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Activity Number: 215 - Contributed Poster Presentations: Section on Statistical Learning and Data Science
Type: Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313753
Title: Context-Dependent Self-Exciting Point Processes: Models, Methods, and Risk Bounds in High Dimensions
Author(s): Lili Zheng* and Garvesh Raskutti and Rebecca Willett
Companies: University of Wisconsin-Madison and UW-Madison and University of Chicago
Keywords: auto-regressive point process; high-dimensional network estimation; context-dependent network

High-dimensional autoregressive point processes model how current events can trigger or inhibit future events, such as activities in a social network. While the primary focus has been on if and when events occur, this paper examines the more nuanced problem of estimating context-dependent networks that reflect how features associated with an event (such as the content of a social network post) modulate the strength of influences among nodes. Specifically, we leverage ideas from compositional time series 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 categorical contexts and a logistic-normal model suited to events with mixed membership in different categories. Importantly, the logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories. We provide theoretical guarantees and numerical results that demonstrate the advantages and disadvantages of the two approaches.

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

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