Title: A Pseudo Knockoff Filter for Correlated Features,
Abstract: 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. Although we have not been able to obtain
exact FDR control of the pseudo knockoff filter, we show that it satisfies an
expectation inequality that offers some insight into FDR control. Moreover, we
provide some partial analysis of the pseudo knockoff filter for the half Lasso
and the least squares statistics. Our analysis indicates that the inverse of
the covariance matrix of the feature matrix plays an important role in
designing and analyzing the pseudo knockoff filter. Our preliminary numerical
experiments show that the pseudo knockoff filter with the half Lasso statistic
has FDR control. Moreover, our numerical experiments show that the
pseudo-knockoff filter could offer more power than the original knockoff filter
with the OMP or Lasso Path statistic when the features are correlated and
non-sparse.