Seminar by Professor Cheng LI, Department of Statistics and Data Science, National University of Singapore

Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based on Gaussian processes, but existing approaches struggle with evaluating the required integrals due to the lack of closed form for general kernel functions. We propose a novel and computationally efficient Hilbert space Gaussian process approximation for the IMSE acquisition function, where a truncated eigenbasis representation of the integral enables closed-form evaluation. We establish sharp global non-asymptotic bounds for both the approximation error of isotropic kernels and the resulting error in the acquisition function. In a series of numerical experiments with gamma-greedy stabilization, the proposed method achieves substantially lower prediction error and reduced computation time compared to existing benchmarks. These results demonstrate that the proposed Hilbert space Gaussian process framework provides an accurate and computationally efficient approach for Gaussian process–based sequential design.

Cheng Li is a Dean’s Chair Associate Professor in the Department of Statistics and Data Science, National University of Singapore. His research focuses on scalable Bayesian inference, Bayesian nonparametrics, Gaussian processes, spatial statistics, machine learning, and stochastic simulation. His work has appeared in leading journals in statistics and machine learning, including Annals of Statistics, Journal of the American Statistical Association, Biometrika, and Journal of Machine Learning Research. He currently serves as an Associate Editor for Bayesian Analysis.