Calibrated Product-of-Experts GPs Improve Uncertainty Quantification.

Gaussian Process (GP) regression, while powerful, faces scalability issues due to its cubic computational cost for large datasets. Product-of-experts GP models (GP-pro) offer a solution by combining local GP models, but they often overestimate posterior variances because local experts are trained on disjoint data subsets. Researchers introduce GP-pro-c, a calibrated product-of-experts GP model that addresses this overestimation using an information-based calibration method. This method leverages the monotonicity and submodularity of information gain in GPs to define a calibration ratio, which effectively reduces the posterior variance of individual local GP models. Experiments across synthetic functions and regression datasets demonstrate that GP-pro-c achieves notable reductions in negative log-likelihood (NLL) and expected normalized calibration error (ENCE) compared to the uncalibrated GP-pro model, all while preserving predictive accuracy and computational efficiency. This approach provides a promising solution for accurate uncertainty estimation in scalable GP models, making them more suitable for high-dimensional and large-scale Bayesian optimization.