Project Grant 2210675

This three-year, $300,000 project grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) will support the development of statistical methods for modeling nonstationary time series data. Specifically, the awardee Cornell University will develop estimation and inference methods for a nonstationary graphical model framework called Nonstationary Graphical Models (NonstGM). This framework captures nonstationary dynamics in multivariate systems through a sparse operator in the Fourier domain, which can then be estimated from data using regularized regression. Key emphasis will be given to locally and periodically stationary structures prevalent in applications. NonstGM models learned from large-scale time series data will be used to build directed graphs with time-varying vector autoregressive models. Validation will utilize extensive numerical experiments and real electroencephalogram datasets. All resulting open-source software packages will aid clinical researchers in understanding connectome abnormalities. Outcomes will also be integrated into graduate courses, providing training and focusing on diversity.