Methods for High-Dimensional and Functional Data, with Applications to Mapping Human Brain Networks

New York University Medical Center, New York NY

Investigators

Abstract

The application proposes a set of methods for analyzing high-dimensional and functional data. Although motivated by problems in mapping the human brain and its network structure, the methodological innovations proposed are much more widely applicable. The main objectives are to develop and disseminate novel methodology in the following three areas. (1) Linear and generalized linear regression of scalar outcomes on image predictors: There has been considerable work in the functional data analysis literature on regressing scalars on one-dimensional functional predictors. The investigator has pioneered an approach well suited to the more challenging problem of high-resolution image predictors, but much further work is needed in this area. (2) Inferring networks from large covariance and correlation matrices: This includes multiple time series and time-frequency methods to infer connections among brain regions from functional neuroimaging data, and techniques for two-sample testing and discrimination with high-dimensional data. (3) Analyzing complex outcomes based on the distances among outcomes: This includes distance-based reliability assessment and permutation tests that use distances to infer differences among groups. In their quest to understand human brain function and mental health disorders, researchers in neuroscience and psychiatry are increasingly collecting large and complex data sets. Such data sets may include large numbers of variables per subject, or even sequences of brain maps for each subject, as are produced by functional magnetic resonance imaging. Novel statistical techniques play a central role in deriving scientifically useful information from these complex data sets, which may ultimately aid in the diagnosis and treatment of psychiatric disorders. The methods developed in this research have potential applications in other scientific domains, including ecology and genetics.