GAP: A General Framework for Information Pooling in Two-Sample Sparse Inference

Abstract

This article develops a general framework for exploiting the sparsity information in two-sample multiple testing problems. We propose to first construct a covariate sequence, in addition to the usual primary test statistics, to capture the sparsity structure, and then incorporate the auxiliary covariates in inference via a three-step algorithm consisting of grouping, adjusting and pooling (GAP). The GAP procedure provides a simple and effective framework for information pooling. An important advantage of GAP is its capability of handling various dependence structures such as those arise from high-dimensional linear regression, differential correlation analysis, and differential network analysis. We establish general conditions under which GAP is asymptotically valid for false discovery rate control, and show that these conditions are fulfilled in a range of settings, including testing multivariate normal means, high-dimensional linear regression, differential covariance or correlation matrices, and Gaussian graphical models. Numerical results demonstrate that existing methods can be significantly improved by the proposed framework. The GAP procedure is illustrated using a breast cancer study for identifying gene–gene interactions.

Keywords:

• Adjusted p-value
• Covariate-assisted Inference
• Dependent tests
• False discovery rate
• Multiple testing with groups
• Uncorrelated screening

Additional information

Funding

The research of Yin Xia was supported in part by NSFC Grants 11771094, 11690013 and “The Recruitment Program of Global Experts” Youth Project. The research of Tony Cai was supported in part by NSF grant DMS-1712735 and NIH grants R01-GM129781 and R01-GM123056. The research of Wenguang Sun was supported in part by NSF grant DMS-CAREER 1255406