A Power Analysis for Model-X Knockoffs with $\ell_{p}$-Regularized Statistics

Understand

Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high dimensional linear regression problems.

• Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance.
• Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact asymptotic predictions of the type I-type II error tradeoff for selection procedures that rely on $\ell_{p}$-regularized estimators.
• In practice, effective ranking by itself is often not sufficient because some calibration for Type I error is required.