UAlberta Math and Statistics Colloquium: Eardi Lila

A novel statistical method is presented for the integrative analysis of Riemannian-valued and high-dimensional functional data. This model is motivated by the need to model the dependence structure between each subject's dynamic functional connectivity -- represented by a temporally indexed collection of positive definite covariance matrices -- and high-dimensional data representing lifestyle, demographic, and psychometric measures. We employ a regression-based reformulation of canonical correlation analysis that allows us to control the complexity of the functional canonical directions within a Riemannian framework, using tangent space sieve approximations, and that of the high-dimensional canonical directions via a sparsity-promoting penalty. The proposed method shows improved empirical performance over alternative approaches. Its application to data from the Human Connectome Project reveals a dominant mode of covariation between dynamic functional connectivity and lifestyle, demographic, and psychometric measures. This mode aligns with results from static connectivity studies but reveals a unique temporal non-stationary pattern that such studies fail to capture.