An Efficient Algorithm for Nonlinear Regression Problems With Huber Loss

• 成果类型: Article
• 署名作者: Chen, Guang-Yong; Su, Xiang-Xiang; Gan, Min; Xue, Peng; Liao, Yi; Chen, C. L. Philip
• 署名单位: Fuzhou University; Qingdao University; South China University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2026.3683294
• 发表日期: 2026
• 关键词: VARIABLE PROJECTION; least-squares; robust; identification; networks

摘要

Nonlinear regression models are essential in various fields, such as system identification, data analysis, and signal processing. Despite their importance, the efficiency of robust parameter estimation is hindered by inherent nonlinearity and nonsmoothness. This article presents an efficient and robust parameter estimation algorithm for nonlinear regression problems by utilizing the smooth Huber loss instead of the L-1 loss. We begin by analyzing the structural characteristics of nonlinear regression with Huber loss, partitioning the parameters into linear and nonlinear components. A key theorem regarding residuals is then established, which aids in addressing the coupling between parameters during optimization. Building on these insights, we introduce the Huber variable projection (HuVP) algorithm, a novel variable projection method that efficiently handles parameter coupling and optimizes in lower dimensional spaces. The convergence properties of HuVP are analyzed, showing that it inherits the advantages of the traditional variable projection algorithm. Numerical experiments demonstrate the effectiveness and robustness of HuVP across different scenarios.