Context-Dependent Self-Exciting Point Processes: Models, Methods, and Risk Bounds in High Dimensions

• Activity Number: 286 - Learning Networks from Point Processes: Neuronal Connectivity Networks and Beyond
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Garvesh Raskutti* and Lili Zheng and Rebecca Willett
• Companies: UW-Madison and University of Wisconsin-Madison and University of Chicago
• Keywords: point process; network

Abstract

High-dimensional autoregressive point processes model how current events can trigger or inhibit future events, such as activity in a social network. Specifically, we leverage ideas from compositional data analysis and regularization tools for machine learning to conduct network estimation for high-dimensional marked point processes. Two models and corresponding estimators are considered in detail: an autoregressive multinomial model suited to noise-free categorical contexts and a logistic-normal model suited to events with mixed membership in different categories and noisy observations. Importantly, the logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories. We provide theoretical guarantees for both estimators and demonstrate through simulations and three real data examples the advantages and disadvantages of both approaches.