One-at-a-time knockoffs

Area of Science:

• Statistical Learning
• Computational Statistics
• Genomics

Background:

• Variable selection is crucial in linear regression for identifying important predictors.
• Controlling the false discovery rate (FDR) is essential for reliable statistical inference.
• Existing methods like the knockoff filter can be computationally intensive and complex.

Purpose of the Study:

• To propose a new methodology, one-at-a-time knockoffs (OATK), for variable selection in linear regression.
• To provide a computationally efficient and simplified alternative to the standard knockoff filter.
• To ensure robust control of the false discovery rate (FDR) while maximizing statistical power.

Main Methods:

• OATK generates knockoff variables by replacing one column at a time in the design matrix, preserving the Gram matrix.
• Variable importance is assessed by comparing coefficients derived from original and knockoff data.
• Theoretical guarantees for FDR control are established under mild correlation assumptions.

Main Results:

• OATK demonstrates effective FDR control across simulations and a real genetic dataset.
• The method consistently achieves higher statistical power compared to existing approaches.
• In a genome-wide association study, OATK identified more significant genetic mutations related to HIV treatment response.

Conclusions:

• OATK is a powerful and computationally advantageous method for variable selection with FDR control.
• Its one-at-a-time approach simplifies implementation and enables further enhancements.
• The methodology shows promise for applications in genomics and other high-dimensional data analyses.