论文标题
SPDE的Matérn字段方法：图表表示
The SPDE Approach to Matérn Fields: Graph Representations
论文作者
论文摘要
本文使用随机部分微分方程的图表来研究高斯马尔可夫随机场近似与非平稳性高斯场。我们建立近似误差可以确保基于图拉普拉斯人的光谱收敛理论的构建。所提出的图表表示将Matérn模型的概括为非结构化点云，并使用线性代数方法促进和采样稀疏矩阵。此外，他们在贝叶斯逆问题，空间统计和基于图的机器学习中桥接并统一了几个模型。我们通过这三个学科中的例子证明了图表表示的统一性促进了遍布思想的交流。
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the theory of spectral convergence of graph Laplacians. The proposed graph representations provide a generalization of the Matérn model to unstructured point clouds, and facilitate inference and sampling using linear algebra methods for sparse matrices. In addition, they bridge and unify several models in Bayesian inverse problems, spatial statistics and graph-based machine learning. We demonstrate through examples in these three disciplines that the unity revealed by graph representations facilitates the exchange of ideas across them.
