A weighted heteroscedastic Gaussian process modeling via particle swarm optimization

Abstract

Gaussian process regression (GPR) algorithm has good adaptability to deal with high dimensional, small sample, and nonlinear problems. The standard GPR algorithm assumes constant noise power throughout the sampling process. However, different sample points are often affected by different degrees of noise, which will reduce the modeling accuracy and increase uncertainty of the prediction in the standard GPR algorithm. In this paper, we introduce a weighting strategy to the standard GPR algorithm, and propose a weighted GPR (W-GPR) algorithm. Different from the standard GPR algorithm, the proposed W-GPR algorithm assigns a weight to each observation. In addition, in order to optimize hyper-parameters in the GPR modeling process, the particle swarm optimization (PSO) algorithm is used instead of the traditional gradient method. By means of a numerical example and one chemical process example, the W-GPR algorithm significantly reduces the uncertainty of the prediction, and improves the accuracy of the model. Further, simulation results demonstrate that the W-GPR model optimized by the PSO algorithm achieves a more accurate and reliable estimation result than the traditional gradient method.