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Title: Connectivity regression via covariate assisted principal regression Authors:  Xi Luo - Univ of Texas Health Science Center at Houston (United States) [presenting]
Yi Zhao - Indiana University (United States)
Brian Caffo - Johns Hopkins University (United States)
Bingkai Wang - Johns Hopkins University (United States)
Stewart Mostofsky - Kennedy Krieger Institute (United States)
Abstract: Modeling covariance matrices as outcomes has been an important topic in many fields, including in financial and neuroimaging analysis. 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. A covariate-assisted principal regression framework is introduced that identifies the components predicted by the covariates through a generalized linear model type link function. We develop computationally efficient optimization algorithms to jointly search the linear projections of the covariance matrices as well as the regression coefficients, and we establish the asymptotic properties. Using extensive simulation studies, our method shows higher accuracy and robustness in coefficient estimation than competing methods. We will illustrate extensions of this framework for high dimensional and longitudinal settings. Applied to a resting-state functional magnetic resonance imaging study, our approach identifies the human brain network changes associated with covariates.