Active Learning via Heteroskedastic Rational Kriging

Abstract. Active learning methods for emulating complex computer models that rely on stationary Gaussian processes tend to produce design points that uniformly fill the entire experimental region, which can be wasteful for functions which vary only in small regions. In this article, we propose a new Gaussian process model that captures the heteroskedasticity of the function. This is achieved by modifying the recently proposed rational kriging model, which has enough flexibility to seamlessly incorporate heteroskedasticity. Active learning using this new model can place design points in the more interesting regions of the response surface, and thus obtain surrogate models with better accuracy. The proposed active learning method is compared with the state-of-the-art methods using simulations and two real datasets. It is found to have comparable or better performance relative to other nonstationary Gaussian process-based methods, but to be faster by orders of magnitude.