Bayesian scalar-on-image regression via random image partition models: automatic identification of regions of interest

Abstract

Scalar-on-image regression aims to investigate changes in a scalar response of interest based on high-dimensional imaging data. These problems are increasingly prevalent in numerous domains, particularly in biomedical studies. For instance, they aim to utilise medical imaging data to capture and study the complex pattern of changes associated with disease to improve diagnostic accuracy. Due to the massive dimension of the images, which can often be in millions, combined with modest sample sizes, typically in the hundreds in most biomedical studies, pose serious challenges. Specifically, scalar-on-image regression belongs to the “large p, small n” paradigm, and hence, many models utilise shrinkage methods. However, neighbouring pixels in images are highly correlated, making standard regression methods, even with shrinkage, problematic due to multicollinearity and the high number of nonzero coefficients. We propose a novel Bayesian scalar-on-image regression model that utilises spatial coordinates of the pixels to group them with similar effects on the response to have a common coefficient, thus, allowing for automatic identification of regions of interest in the image for predicting the response of interest. In this thesis, we explore two classes of priors for the spatially-dependent partition process, namely, Potts-Gibbs random partition models (Potts-Gibbs) and Ewens-Pitman attraction (EPA) distribution and provide a thorough comparison of the models.

In addition, Bayesian shrinkage priors are utilised to identify the covariates and regions that are most relevant for the prediction. The proposed model is illustrated using the simulated data sets and to identify brain regions of interest in Alzheimer’s disease.