Marginal false discovery rates for penalized regression models

TL;DR

This paper introduces a method for estimating marginal false discovery rates in penalized regression models, enabling more reliable feature selection in high-dimensional data analysis.

Contribution

It proposes a novel approach to assess feature selection reliability using marginal FDR, which is easier to estimate and more scalable to high dimensions than classical methods.

Findings

Marginal FDR estimation is accurate with mild predictor correlation.

The method is slightly conservative with stronger predictor correlation.

Application to gene expression and GWAS data demonstrates practical utility.

Abstract

Penalized regression methods are an attractive tool for high-dimensional data analysis, but their widespread adoption has been hampered by the difficulty of applying inferential tools. In particular, the question "How reliable is the selection of those features?" has proved difficult to address. In part, this difficulty arises from defining false discoveries in the classical, fully conditional sense, which is possible in low dimensions but does not scale well to high-dimensional settings. Here, we consider the analysis of marginal false discovery rates for penalized regression methods. Restricting attention to the marginal FDR permits straightforward estimation of the number of selections that would likely have occurred by chance alone, and therefore provides a useful summary of selection reliability. Theoretical analysis and simulation studies demonstrate that this approach is quite accurate when the correlation among predictors is mild, and only slightly conservative when the correlation is stronger. Finally, the practical utility of the proposed method and its considerable advantages over other approaches are illustrated using gene expression data from The Cancer Genome Atlas and GWAS data from the Myocardial Applied Genomics Network.