We propose a Gaussian process controlled B-spline surface (GPBSS), which integrates the flexibility of B-spline basis functions into the probabilistic framework of Gaussian processes. By leveraging the sparsity inherent in B-spline bases, GPBSS achieves a linear time complexity, making it particularly effective for large-scale data sets in low-dimensional spaces. Compared with current benchmark approximations of the standard Kriging model, GPBSS offers a unique balance between computational efficiency and prediction accuracy. Furthermore, we extend the application of the GPBSS model to Bayesian optimization, enabling efficient optimization of black box functions. To validate the performance of GPBSS, we conduct a regression study on four large-scale data sets and an optimization study on three complex objective functions. The results demonstrate that our proposed model not only significantly enhances computational efficiency but also excellently balances its prediction accuracy. Its favorable tradeoff makes GPBSS a valuable tool for data-intensive regression and optimization tasks in low-dimensional scenarios such as medical imaging, geospatial analysis, and additive manufacturing, where data are sampled at high rates or over long intervals. History: Eunshin Byon served as the senior editor for this article. Funding: This work was funded by the National Natural Science Foundation of China Grants 72471142, 72101147, 52275499, and 92467101. Supplemental Material: The code capsule is available at https://github.com/Yongxiang-Li/GPBSS and in the e-companion to this article (available at https://doi.org/10.1287/ijds.2024.0061 ).
Li et al. (Tue,) studied this question.