Group variable selection via convex Log-Exp-Sum penalty with application to a breast cancer survivor study

TL;DR

This paper introduces a convex Log-Exp-Sum penalty for group variable selection that effectively identifies important groups and variables within groups, with proven theoretical guarantees and successful application to breast cancer survivor data.

Contribution

It proposes a novel convex penalty method for simultaneous group and within-group variable selection, addressing limitations of non-convex approaches.

Findings

Accurate identification of important groups and variables.

The method achieves good prediction performance.

Clinically meaningful insights from breast cancer data.

Abstract

In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. Among existing successful group variable selection methods, some methods fail to conduct the within group selection. Some methods are able to conduct both group and within group selection, but the corresponding objective functions are non-convex. Such a non-convexity may require extra numerical effort. In this paper, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting where the number of covariates can be much larger than the sample size. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and lead immediately to testable clinical hypotheses.