CDS&E: Spectral Analysis of High-Dimensional Point Processes from Neuronal Spike Train Data

This project develops new statistical machine learning tools and theory for inferring brain functional connectivity networks from neuronal spike train data, as well as changes in these networks. The methods and software proposed in this project are motivated by new technological advances that facilitate live recording of neuronal activities while subjects are presented with stimuli and or perform cognitive tasks. The networks estimated using the proposed methods will shed light into how neurons interact with each other to process information presented in new stimuli. The key difference between the methods proposed in this project and existing approaches is that analyses are conducted in the "spectral domain" rather than the usual time domain. The spectral domain is more informative for neuroscience applications as it naturally captures neuronal syncing and rhythms. However, inferring functional connectivity networks in the spectral domain analysis gives rise to new theoretical and methodological challenges. To address these challenges, the project develops a new theoretical framework for analyzing spike train data in the spectral domain and leverages this framework to develop regularized estimation procedures that facilitate estimation of brain connectivity networks in high-dimensional settings, when the number of observed neurons is large compared to the number of observations. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.