FANOK: Knockoffs in Linear Time
This work addresses the scalability problem for researchers and practitioners using knockoffs for false discovery rate control in high-dimensional data.
The paper tackles the computational challenge of implementing Gaussian model-X knockoffs for large-scale feature selection by developing efficient algorithms that reduce complexity from O(p^3) to O(pk^2) and linear in dimension, enabling testing on problems with up to 500,000 features.
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 the knockoff distribution requires solving a large scale semidefinite program for which we derive several efficient methods. One handles generic covariance matrices, has a complexity scaling as $O(p^3)$ where $p$ is the ambient dimension, while another assumes a rank $k$ factor model on the covariance matrix to reduce this complexity bound to $O(pk^2)$. We also derive efficient procedures to both estimate factor models and sample knockoff covariates with complexity linear in the dimension. We test our methods on problems with $p$ as large as $500,000$.