Bayesian Functional Graphical Models

• Activity Number: 502 - Recent Developments in Modeling of Multivariate Functional Data
• Type: Invited
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Lin Zhang* and Veera Baladandayuthapani and Quinton Neville and Karina Quevedo and Jeffrey Morris
• Companies: University of Minnesota and University of Michigan and University of Minnesota and University of Minnesota and University of Pennsylvania
• Keywords: Bayesian graphical modeling; functional data; functional graphical model; hypoexponential; shrinkage priors

Abstract

We develop a Bayesian functional graphical modeling framework for correlated multivariate functional data, which allows the graphs to vary over the functional domain. The model involves estimation of graphical models that evolve functionally in a nonparametric fashion while accounting for within-functional correlations and borrowing strength across functional positions so contiguous locations are encouraged but not forced to have similar graph structure and edge strength. We utilize a strategy that combines nonparametric basis function modeling with modified Bayesian graphical regularization techniques, which induces a new class of hypoexponential normal scale mixture distributions that not only leads to adaptively shrunken estimators of the conditional cross-covariance but also facilitates a thorough theoretical investigation of the shrinkage properties. Our approach scales up to large functional datasets collected on a fine grid. We show through simulations and real data analysis that the Bayesian functional graphical model can efficiently reconstruct the functionally--evolving graphical models by accounting for within-function correlations.