16: Bayesian Multi-tasking Inference using High-dimensional Correlated Functional Variable Networks

Music City Center 

While functional variable selection plays an important role in reducing the dimension of variables, the development of simultaneous selections of functional domain subsets and the identification of functional graphical nodes are still quite limited. Functional variable selection for recovering sparsity in nonadditive and nonparametric models with high dimensional variables has been challenging. Our main interest is to identify subsets on the domain of the functional covariates and graph structure among locations and test the significant association of subsets and graph selection with response. No existing functional variable selection methods can conduct these multi-tasking inferences. In this presentation, we develop a Bayesian multi-tasking inference method under a joint functional kernel graphical model framework. Our method unifies Bayesian optimization, an Ising graphical model, and score-type test using a Bayesian approach so that we can perform (1) selection of subsets within the domain of the functional covariates, (2) the identification of relevant brain locations to correct for the confounding effect of correlation between the signals, and (3) test the significance of selection and identification. The advantage of our multi-tasking inference method is demonstrated using simulation and our motivating example of fMRI in autism spectrum disorder.