Chapter 2 - Kernel machine regression in neuroimaging genetics

Abstract

This chapter reviews the mathematical basis and recent development of kernel machine regression, a machine learning technique that is particularly powerful in studying nonlinear relations in multidimensional data. We start with an intuitive explanation of kernel methods from the perspective of linear regression analysis and provide an illustrative synthetic example. We then formally introduce the kernel machine regression framework, establish its connection to mixed effects models in statistics, derive model fitting and statistical inference procedures, and highlight some recent theoretical extensions. Applications of kernel machine regression to biomedical research are selectively reviewed, with a focus on genetic association studies and imaging genetics, to demonstrate its generality, flexibility and computational efficiency in handling high-dimensional data and detecting complex associations. We close the chapter with a discussion of future directions. A rigorous mathematical treatment of the kernel methods and some technical aspects of the material presented in this chapter are provided in the appendix.