p-Huber损失函数及其鲁棒性研究

p-Huber Loss Functions and Its Robustness

摘要: 由于应用领域真实数据的复杂性，数据常常受到离群值的污染，因此研究对离群值具有鲁棒性的统计机器学习算法就显得越来越重要。本文在Huber损失的基础上提出了一种更具鲁棒性的非凸p-Huber损失函数，通过仿真实验比较了基于p-Huber损失的回归学习算法与基于L1损失、Huber损失、MCCR损失的回归算法的拟合效果。数据实验结果显示基于p-Huber损失函数的回归学习算法在有离群值的情况下其预测效果要优于常见的损失函数的预测效果。

Abstract: The data is often contaminated by outliers because of the complexity of the real data in the real applications. Hence it is getting more and more important to invent some statistical machine learning algorithms that are robust to outliers. In this paper, we propose a robust and non-convex p-Huber loss function based on the Huber loss. In the numerical analysis, the fitting effect of regression learning algorithm based on p-Huber loss and regression algorithm based on L1 loss, Huber loss and MCCR loss are compared. The numerical results show that the p-Huber loss function outperforms all of other common loss functions mentioned in the paper when there are outliers in the data.