Accurate Estimation of Cross-Excitation in Multivariate Hawkes Process Models of Infectious Diseases

Multivariate Hawkes processes are a popular model for estimating Granger causality from event sequences on networks. In this work we show that under certain parameter regimes, such as those that arise when modeling infectious disease transmission, false discovery of cross-excitation becomes a major problem. We first provide evidence through simulation that substantial spurious cross-excitation is present when the largest eigenvalue of the productivity matrix approaches the critical value of 1, which leads to multicollinearity. We then propose and compare several methods for mitigating false cross-excitation, through different types of regularization and staged estimation. Our experimental results include both synthetic data as well as transmission data from the Covid-19 pandemic.