Spatial Bayesian variable selection and grouping for high-dimensional scalar-on-image regression

Abstract

Multi-subject functional magnetic resonance imaging (fMRI) data has been increasingly used to study the population-wide relationship between human brain activity and individual biological or behavioral traits. A common method is to regress the scalar individual response on imaging predictors, known as a scalar-on-image (SI) regression. Analysis and computation of such massive and noisy data with complex spatio-temporal correlation structure is challenging. In this article, motivated by a psychological study on human affective feelings using fMRI, we propose a joint Ising and Dirichlet Process (Ising-DP) prior within the framework of Bayesian stochastic search variable selection for selecting brain voxels in high-dimensional SI regressions. The Ising component of the prior makes use of the spatial information between voxels, and the DP component groups the coefficients of the large number of voxels to a small set of values and thus greatly reduces the posterior computational burden. To address the phase transition phenomenon of the Ising prior, we propose a new analytic approach to derive bounds for the hyperparameters, illustrated on 2-and 3-dimensional lattices. The proposed method is compared with several alternative methods via simulations, and is applied to the fMRI data collected from the KLIFF hand-holding experiment.

Radiologic Image-Based Statistical Shape Analysis of Brain Tumours

“…Recent studies of scalar‐on‐image regression models in neuroimaging data applications incorporated the entire image (see, for example, Reiss and Ogden (), Li et al . () and Goldsmith et al . ()); such methods are not applicable in the current setting since MRIs of GBM tumours cannot even be coregistered.…”

Bayesian Analysis of Functional Magnetic Resonance Imaging Data with Spatially Varying Auto-Regressive Orders

“…To avoid the phase transition boundary, we adopt an analytical approach similar to Li et al . () to quantify the value for the bounds of both β 0 p and β 1 p . An outline of the bound derivation is given below in Section .…”

“…Here, we adopt an approach that is similar to that considered in Li et al . () and construct some theoretical bounds to prevent phase transition. The resulting hyperparameter values are then chosen as fixed values within the estimated bounds.…”

“…To avoid the phase transition problem that is associated with the Ising model, we derive theoretical bounds as in Li et al . () and use these bounds to prevent critical slowing of the algorithm. We compare our model with the GLM–AR model of Penny et al .…”

MWPCR: Multiscale Weighted Principal Component Regression for High-Dimensional Prediction

“…Many existing supervised learning and variable selection methods (Hastie et al, 2009; Clarke et al, 2009; Fan and Fan, 2008; Bickel and Levina, 2004; Buhlmann et al, 2012; Tibshirani, 1996), however, can be sub-optimal for high-dimensional prediction problem considered here, since the effect of high dimensional data x (e.g., image biomarker) on y is often non-sparse (Li et al, 2015; Zhou et al, 2013; Friston, 2009; Hinrichs et al, 2009). First, the existing unstructured regularization methods can suffer from diverging spectra and noise accumulation in high dimensional feature space (Reiss and Ogden, 2010; Bickel and Levina, 2004; Buhlmann et al, 2012; Fan and Fan, 2008), whereas the structured ones (e.g., fused Lasso or Ising prior) can be computationally challenging for high-dimensional imaging predictor (Vincent et al, 2011; Cuingnet et al, 2012; Fan et al, 2012; Goldsmith et al, 2014).…”