用神经网络加速高斯过程的参数估计，大幅提升计算效率。
Amortized Bayesian Local Interpolation NetworK: Fast covariance parameter estimation for Gaussian Processes
- 用两个预训练神经网络直接预测克里金权重和空间方差
- 在7000个气象站数据上实现更快的预测速度和更低的误差
- 适合需要快速地理建模且需完整后验推断的研究者
高斯过程（GPs）在地质统计建模中广泛应用，具备高度灵活性与可解释性，可通过克里金法对未观测空间位置进行预测。但克里金权重的估计依赖于协方差矩阵的求逆，导致大规模空间数据集下计算瓶颈。本文提出一种渐进贝叶斯局部插值网络（A-BLINK），利用两个预训练深度神经网络，从空间坐标和协方差函数参数映射到克里金权重与空间方差。该方法跳过矩阵求逆步骤，显著提升预测速度，在频率学与贝叶斯设置下均优于现有可扩展GP方法。模拟研究显示，其参数估计误差更低，计算效率更高；在基于超过7000个气象站的1991–2020年美国气候正常温度数据集上也验证了有效性。
原文摘要 · Abstract (English)
Gaussian processes (GPs) are a ubiquitous tool for geostatistical modeling with high levels of flexibility and interpretability, and the ability to make predictions at unseen spatial locations through a process called Kriging. Estimation of Kriging weights relies on the inversion of the process' covariance matrix, creating a computational bottleneck for large spatial datasets. In this paper, we propose an Amortized Bayesian Local Interpolation NetworK (A-BLINK) for fast covariance parameter estimation, which uses two pre-trained deep neural networks to learn a mapping from spatial location coordinates and covariance function parameters to Kriging weights and the spatial variance, respectively. The fast prediction time of these networks allows us to bypass the matrix inversion step, creating large computational speedups over competing methods in both frequentist and Bayesian settings, and also provides full posterior inference and predictions using Markov chain Monte Carlo sampling methods. We show significant increases in computational efficiency over comparable scalable GP methodology in an extensive simulation study with lower parameter estimation error. The efficacy of our approach is also demonstrated using a temperature dataset of US climate normals for 1991--2020 based on over 7,000 weather stations.
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