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Title: Covariate assisted principal regression for covariance matrix outcomes Authors:  Xi Luo - University of Texas Health Science Center at Houston (United States) [presenting]
Yi Zhao - Indiana University (United States)
Brian Caffo - Johns Hopkins University (United States)
Stewart Mostofsky - Kennedy Krieger Institute (United States)
Abstract: Modeling variances in data has been an important topic in many fields, including finance and neuroimaging. We consider the problem of regressing covariance matrices on vector covariates, collected from each observational unit. The main aim is to uncover the variation in the covariance matrices across units that are explained by the covariates. Covariate Assisted Principal (CAP) regression is introduced, which is an optimization-based method for identifying the components predicted by (generalized) linear models of the covariates. We develop computationally efficient algorithms to jointly search the linear projections of the covariance matrices as well as the regression coefficients. We establish the asymptotic properties. Using extensive simulation studies, our method shows higher accuracy and robustness in coefficient estimation than competing methods. Applied to a resting-state functional magnetic resonance imaging study, our approach identifies the human brain network changes associated with age and sex.