LEAPS-MPS: Covariate-Assisted Analysis of Spectral Matrices with Applications to Physiological Signals

Cuny Baruch College, New York NY

Investigators

Abstract

Researchers from a wide range of scientific fields record physiological signals over time. These signals contain valuable information about biological processes, a deeper understanding of which is essential for advancing health. Examples of such signals include measures of electrical activity, such as electroencephalography (EEG); measures of brain activity by blood flow, such as Functional magnetic resonance imaging (fMRI); and measures of movement, such as center-of-pressure trajectory. Researchers' ability to fully utilize the information contained in these signals is currently hindered by a lack of formal statistical methods for the analysis of physiological signals collected under modern study designs, where signals may be collected from multiple subjects and may be associated with a variety of factors and variables. The application of this research will advance the full use of information contained in recorded physiological signals and lay the foundation for advancing the understanding, diagnosis, and treatment of a wide range of diseases. This project will also directly support personalized transdisciplinary training and mentoring programs for both graduate and undergraduate students, especially those from underrepresented groups. The second-order properties of physiological signals, which can be quantified by spectral matrices, contain valuable information about biological mechanisms. This project will present a comprehensive set of formal statistical methods for the analysis of spectral matrices of high-dimensional replicated time series collected from modern studies. Methods proposed in this project will help researchers understand the relationship between spectral matrices of multivariate replicated time series and other variables, such as biological covariates and clinical outcomes. Three specific tasks will be performed: (1) Develop a nonparametric dimension reduction method for modeling covariate-dependent spectral matrices using the conditionally incoherent components proposed in this project. This will allow existing methods for univariate time series to be applied to multivariate data, significantly easing analysis. (2) Introduce a novel covariate-assisted graphical model for high-dimensional time series. This will enable researchers to quantify the conditional partial relationships between high-dimensional time series, given the covariates. (3) Develop a novel regression model of spectral matrices on covariates. This model will allow for the formal assessment of associations between other study variables and high-dimensional spectral matrices. Additionally, user-friendly analytical tools across multiple software programs will be developed to increase the usability of the proposed methods in other scientific communities. 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.