Graph Huber: a robust regression model for graph data

G-Huber: 一种面向图数据的鲁棒回归模型

¹ School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024, China
² School of Mathematics, Northwestern University, Xi'an 710100, China

Received: 24 January 2024

Abstract

As it is increasingly prevalent that data contains noise or obeys heavy-tailed distribution, a robust regression model becomes one of focal and hot topics in many study fields. However, most existing robust regression models are based on the assumption of sample independence and negligent of the correlation between samples, thus being unable to be effectively used to solve a graph data problem. Therefore, this paper uses graphs to represent the correlation between samples and studies robust regression models oriented to graph data. Specifically, based on the robust Huber regression, the paper proposes a graph Huber regression model, which contains information on the correlation between samples and has a certain robustness. Then it gives an algorithm for solving the regression model. The experimental results show that the performance of the regression model is far superior to that of the graph LASSO, especially when its errors obey heavy-tailed distribution. The paper provides an effective method for analyzing and processing graph data that contains noise or obeys heavy-tailed distribution.

摘要

随着数据中含有噪声或服从重尾分布的现象越来越普遍, 鲁棒回归模型成为了众多研究领域关注和研究的重点内容之一。然而, 现有的鲁棒回归模型大多基于样本独立假设, 忽略了样本之间的相关性, 即并不能有效地用于处理图数据问题。因此, 借助图来表示数据之间的相关性, 展开了面向图数据的鲁棒回归模型研究。具体地, 基于具有鲁棒性的Huber回归, 提出了图Huber回归模型, 所提模型既包含了样本之间的相关性信息, 又具有一定的鲁棒性。在此基础上, 给出了相应的求解算法。实验结果表明所提模型的表现性能远优于图LASSO, 尤其当回归模型误差为重尾分布时。由此说明, 该研究工作为图数据中存在噪声或重尾分布问题提供了一种有效的分析和处理方法。