Bayesian estimation of covariate assisted principal regression for brain functional connectivity

Area of Science:

• Statistics
• Machine Learning
• Neuroimaging Analysis

Background:

• Covariance matrices are crucial for understanding data relationships.
• Existing methods may not fully capture covariate-dependent structures in covariance.
• Analyzing high-dimensional covariance data with covariates presents challenges.

Purpose of the Study:

• To develop a Bayesian approach for covariate-assisted principal regression with covariance matrix outcomes.
• To identify low-dimensional structures in covariance matrices influenced by covariates.
• To model and quantify covariance heterogeneity based on covariates.

Main Methods:

• Bayesian reformulation of principal regression.
• Geometric approach to covariance matrices using Euclidean geometry.
• Joint estimation and uncertainty quantification of parameters related to heteroscedasticity.

Main Results:

• Successfully identified low-dimensional components in covariance matrices associated with covariates.
• Enabled modeling of covariance heterogeneity driven by covariates.
• Demonstrated effective joint estimation and uncertainty quantification.

Conclusions:

• The proposed Bayesian method provides a robust framework for analyzing covariate-assisted covariance matrices.
• The approach enhances understanding of covariate effects on data variability.
• Applicable to complex datasets, including neuroimaging data for brain functional connectivity analysis.