P-Huber Loss Functions And Its Robustness

The data is often contaminated by outliers because of the complexity of the real data in the real applications.Therefore,it is very important to invent statistical machine learning algorithms that are robust to outliers.To solve this problem,in this paper,we propose a new robust and non-convex p-Huber loss function based on the Huber loss function,and provide its properties and the corresponding regularization regression algorithms.In the numerical experiments,the p-Huber regression algorithms proposed in this paper are applied to Sinc function,Friedman’s benchmark functions and real data respectively.We compare the robustness and performance of the p-Huber loss function and L₁ loss function,Huber loss function and MCCR loss function in the presence of Gaussian noise and both Gaussian noise and outliers.Simulation results show that the regression algorithms based on p-Huber loss function are more robust to outliers and perform much better than the other three loss functions.Finally,we use the p-Huber loss function to analyze the prognostic data of breast cancer in Wisconsin,USA.The results show that the robustness and prediction effect based on the p-Huber loss function is better than the other loss functions,which further verifies the effectiveness of the p-Huber loss function proposed in this paper.