A0335
Title: Cox-Hawkes: Doubly stochastic spatiotemporal Poisson processes
Authors: Xenia Miscouridou - Imperial College London (United Kingdom) [presenting]
Abstract: Hawkes processes are point process models used to capture self-excitatory behaviour in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events. A new class of spatiotemporal Hawkes processes is developed to capture both triggering and clustering behaviour, and an efficient method is provided for performing inference. A log-Gaussian Cox process (LGCP) is used as prior for the background rate of the Hawkes process, which gives arbitrary flexibility to capture a wide range of underlying background effects (for infectious diseases, these are called endemic effects). The Hawkes process and LGCP are computationally expensive due to the former having a likelihood with quadratic complexity in the number of observations and the latter involving inversion of the precision matrix, which is cubic in observations. A novel approach is proposed to perform MCMC sampling for the Hawkes process with LGCP background, using pre-trained Gaussian Process generator,s which provide direct and cheap access to samples during inference. The efficacy and flexibility of the approach in experiments are shown on simulated data, and the methods are used to uncover the trends in a dataset of reported crimes in the US.
