论文标题
高度多元空间数据的图形高斯过程模型
Graphical Gaussian Process Models for Highly Multivariate Spatial Data
论文作者
论文摘要
对于多元空间高斯过程（GP）模型，跨互相函数的习惯规范不会利用关系间变化图，以确保变量之间的过程级别的条件独立性。这是不希望的，尤其是对于高度多元设置，在这种情况下，流行的跨互相功能，例如多元Matérn，随着参数和浮点操作的数量分别以二次和立方体的规模扩大，在变量数量中，参数和浮点操作的数量分别占据。我们使用称为“缝合”的通用结构提出了一类多元“图形高斯过程”，该构造从图形上制作了交叉协方差函数，并确保变量之间的过程级别的条件独立性。对于Matérn函数家族，缝线产生了一个多变量GP，其单变量成分是MatérnGPS，并符合图形模型指定的过程级别的条件独立性。对于高度多元设置和可分解的图形模型，缝线提供了巨大的计算增益和参数维度的降低。我们使用仿真示例和用于空气污染建模的应用，证明了图形MatérnGP的实用性，可以共同对高度多元空间数据进行建模。
For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Matérn suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. We propose a class of multivariate "Graphical Gaussian Processes" using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Matérn family of functions, stitching yields a multivariate GP whose univariate components are Matérn GPs, and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn GP to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.
