This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based on the expectation-maximization algorithm, which exploits the structure of the recursive model. In particular, we derive closed-form update formulas when the scaling factor is modeled as a parametric linear predictor. This approach is compared with the fully coupled likelihood maximization of the classical non-recursive formulation introduced by Kennedy and O'Hagan. A series of benchmark experiments, covering applications of increasing complexity, highlights the performance of both approaches. The results demonstrate that the proposed recursive strategy significantly reduces training time, especially when large low-fidelity datasets are available, while maintaining competitive predictive accuracy and uncertainty estimation.

翻译：本文针对噪声且非嵌套的高低保真度数据这一具有挑战性的场景，研究了自回归多保真高斯过程回归的递归公式。我们提出了一种基于期望最大化算法的解耦优化策略，该策略充分利用了递归模型的结构特性。特别地，当缩放因子被建模为参数化线性预测器时，我们推导出了闭环更新公式。该方法与Kennedy和O'Hagan提出的经典非递归公式的完全耦合似然最大化方法进行了对比。一系列涵盖复杂度递增应用的基准实验，展示了两类方法的性能表现。结果表明，所提出的递归策略能显著缩短训练时间（尤其是当可获得大量低保真度数据集时），同时保持具有竞争力的预测精度与不确定性估计。