Thursday, May 26, 2022 • 3:30–4:45 pm (CT) • Light Hall, Room 202
Organizer: Yize Zhao, Yale University
Chair: Eardi Lila, University of Washington
Bayesian functional graphical models
Lin Zhang, University of Minnesota
Veera Baladandayuthapani, University of Michigan
Quinton Neville, University of Minnesota
Karina Quevedo, University of Minnesota
Jeffrey Morris, University of Pennsylvania
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.
Bayesian supervised clustering of undirected networks to model group-specific impacts of the brain network on human creativity
Sharmistha Guha, Texas A&M University
Rajarshi Guhaniyogi, Texas A&M University
This talk focuses on model-based clustering of subjects based on the shared relationships of subject-specific networks and covariates in scenarios when there are differences in the relationship between networks and covariates for different groups of subjects. It is also of interest to identify the network nodes significantly associated with each covariate in each cluster of subjects.
To address these methodological questions, we propose a novel nonparametric Bayesian mixture modeling framework with an undirected network response and scalar predictors. The symmetric matrix coefficients corresponding to the scalar predictors of interest in each mixture component involve low-rankness and group sparsity within the low-rank structure. While the low-rank structure in the network coefficients adds parsimony and computational efficiency, the group sparsity within the low-rank structure enables drawing inference on network nodes and cells significantly associated with each scalar predictor. Our principled Bayesian framework allows precise characterization of uncertainty in identifying significant network nodes in each cluster. Empirical results in various simulation scenarios illustrate substantial inferential gains of the proposed framework in comparison with competitors. Analysis of a real brain connectome dataset using the proposed method provides interesting insights into the brain regions of interest (ROIs) significantly related to creative achievement in each cluster of subjects. Supplementary material shows the convergence rate for the posterior predictive density of the proposed model.
Thresholded prior for integrating brain regional and network predictors
Zhe Sun, Yale University
Yize Zhao, Yale University
Cognitive development in children or cognitive decline occurs in health and pathological aging and may be preceded by subtle changes in the brain. This observation has prompted the use of brain imaging data to predict the current cognitive functioning of a person or related surrogate markers. Functional Magnetic Resonance Imaging (fMRI) has been proposed as a source of information to study physiological changes that accompany brain activation. In particular, the n-back task is arguably the most ubiquitous cognitive task for investigating working memory performance, a fundamental cognitive function that is highly dependent on the integrity of the prefrontal cortex; The investigation of intrinsic connectivity networks by resting-state fMRI has proven capable of revealing fundamental elements of human brain architecture and organization. Optimal integration of data from different fMRI modalities is an active area of research aimed at increasing diagnostic accuracy. On the other side, how to select features from high-dimensional measures as biomarkers for building a model to predict brain physiology is an important and challenging problem. We build a model to predict cognitive behavior from multimodality brain imaging data, specifically working memory fMRI and resting-state connectivity fMRI, and identify potential biomarkers by imposing a jointly sparse structure. By rank-R PARAFAC decomposition of the coefficient matrix for the network predictor, we could achieve subnetwork topography simultaneously. We apply our method to the Adolescent Brain Cognitive Development (ABCD) Study, and the identified associated region-level and subnetwork-level neuroimaging biomarkers shed lights on the linkage between brain function and cognitive behavior.
