A pseudo knockoff filter for correlated features

In 2015, Barber and Candes introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and prove that this method achieves exact FDR control. Inspired by the work of Barber and Candes (2015), we propose and analyze a pseudo-knockoff filter that inherits some advantages of the original knockoff filter and has more flexibility in constructing its knockoff matrix. Moreover, we perform a number of numerical experiments that seem to suggest that the pseudo knockoff filter with the half Lasso statistic has FDR control and offers more power than the original knockoff filter with the Lasso Path or the half Lasso Statistic for the numerical examples that we consider in this paper. Although we cannot establish rigorous FDR control for the pseudo knockoff filter, we provide some partial analysis of the pseudo knockoff filter with the half Lasso statistic and establish a uniform FDP bound and an expectation inequality.