# High-Dimensional False Discovery Rate Control for Dependent Variables

arXiv: https://arxiv.org/abs/2401.15796 · HTML: https://mlsanity.com/paper/2401.15796/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 53 references that are in the map.
- First posted on arXiv 28 Jan 2024.

## Builds on (most cited first, 10 of 10)

- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Gene Hunting with Knockoffs for Hidden Markov Models](https://mlsanity.com/paper/1706.04677/) (2017)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)
- [Derandomizing Knockoffs](https://mlsanity.com/paper/2012.02717/) (2020)
- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [Sparse PCA with False Discovery Rate Controlled Variable Selection](https://mlsanity.com/paper/2401.08375/) (2024)
- [False Discovery Rate Control for Gaussian Graphical Models via Neighborhood Screening](https://mlsanity.com/paper/2401.09979/) (2024)

## Built on by (most cited first, 3 of 3)

- [Reproducible Physiological Features in Affective Computing: A Preliminary Analysis on Arousal Modeling](https://mlsanity.com/paper/2508.10561/) (2025)
- [Learning False Discovery Rate Control via Model-Based Neural Networks](https://mlsanity.com/paper/2602.05798/) (2026)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)

## Abstract (arXiv)

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged, providing guarantees even in high-dimensional settings where the number of variables surpasses the number of samples. However, these methods often fail to reliably control the FDR in the presence of highly dependent variable groups, a common characteristic in fields such as genomics and finance. To tackle this critical issue, we introduce a novel framework that accounts for general dependency structures. Our proposed dependency-aware T-Rex selector integrates hierarchical graphical models within the T-Rex framework to effectively harness the dependency structure among variables. Leveraging martingale theory, we prove that our variable penalization mechanism ensures FDR control. We further generalize the FDR-controlling framework by stating and proving a clear condition necessary for designing both graphical and non-graphical models that capture dependencies. Additionally, we formulate a fully integrated optimal calibration algorithm that concurrently determines the parameters of the graphical model and the T-Rex framework, such that the FDR is controlled while maximizing the number of selected variables. Numerical experiments and a breast cancer survival analysis use-case demonstrate that the proposed method is the only one among the state-of-the-art benchmark methods that controls the FDR and reliably detects genes that have been previously identified to be related to breast cancer. An open-source implementation is available within the R package TRexSelector on CRAN.