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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
Abstract #309322
Title: Context-Dependent Self-Exciting Point Processes: Models, Methods, and Risk Bounds in High Dimensions
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

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.

Authors who are presenting talks have a * after their name.

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