$\text{G}^2\text{M}$: A Generalized Gaussian Mirror Method to Boost Feature Selection Power
Hongyu Shen, Zhizhen Jane Zhao
Recent advances in false discovery rate (FDR)-controlled methods have enhanced reliability by limiting false positives, making them particularly suitable for applications in complex scenarios. This paper identifies the limitation of a so-called "mirror statistics" that is introduced in a prominent FDR-controlled framework---data splitting. Particularly, the paper addresses a unit variance constraint on the mirror test statistics that potentially reduces the feature selection power. From another angle, we generalize the mirror statistics with the Gaussian mirror framework, considering the variance information in forming a new test statistics, and name it the "generalized Gaussian mirror" ($\text{G}^2\text{M}$) method. We demonstrate both theoretically and empirically that the proposed test statistics achieves higher power than those of Gaussian mirror and data splitting. Comparisons with other FDR-controlled frameworks across synthetic, semi-synthetic, and real datasets highlight the superior performance of the $\text{G}^2\text{M}$ method in achieving higher power while maintaining FDR control. These findings suggest the potential for the $\text{G}^2\text{M}$ method for practical applications in real-world problems.