FANOK: Knockoffs in Linear Time

We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large-scale feature selection problems. Identifying knockoff distribution requires solving semidefinite program for which we derive several efficient methods. One handles generic covariance matrices and has complexity scaling as $\mathcal{O}(p^3)$, where $p$ is ambient dimension, while another assumes rank-$k$ factor model matrix reduce this bound $\mathcal{O}(pk^2)$. review an procedure estimate models show under assumption, can sample covariates with linear in dimension. test our methods problems large 500 000.