Scaling Hawkes processes to one million COVID-19 cases

Abstract: Hawkes stochastic point process models have emerged as valuable statistical tools for analyzing viral contagion. The spatiotemporal Hawkes process characterizes the speeds at which viruses spread within human populations. Unfortunately, likelihood-based inference using these models requires $O(N^2)$ floating-point operations, for $N$ the number of observed cases. Recent work responds to the Hawkes likelihood's computational burden by developing efficient graphics processing unit (GPU)-based routines that enable Bayesian analysis of tens-of-thousands of observations. We build on this work and develop a high-performance computing (HPC) strategy that divides 30 Markov chains between 4 GPU nodes, each of which uses multiple GPUs to accelerate its chain's likelihood computations. We use this framework to apply two spatiotemporal Hawkes models to the analysis of one million COVID-19 cases in the United States between March 2020 and June 2023. In addition to brute-force HPC, we advocate for two simple strategies as scalable alternatives to successful approaches proposed for small data settings. First, we use known county-specific population densities to build a spatially varying triggering kernel in a manner that avoids computationally costly nearest neighbors search. Second, we use a cut-posterior inference routine that accounts for infections' spatial location uncertainty by iteratively sampling latent locations uniformly within their respective counties of occurrence, thereby avoiding full-blown latent variable inference for 1,000,000 infection locations.