[Paper Review] Bayesian Mixed Effect Sparse Tensor Response Regression Model with Joint Estimation of Activation and Connectivity

Daniel Spencer, Rajarshi Guhaniyogi+1 more|arXiv (Cornell University)|Mar 30, 2019

Tensor decomposition and applications36 references4 citations

TL;DR

This paper proposes a Bayesian mixed-effects sparse tensor response regression model that jointly estimates voxel-level brain activation and region-of-interest (ROI) connectivity in multi-subject fMRI data. By combining low-rank PARAFAC tensor decomposition with multiway stick-breaking shrinkage priors and a Bayesian Gaussian graphical model, the method enables simultaneous, uncertainty-quantified inference of activation and connectivity patterns, outperforming vectorized alternatives in identifying risk-related brain responses in a balloon-analog risk-taking task.

ABSTRACT

Brain activation and connectivity analyses in task-based functional magnetic resonance imaging (fMRI) experiments with multiple subjects are currently at the forefront of data-driven neuroscience. In such experiments, interest often lies in understanding activation of brain voxels due to external stimuli and strong association or connectivity between the measurements on a set of pre-specified group of brain voxels, also known as regions of interest (ROI). This article proposes a joint Bayesian additive mixed modeling framework that simultaneously assesses brain activation and connectivity patterns from multiple subjects. In particular, fMRI measurements from each individual obtained in the form of a multi-dimensional array/tensor at each time are regressed on functions of the stimuli. We impose a low-rank PARAFAC decomposition on the tensor regression coefficients corresponding to the stimuli to achieve parsimony. Multiway stick breaking shrinkage priors are employed to infer activation patterns and associated uncertainties in each voxel. Further, the model introduces region specific random effects which are jointly modeled with a Bayesian Gaussian graphical prior to account for the connectivity among pairs of ROIs. Empirical investigations under various simulation studies demonstrate the effectiveness of the method as a tool to simultaneously assess brain activation and connectivity. The method is then applied to a multi-subject fMRI dataset from a balloon-analog risk-taking experiment in order to make inference about how the brain processes risk.

Motivation & Objective

• To address the challenge of simultaneously modeling voxel-level brain activation and ROI-level functional connectivity in multi-subject fMRI data.
• To develop a computationally feasible and statistically principled Bayesian framework that preserves the tensor structure of neuroimaging data.
• To enable joint inference of activation and connectivity with quantified uncertainty, avoiding the limitations of separate or vectorized analyses.
• To overcome computational and modeling challenges posed by high-dimensional fMRI data across multiple subjects.
• To provide a flexible, open-source modeling approach applicable beyond neuroimaging to other tensor-valued data.

Proposed method

• A Bayesian mixed-effects tensor response regression model is formulated, with fMRI time series as tensor-valued responses and stimuli as predictors.
• Low-rank PARAFAC decomposition is applied to the tensor regression coefficients to achieve model parsimony and reduce dimensionality.
• Multiway stick-breaking shrinkage priors are used to identify significant activation patterns at the voxel level while quantifying uncertainty.
• Region-specific random effects are modeled jointly with a Bayesian Gaussian graphical model to infer functional connectivity between ROIs.
• Posterior inference is conducted via MCMC sampling, with effective sample size and DIC used to assess convergence and model fit.
• The model is implemented in R using the coda package for posterior diagnostics and visualization of activation and connectivity patterns.

Experimental results

Research questions

• RQ1 Can a unified Bayesian framework jointly estimate voxel-level activation and ROI-level functional connectivity in multi-subject fMRI data?
• RQ2 How does preserving the tensor structure of fMRI data improve inference accuracy compared to vectorized response models?
• RQ3 What is the impact of low-rank tensor decomposition on identifying meaningful activation and connectivity patterns in neuroimaging data?
• RQ4 How well does the model quantify uncertainty in activation and connectivity estimates across different rank models?
• RQ5 Does the inclusion of region-specific random effects and a graphical prior enhance the detection of biologically plausible connectivity networks?

Key findings

• The Rank 3 model achieved the lowest Deviance Information Criterion (DIC) value of 22.5428, indicating the best overall model fit among the five rank models tested.
• The tensor model with Rank 3 produced more differentiated estimates of activation strength than the vectorized GDP model, particularly in the Frontal Lobe, suggesting improved sensitivity.
• Posterior median coefficient estimates revealed that higher perceived risk was associated with increased blood flow in regions such as the Frontal Lobe and Insula, and decreased flow in the Occipital Lobe.
• The model identified significant positive partial correlations between the Frontal Lobe and the Insula, Parietal Lobe, and Putamen, and a significant negative partial correlation with the Occipital Lobe.
• Effective sample sizes for posterior draws were consistently high (median ESS ≥ 845), indicating good mixing and reliable posterior inference.
• The proposed tensor model significantly outperformed the vectorized GDP model in DIC and provided more nuanced, spatially resolved activation and connectivity patterns.