Efficient Group Lasso Regularized Rank Regression with Simulation-Based Tuning

2026-07-14 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

The paper introduces an efficient group lasso regularized rank regression method designed for high-dimensional data prone to heavy-tailed noise and outliers. This approach utilizes a non-smooth Wilcoxon score-based rank objective and incorporates structured group sparsity regularization. A key innovation is a data-driven, simulation-based tuning rule for the regularization parameter, extending a lasso-specific scheme to the group lasso setting, thus avoiding computationally intensive cross-validation. The authors also establish a finite-sample error bound for the estimator. For computation, a proximal augmented Lagrangian method (PALM) is developed, which resolves singularity issues found in existing methods and enables efficient semismooth Newton updates. Numerical experiments on simulated and real-world datasets demonstrate its robustness, effectiveness, and scalability, often completing tasks in half the time or less compared to alternatives like PPMM.

Key takeaway

For Data Scientists working with high-dimensional datasets susceptible to heavy-tailed noise or outliers, consider adopting the group lasso regularized rank regression. This method offers superior robustness and group-level sparsity selection without the computational burden of cross-validation for parameter tuning. You should explore implementing the proposed Proximal Augmented Lagrangian Method (PALM) for its demonstrated efficiency, which can significantly reduce computation time compared to traditional methods like PPMM, especially for large-scale problems.

Key insights

Group lasso rank regression with data-driven tuning offers robust, efficient high-dimensional estimation against heavy-tailed noise.

Principles

• Wilcoxon rank objective improves robustness to outliers.
• Group lasso induces structured sparsity.
• Data-driven tuning avoids cross-validation cost.

Method

The method involves minimizing a Wilcoxon score-based rank objective with group lasso regularization. A simulation-based rule determines the regularization parameter. Optimization uses a proximal augmented Lagrangian method with semismooth Newton updates.

In practice

• Apply to genomics and neuroimaging data.
• Use for high-dimensional feature selection.
• Implement PALM for faster optimization.

Topics

• Group Lasso
• Rank Regression
• High-Dimensional Regression
• Robust Statistics
• Proximal Augmented Lagrangian Method
• Semismooth Newton Method
• Data-Driven Parameter Tuning

Code references

• yunanwu123/TFRE
• YangjingZhang/SparseGroupLasso

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.