Screening Strategies for Reconstructing Brain Connectivity Networks with Multivariate Hawkes Process

• Activity Number: 640 - The State-of-the-Art in Modeling and Testing of High-Dimensional Brain Images and Networks
• Type: Invited
• Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): Ali Shojaie* and Shizhe Chen and Daniela Witten
• Companies: University of Washington and Columbia University and University of Washington
• Keywords: Spike Train Data ; Brain Networks ; High-Dimensional Estimation ; Screening

Abstract

We consider the task of learning the structure of brain connectivity networks from spike-train data. We propose two simple and computationally inexpensive screening approaches for the high-dimensional Hawkes process: an edge screening procedure, and a connecting component screening procedure. We show in mutually-exiting Hawkes processes, the edge screening approach has the sure screening property: with high probability, the screened edge set is a superset of the true edge set. Moreover, this is achieved under a subset of the assumptions required for penalized estimation approaches to recover the graph. On the other hand, we show that the connected component screening detects the true connected components of the underlying with high probability, even if the Hawkes process is not mutually exiting. We demonstrate the proposed screening procedures using simulated and real data examples.