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This paper presents a new approach to a robust Gaussian process (GP)regression. Most existing approaches replace an outlier-prone Gaussianlikelihood with a non-Gaussian likelihood induced from a heavy taildistribution, such as the Laplace distribution and Student-t distribution.However, the use of a non-Gaussian likelihood would incur the need for acomputationally expensive Bayesian approximate computation in the posteriorinferences. The proposed approach models an outlier as a noisy and biasedobservation of an unknown regression function, and accordingly, the likelihoodcontains bias terms to explain the degree of deviations from the regressionfunction. We entail how the biases can be estimated accurately with otherhyperparameters by a regularized maximum likelihood estimation. Conditioned onthe bias estimates, the robust GP regression can be reduced to a standard GPregression problem with analytical forms of the predictive mean and varianceestimates. Therefore, the proposed approach is simple and very computationallyattractive. It also gives a very robust and accurate GP estimate for manytested scenarios. For the numerical evaluation, we perform a comprehensivesimulation study to evaluate the proposed approach with the comparison to theexisting robust GP approaches under various simulated scenarios of differentoutlier proportions and different noise levels. The approach is applied to datafrom two measurement systems, where the predictors are based on robustenvironmental parameter measurements and the response variables utilize morecomplex chemical sensing methods that contain a certain percentage of outliers.The utility of the measurement systems and value of the environmental data areimproved through the computationally efficient GP regression and bias model.

Robust Gaussian Process Regression with a Bias Model