AI 中文总结
针对高斯过程回归复杂度高的问题，提出自适应Nyström方法，通过交织 landmark 扩展与超参数优化提升性能，实验显示其精度、稳定性优于随机选择，且具线性缩放特性。
AI 中文摘要
高斯过程回归（GPR）是一种用于不确定性量化的稳健框架，但其O(n³)的复杂度限制了可扩展性。低秩Nyström近似可将该负担降至O(nm²)，但精度高度依赖于 landmark 点的选择。我们提出一种自适应Nyström方法，该方法贪婪地选择 landmark 以最小化核近似误差的迹残差。与静态近似不同，我们的方法将 landmark 扩展与超参数优化交织，使选择过程能随协方差结构的优化而自适应调整。对五个基准函数的数值实验表明，该方法在精度和稳定性上均显著优于随机 landmark 选择，其预测性能可与精确GP推断相媲美，同时保持与样本量呈线性缩放的特性，为大规模计算机实验提供了一种原则性且高效的框架。
英文摘要
Gaussian Process Regression (GPR) is a robust framework for uncertainty quantification, yet its $O(n^3)$ complexity limits its scalability. Low-rank Nyström approximations can reduce this burden to $O(nm^2)$, but their accuracy depends heavily on the selection of landmark points. We propose an adaptive Nyström approach that greedily selects landmarks to minimize the trace residual of the kernel approximation error. Unlike static approximations, our method interleaves landmark expansion with hyperparameter optimization, allowing the selection process to adapt as the covariance structure is refined. Numerical experiments on five benchmark functions demonstrate that this method significantly outperforms random landmark selection in both accuracy and stability. It achieves predictive performance comparable to exact GP inference while maintaining linear scaling with respect to the sample size, providing a principled and efficient framework for large-scale computer experiments.
Comments13 pages, 1 figure. Accepted by 2026 Winter Simulation Conference
