Bayesian Multiresolution Variable Selection for Ultra-High Dimensional Neuroimaging Data

Abstract

Ultra-high dimensional variable selection has become increasingly important in analysis of neuroimaging data. For example, in the Autism Brain Imaging Data Exchange (ABIDE) study, neuroscientists are interested in identifying important biomarkers for early detection of the autism spectrum disorder (ASD) using high resolution brain images that include hundreds of thousands voxels. However, most existing methods are not feasible for solving this problem due to their extensive computational costs. In this work, we propose a novel multiresolution variable selection procedure under a Bayesian probit regression framework. It recursively uses posterior samples for coarser-scale variable selection to guide the posterior inference on finer-scale variable selection, leading to very efficient Markov chain Monte Carlo (MCMC) algorithms. The proposed algorithms are computationally feasible for ultra-high dimensional data. Also, our model incorporates two levels of structural information into variable selection using Ising priors: the spatial dependence between voxels and the functional connectivity between anatomical brain regions. Applied to the resting state functional magnetic resonance imaging (R-fMRI) data in the ABIDE study, our methods identify voxel-level imaging biomarkers highly predictive of the ASD, which are biologically meaningful and interpretable. Extensive simulations also show that our methods achieve better performance in variable selection compared to existing methods.

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

“…For instance, Bezener et al (2018) use pre-defined regions to aggregate voxels and reduce the dimension of the spatial field underlying fMRI data while maintaining spatial dependence. Zhao et al (2018) mitigate the computational burden with a multi-resolution MCMC approach that successively refines resolutions in interesting areas of a brain image. Heaton et al (2018) review many large scale Gaussian process techniques that have been proposed recently.…”

Randomized block-coordinate adaptive algorithms for nonconvex optimization problems

“…Deep learning has achieved great success in many domains including image recognition [1,2], natural language processing [3,4], constrained learning [5], and intelligent decision [6,7]. On the other hand, deep neural networks are typically of high complexity with ultra-high-dimensional features [8,9,10]. To solve optimization problems in deep learning tasks is thus becoming increasingly difficult due to prohibitive computations as well as the unpopularity of expensive high-performance devices.…”

Bayesian Interaction Selection Model for Multimodal Neuroimaging Data Analysis

“…Recently, Zhao et al. (2018) has developed a multiresolution‐based Bayesian variable selection model and showed an improved posterior mixing and feature selection accuracy for ultra‐high dimensional imaging data. One of the limitations of this method is the resolution parameters are not connected within a joint inference paradigm, leading to hurdles for the fine‐scale parameters to explore the whole sample space.…”

“…Such a multilevel learning idea has been adopted previously to construct model stages under different scales to optimize computational efficiency and refine model estimation (Kou et al, 2012). Recently, Zhao et al (2018) has developed a multiresolution-based Bayesian variable selection model and showed an improved posterior mixing and feature selection accuracy for ultra-high dimensional imaging data. One of the limitations of this method is the resolution parameters are not connected within a joint inference paradigm, leading to hurdles for the fine-scale parameters to explore the whole sample space.…”