A weighted Gaussian process regression for multivariate modelling

This paper develops three weighted Gaussian process regression (GPR) approaches for multivariate modelling. Taking into account weighted strategy in the traditional univariate GPR, the heteroscedastic noise problem has been solved. The present paper extends the univariate weighted GPR algorithm to the multivariate case. Considering the correlation and weight between data, as well as the correlation between outputs, the covariance functions of the proposed approaches are formulated. By formulating different process noise mechanisms, the proposed methods can solve different multivariate modelling problems. The effectiveness of the proposed algorithm is demonstrated by a numerical example as well as a six-level drawing of a Carbon fiber example.