# RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs

arXiv: https://arxiv.org/abs/1709.00092 · HTML: https://mlsanity.com/paper/1709.00092/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2017.

## Built on by (most cited first, 6 of 6)

- [Sequential Knockoffs for Variable Selection in Reinforcement Learning](https://mlsanity.com/paper/2303.14281/) (2023)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)
- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)
- [DeepLINK-T: deep learning inference for time series data using knockoffs and LSTM](https://mlsanity.com/paper/2404.04317/) (2024)
- [Error-based Knockoffs Inference for Controlled Feature Selection](https://mlsanity.com/paper/2203.04483/) (2022)
- [Sparse minimum Redundancy Maximum Relevance for feature selection](https://mlsanity.com/paper/2508.18901/) (2025)

## Abstract (arXiv)

Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model-free knockoffs procedure introduced recently in Cand`es, Fan, Janson and Lv (2016) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-free knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs procedure.