New Spatio-temporal Hawkes Process Models For Social Good

As more and more datasets with self-exciting properties become available, the demand for robust models that capture contagion across events is also getting stronger. Hawkes processes stand out given their ability to capture a wide range of contagion and self-excitation patterns, including the transmission of infectious disease, earthquake aftershock distributions, near-repeat crime patterns, and overdose clusters. The Hawkes process is flexible in modeling these various applications through parametric and non-parametric kernels that model event dependencies in space, time and on networks.

In this thesis, we develop new frameworks that integrate Hawkes Process models with multi-armed bandit algorithms, high dimensional marks, and high-dimensional auxiliary data to solve problems in search and rescue, forecasting infectious disease, and early detection of overdose spikes.

In Chapter 3, we develop a method applications to the crisis of increasing overdose mortality over the last decade.  We first encode the molecular substructures found in a drug overdose toxicology report. We then cluster these overdose encodings into different overdose categories and model these categories with spatio-temporal multivariate Hawkes processes. Our results demonstrate that the proposed methodology can improve estimation of the magnitude of an overdose spike based on the substances found in an initial overdose. 

In Chapter 4, we build a framework for multi-armed bandit problems arising in event detection where the underlying process is self-exciting. We derive the expected number of events for Hawkes processes given a parametric model for the intensity and then analyze the regret bound of a Hawkes process UCB-normal algorithm. By introducing the Hawkes Processes modeling into the upper confidence bound construction, our models can detect more events of interest under the multi-armed bandit problem setting. We apply the Hawkes bandit model to spatio-temporal data on crime events and earthquake aftershocks. We show that the model can quickly learn to detect hotspot regions, when events are unobserved, while striking a balance between exploitation and exploration. 

In Chapter 5, we present a new spatio-temporal framework for integrating Hawkes processes with multi-armed bandit algorithms. Compared to the methods proposed in Chapter 4, the upper confidence bound is constructed through Bayesian estimation of a spatial Hawkes process to balance the trade-off between exploiting and exploring geographic regions. The model is validated through simulated datasets and real-world datasets such as flooding events and improvised explosive devices (IEDs) attack records. The experimental results show that our model outperforms baseline spatial MAB algorithms through rewards and ranking metrics.

In Chapter 6, we demonstrate that the Hawkes process is a powerful tool to model the infectious disease transmission. We develop models using Hawkes processes with spatial-temporal covariates to forecast COVID-19 transmission at the county level. In the proposed framework, we show how to estimate the dynamic reproduction number of the virus within an EM algorithm through a regression on Google mobility indices. We also include demographic covariates as spatial information to enhance the accuracy. Such an approach is tested on both short-term and long-term forecasting tasks. The results show that the Hawkes process outperforms several benchmark models published in a public forecast repository. The model also provides insights on important covariates and mobility that impact COVID-19 transmission in the U.S.

Finally, in chapter 7, we discuss implications of the research and future research directions.