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Activity Number: 509 - Statistical Methodology
Type: Contributed
Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #304440
Title: Covariate Assisted Principal Regression for Covariance Matrix Outcomes
Author(s): Yi Zhao* and Bingkai Wang and Stewart Mostofsky and Brian Caffo and Xi Luo
Companies: Johns Hopkins Bloomberg School of Public Health and Johns Hopkins Bloomberg School of Public Health and Johns Hopkins University and Johns Hopkins Bloomberg School of Public Health and The University of Texas Health Science Center at Houston
Keywords: covariance regression; common diagonalization; heteroscedasticity; linear projection

Modeling variances in data has been an important topic in many fields, including in financial and neuroimaging analysis. We consider the problem of regressing covariance matrices on a 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. This study introduces Covariate Assisted Principal (CAP) regression, 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 projection directions and regression coefficients, and 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 meaningful findings and equips network-level interpretations.

Authors who are presenting talks have a * after their name.

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