Hard Thresholding Pursuit Algorithms for Least Absolute Deviations Problem

2026-01-10

arXiv.org

AI Summary

This work proposes a fully parameter-free, graded fast hard thresholding pursuit algorithm (GFHTP₁) for efficient and robust sparse signal recovery from measurements corrupted by outliers of arbitrary magnitude. By integrating the least absolute deviation criterion with an adaptive iterative hard thresholding strategy, the method eliminates the need for prior knowledge of sparsity level or manual parameter tuning, thereby achieving fully adaptive robust recovery. Unlike existing approaches that rely on sparsity priors or careful parameter selection, GFHTP₁ operates entirely without such assumptions, offering enhanced practicality in real-world scenarios. Experimental results demonstrate that the proposed algorithm consistently outperforms state-of-the-art methods in both robustness against severe outliers and computational efficiency, making it a compelling solution for robust sparse recovery under challenging measurement conditions.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Least absolute deviations (LAD) is a statistical optimality criterion widely utilized in scenarios where a minority of measurements are contaminated by outliers of arbitrary magnitudes. In this paper, we delve into the robustness of the variant of adaptive iterative hard thresholding to outliers, known as graded fast hard thresholding pursuit (GFHTP$_1$) algorithm. Unlike the majority of the state-of-the-art algorithms in this field, GFHTP$_1$ does not require prior information about the signal's sparsity. Moreover, its design is parameterless, which not only simplifies the implementation process but also removes the intricacies of parameter optimization. Numerical experiments reveal that the GFHTP$_1$ algorithm consistently outperforms competing algorithms in terms of both robustness and computational efficiency.

Problem

• Least Absolute Deviations
• Outliers
• Robustness
• Sparsity
• Hard Thresholding

Innovation

• Hard Thresholding Pursuit
• Least Absolute Deviations
• Outlier Robustness
• Parameter-Free Algorithm
• Sparsity-Free