保持速率的收缩支撑高斯过程预测

中文摘要 AI 辅助

高斯过程预测是空间统计中的核心工具，但标准实现需要稠密矩阵运算，这对于大型数据集而言变得不可行。我们提出了一种用于高斯过程预测的尺度调整的紧支撑工作相关性，采用广义Wendland族，其支撑半径$\phi_n$允许随样本量$n$减小。在固定域渐近和准均匀设计下，固定的支撑半径不会产生渐近稀疏性，而收缩的支撑半径可以使协方差矩阵变得稀疏。我们证明，$\phi_n$和正则化参数可以联合选择，使得所得预测器保持最优的积分均方预测误差率，同时减少非零协方差条目的数量以及相关的稀疏矩阵-向量乘法成本。我们还为核岭回归建立了类似的保持速率的稀疏化结果。模拟和ERA5温度应用表明，所提出的方法在保持稀疏线性代数提供的计算效率的同时，实现了有竞争力的预测精度。

英文摘要

Gaussian process prediction is a central tool in spatial statistics, but standard implementations require dense matrix operations that become prohibitive for large datasets. We propose a scale-adjusted compactly supported working correlation for Gaussian process prediction, using the generalized Wendland family with a support radius $ϕ_n$ that is allowed to decrease with the sample size $n$. Under fixed-domain asymptotics with quasi-uniform designs, a fixed support radius does not yield asymptotic sparsity, whereas a shrinking support radius can make the covariance matrix sparse. We show that $ϕ_n$ and the regularization parameter can be jointly chosen so that the resulting predictor preserves the optimal integrated mean squared prediction error rate while reducing the number of nonzero covariance entries and the associated sparse matrix-vector multiplication cost. We also establish an analogous rate-preserving sparsification result for kernel ridge regression. Simulations and an ERA5 temperature application show that the proposed method achieves competitive prediction accuracy while retaining the computational efficiency provided by sparse linear algebra.

发表机构

• The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
• Renmin University of China（中国人民大学）
• King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
• National University of Singapore（新加坡国立大学）

机构由 AI 辅助整理，请以论文原文为准。