Statistics Seminar - Yao Xie (Georgia Tech) "Point Processes with Event Time Uncertainty"

Title: Point Processes with Event Time Uncertainty

Abstract: Point processes are widely used to model continuous-time event data, including medical records, crime reports, and interactions in social networks. In many applications, however, event times are not observed exactly because of temporal aggregation, reporting delays, censoring, or measurement errors. This raises a basic statistical question: can we recover how past events influence future occurrences when their timestamps are observed only approximately?

In this talk, I will introduce a framework for modeling self-exciting point processes, including Hawkes processes, under event-time uncertainty. Starting from a continuous-time model, we impose a time grid and derive a discrete-time representation that supports efficient inference using first-order optimization and variational inequalities. We establish parameter recovery guarantees and an O(1/k) convergence rate after k iterations. The framework also allows the influence structure to vary over time and extends naturally to network-valued event data. Numerical studies on simulated and real data, including sepsis-associated clinical events and Atlanta crime records, illustrate the effects of timestamp uncertainty and the performance of the proposed approach. This is joint work with Xiuyuan Cheng and Tingnan Gong.