Linking Across Data Granularity: Fitting Multivariate Hawkes Processes to Partially Interval-Censored Data

This work introduces a novel multivariate temporal point process, the Partial Mean Behavior Poisson (PMBP) process, which can be leveraged to fit the multivariate Hawkes process to partially interval-censored data consisting of a mix of event timestamps on a subset of dimensions and interval-censored event counts on the complementary dimensions. First, we define the PMBP process via its conditional intensity and derive the regularity conditions for subcriticality. We show that both the Hawkes process and the MBP process (Rizoiu et al. (2021)) are special cases of the PMBP process. Second, we provide numerical schemes that enable calculating the conditional intensity and sampling event histories of the PMBP process. Third, we demonstrate the applicability of the PMBP process by empirical testing using synthetic and real-world datasets: We test the capability of the PMBP process to recover multivariate Hawkes parameters given sample event histories of the Hawkes process. Next, we evaluate the PMBP process on the Youtube popularity prediction task and show that it outperforms the current state-of-the-art Hawkes Intensity process (Rizoiu et al. (2017b)). Lastly, on a curated dataset of COVID19 daily case counts and COVID19-related news articles for a sample of countries, we show that clustering on the PMBP-fitted parameters enables a categorization of countries with respect to the country-level interaction of cases and news reporting.