# Beyond False Discovery Rate: A Stepdown Group SLOPE Approach for Grouped Variable Selection

arXiv: https://arxiv.org/abs/2603.00955 · HTML: https://mlsanity.com/paper/2603.00955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 63 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [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)
- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [DeepPINK: reproducible feature selection in deep neural networks](https://mlsanity.com/paper/1809.01185/) (2018)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Robust inference with knockoffs](https://mlsanity.com/paper/1801.03896/) (2018)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [Gaussian Process Neural Additive Models](https://mlsanity.com/paper/2402.12518/) (2024)
- [False Discovery Rate Control via Debiased Lasso](https://mlsanity.com/paper/1803.04464/) (2018)
- [The Strong Screening Rule for SLOPE](https://mlsanity.com/paper/2005.03730/) (2020)
- [Sparse-group SLOPE: adaptive bi-level selection with FDR-control](https://mlsanity.com/paper/2305.09467/) (2023)
- [Solving the OSCAR and SLOPE Models Using a Semismooth Newton-Based Augmented Lagrangian Method](https://mlsanity.com/paper/1803.10740/) (2018)
- [Coordinate Descent for SLOPE](https://mlsanity.com/paper/2210.14780/) (2022)
- [Sparse Graphical Modelling via the Sorted L1-Norm](https://mlsanity.com/paper/2204.10403/) (2022)
- [False Discovery Rates in Biological Networks](https://mlsanity.com/paper/1907.03808/) (2019)
- [Structure Learning of Gaussian Markov Random Fields with False Discovery Rate Control](https://mlsanity.com/paper/1910.10860/) (2019)
- [Error-based Knockoffs Inference for Controlled Feature Selection](https://mlsanity.com/paper/2203.04483/) (2022)
- [Group SLOPE Penalized Low-Rank Tensor Regression](https://mlsanity.com/paper/2208.11391/) (2022)

## Abstract (arXiv)

High-dimensional feature selection is routinely required to balance statistical power with strict control of multiple-error metrics such as the k-Family-Wise Error Rate (k-FWER) and the False Discovery Proportion (FDP), yet some existing frameworks are confined to the narrower goal of controlling the expected False Discovery Rate (FDR) and can not exploit the group-structure of the covariates, such as Sorted L-One Penalized Estimation (SLOPE). We introduce the Group Stepdown SLOPE, a unified optimization procedure which is capable of embedding the Lehmann-Romano stepdown rules into SLOPE to achieve finite-sample guarantees under k-FWER and FDP thresholds. Specifically, we derive closed-form regularization sequences under orthogonal designs that provably bound k-FWER and FDP at user-specified levels, and extend these results to grouped settings via gk-SLOPE and gF-SLOPE, which control the analogous group-level errors gk-FWER and gFDP. For non-orthogonal general designs, we provide a calibrated data-driven sequence inspired by Gaussian approximation and Monte-Carlo correction, preserving convexity and scalability. Extensive simulations are conducted across sparse, correlated, and group-structured regimes. Empirical results corroborate our theoretical findings that the proposed methods achieve nominal error control, while yielding markedly higher power than competing stepdown procedures, thereby confirming the practical value of the theoretical advances.