Graph Huber: a robust regression model for graph data

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.