Covariate Assisted Principal regression for covariance matrix outcomes

Yi Zhao, Bingkai Wang, Stewart H. Mostofsky, Brian S. Caffo, Xi Luo

Research output: Contribution to journalArticlepeer-review


In this study, we consider the problem of regressing covariance matrices on associated covariates. Our goal is to use covariates to explain variation in covariance matrices across units. As such, we introduce Covariate Assisted Principal (CAP) regression, an optimization-based method for identifying components associated with the covariates using a generalized linear model approach. We develop computationally efficient algorithms to jointly search for common linear projections of the covariance matrices, as well as the regression coefficients. Under the assumption that all the covariance matrices share identical eigencomponents, we establish the asymptotic properties. In simulation studies, our CAP method shows higher accuracy and robustness in coefficient estimation over competing methods. In an example resting-state functional magnetic resonance imaging study of healthy adults, CAP identifies human brain network changes associated with subject demographics.

Original languageEnglish (US)
Pages (from-to)629-645
Number of pages17
Issue number3
StatePublished - Jul 1 2021


  • Common diagonalization
  • Heteroscedasticity
  • Linear projection

ASJC Scopus subject areas

  • General Medicine


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