Sparse Bayesian Grouped Regression with Application to Genome-Wide Association Studies

Abstract

Statistical variable selection, also known as feature selection, has become an indispensable tool in many research areas involving machine learning and data mining. The object of statistical variable selection is to select the best subset of predictors for fitting or predicting the response variable from a potentially large collection of candidate predictors. It is particularly important in high-dimensional problems such as cancer genetics, where there are potentially thousands of predictors and only a few are associated with the outcome. Moreover, predictors may have underlying group structures in them, so it is desirable to take the underlying group effects into consideration when performing variable selection and handle the grouping structure present in the model when selecting important variables.

This thesis presents a Bayesian grouped regression model with continuous global-local shrinkage priors to tackle the high-dimensional variable selection problem by introducing shrinkage parameters at the group level as well as within each group. This model is able to handle complex group hierarchies that include overlapping and multilevel group structures, and also enjoys the advantages of handling sparsity as well as strong signals. The proposed method is also applied to a real high-dimensional GWAS breast cancer dataset, Haiman-Hopper dataset, to analyse the breast cancer genome-wide association study.