow to perform model selection on the graph of interactions of the Hawkes model. In this work, we propose a novel adaptive Bayesian variational method that performs model selection and can estimate a sparse graphical parameter. Moreover, for the popular sigmoid Hawkes processes, our algorithm is parallelisable which thus allows it to scale to point processes with more than 50 dimensions and 100 000 events. Furthermore, we unify existing variational Bayes approaches under a general nonparametric inference framework, and analyse the asymptotic properties of these methods under easily verifiable conditions on the prior, the variational class, and the nonlinear model.