# Efficient Group Lasso Regularized Rank Regression with Simulation-Based Tuning

arXiv: https://arxiv.org/abs/2510.11546 · HTML: https://mlsanity.com/paper/2510.11546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Adaptive Huber Regression](https://mlsanity.com/paper/1706.06991/) (2017)
- [Can parametric statistical methods be trusted for fMRI based group studies?](https://mlsanity.com/paper/1511.01863/) (2015)
- [A Unified Approach to Error Bounds for Structured Convex Optimization Problems](https://mlsanity.com/paper/1512.03518/) (2015)
- [An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems](https://mlsanity.com/paper/1712.05910/) (2017)
- [An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for Linear Programming](https://mlsanity.com/paper/1903.09546/) (2019)
- [On efficiently solving the subproblems of a level-set method for fused lasso problems](https://mlsanity.com/paper/1706.08732/) (2017)
- [GroupCDL: Interpretable Denoising and Compressed Sensing MRI via Learned Group-Sparsity and Circulant Attention](https://mlsanity.com/paper/2407.18967/) (2024)

## Abstract (arXiv)

High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate the group sparsity regularization. By extending the tuning-free property originally developed for the rank Lasso, we introduce a simulation-based tuning rule and further establish a finite-sample error bound for the resulting estimator. To solve the associated optimization problem, we develop a proximal augmented Lagrangian method, for which we provide a novel convergence analysis by proving the metric subregularity of the underlying non-polyhedral KKT mapping, while enabling efficient semismooth Newton updates for the subproblems. Extensive numerical experiments demonstrate the robustness and effectiveness of our proposed estimator against several leading alternatives, and showcase the efficiency and scalability of our algorithm compared to the state-of-the-art baseline in both simulated and real-data settings.