Statistical Inference for Networks of High-Dimensional Point Processes

• Activity Number: 545 - Statistical Advances in Learning Large-Scale Networks from Massive Data Sets
• Type: Topic Contributed
• Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Mladen Kolar* and Xu Wang and Ali Shojaie
• Companies: The University of Chicago and University of Washington and University of Washington
• Keywords: high-dimensional inference; networks of point processes; Hawkes process

Abstract

Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily addressed estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional Hawkes processes. The key ingredient for the inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarize the entire history of the process. Combining recent results on martingale central limit theory with the new concentration inequality, we then characterize the convergence rate of the test statistics. The finite sample validity of the inferential tools is illustrated via extensive simulations and further applied to a neuron spike train data set.

Joing work with Xu Wang and Ali Shojaie.