Scalable Bayesian Variable Selection for Structured High-dimensional Data

TL;DR

This paper introduces a scalable Bayesian variable selection method for high-dimensional structured data, leveraging network information to improve selection and prediction in genomics applications.

Contribution

It proposes an adaptive Bayesian shrinkage model with an efficient EM algorithm, capable of handling tens of thousands of variables and providing theoretical guarantees.

Findings

Method outperforms existing approaches in variable selection and prediction.

Scalable to datasets with up to 100,000 variables.

Effective in genomics data analysis.

Abstract

Variable selection for structured covariates lying on an underlying known graph is a problem motivated by practical applications, and has been a topic of increasing interest. However, most of the existing methods may not be scalable to high dimensional settings involving tens of thousands of variables lying on known pathways such as the case in genomics studies. We propose an adaptive Bayesian shrinkage approach which incorporates prior network information by smoothing the shrinkage parameters for connected variables in the graph, so that the corresponding coefficients have a similar degree of shrinkage. We fit our model via a computationally efficient expectation maximization algorithm which scalable to high dimensional settings (p~100,000). Theoretical properties for fixed as well as increasing dimensions are established, even when the number of variables increases faster than the sample size. We demonstrate the advantages of our approach in terms of variable selection, prediction, and computational scalability via a simulation study, and apply the method to a cancer genomics study.