  Model-X knockoff, among various feature selection methods, received much
attention recently due to its guarantee on false discovery rate (FDR) control.
Subsequent to its introduction in parametric design, knockoff is advanced to
handle arbitrary data distributions using deep learning-based generative
modeling. However, we observed that current implementations of the deep Model-X
knockoff framework exhibit limitations. Notably, the "swap property" that
knockoffs necessitate frequently encounter challenges on sample level, leading
to a diminished selection power. To overcome, we develop "Deep Dependency
Regularized Knockoff (DeepDRK)", a distribution-free deep learning method that
strikes a balance between FDR and power. In DeepDRK, a generative model
grounded in a transformer architecture is introduced to better achieve the
"swap property". Novel efficient regularization techniques are also proposed to
reach higher power. Our model outperforms other benchmarks in synthetic,
semi-synthetic, and real-world data, especially when sample size is small and
data distribution is complex.
