Robust Gaussian process regression based on bias trimming

This paper presents a new robust Gaussian process regression (GPR) algorithm based on identifying and trimming outliers, and it can reduce the computation time and improve the accuracy compared with other robust algorithms. Currently, most existing robust GPR approaches model noise with heavy-tailed distributions that are less sensitive to outliers, such as the Laplace and Student-t distributions. However, a model that is designed this way will be analytically intractable, and the computationally expensive Bayesian approximation method needs to be adopted to obtain the posterior distribution. In our method, the deviation between normal points and outliers is modeled as a bias value, so the non-Gaussian likelihood approach, which consumes substantial time, is not necessary. Nevertheless, the decrease in calculation time is accompanied by a decrease in accuracy. To solve this problem, the trimming algorithm with an adaptive threshold is adopted to improve the prediction precision. Therefore, the proposed approach is simple but very computationally attractive. We conducted various simulation experiments to numerically evaluate the model with different outlier ratios and noise levels. We compared the approach with existing robust Gaussian process methods and other kinds of anomaly detection algorithms to demonstrate the excellent performance of the proposed method. Finally, industrial datasets are used to verify the method, and the results illustrate that it can significantly improve the practicality of the measurement system.