A1029
Title: Beyond massive univariate tests: Covariance regression reveals complex patterns of brain functional connectivity
Authors: Yi Zhao - Indiana University (United States) [presenting]
Abstract: Studies of brain functional connectivity typically involve massive univariate tests, performing statistical analysis on each individual connection. The problem of regressing covariance matrices is considered on associated covariates. The goal is to use covariates to explain variation in covariance matrices across units. As such, covariate-assisted principal (CAP) regression is introduced, an optimization-based method for identifying components associated with the covariates using a generalized linear model approach. For high-dimensional data, a well-conditioned linear shrinkage estimator of the covariance matrix is introduced. With multiple covariance matrices, the shrinkage coefficients are proposed to be common across matrices. Theoretical studies demonstrate that the proposed covariance matrix estimator is optimal in achieving the uniform minimum quadratic loss asymptotically among all linear combinations of the identity matrix and the sample covariance matrix. Under regularity conditions, the proposed estimator of the model parameters is consistent. Computationally efficient algorithms are developed to jointly search for common linear projections of the covariance matrices, as well as the regression coefficients. The superior performance of the proposed approach over existing methods is illustrated through simulation studies and a fMRI dataset.
