A0527
Title: Scalable variational Bayes methods for interacting point processes
Authors: Deborah Sulem - Barcelona School of Economics (Spain) [presenting]
Vincent Rivoirard - Paris Dauphine University (France)
Judith Rousseau - University of Oxford (United Kingdom)
Abstract: Multivariate Hawkes processes are temporal point processes extensively applied to model event data with dependence on past occurrences and interaction phenomena, e.g., neuronal spike trains, online messages, and financial transactions. In the nonparametric setting, learning the temporal dependence structure of Hawkes processes is often a computationally expensive task, all the more with Bayesian estimation methods. An efficient algorithm targeting a mean-field variational approximation of the posterior distribution has recently been proposed. Existing variational Bayes inference approaches under a general framework are unified, and it is theoretically analysed under easily verifiable conditions on the prior, the variational class, and the model. Then, in the context of the popular sigmoid Hawkes model, adaptive and sparsity-inducing mean-field variational methods are designed. In particular, a two-step algorithm based on the thresholding heuristic is proposed to select the Granger-causal graph parameter of the Hawkes model. Our approach enjoys several benefits through an extensive set of numerical simulations: it is computationally efficient, can reduce the problem's dimensionality by selecting the graph parameter, and can adapt to the smoothness of the underlying parameter.
