A Multi-Resolution Approximation for Massive Spatial Datasets

Automated sensing instruments on satellites and aircraft have enabled the collection of massive amounts of high-resolution observations of spatial fields over large spatial regions. If these datasets can be efficiently exploited, they can provide new insights on a wide variety of issues. However, traditional spatial-statistical techniques such as kriging are not computationally feasible for big datasets. We propose a multi-resolution approximation (M-RA) of Gaussian processes observed at irregular locations in space. The M-RA process is specified as a linear combination of basis functions at multiple levels of spatial resolution, which can capture spatial structure from very fine to very large scales. The basis functions are automatically chosen to approximate a given covariance function, which can be nonstationary. All computations involving the M-RA, including parameter inference and prediction, are highly scalable for massive datasets. Crucially, the inference algorithms can also be parallelized to take full advantage of large distributed-memory computing environments. In comparisons using simulated data and a large satellite dataset, the M-RA outperforms a related state-of-the-art method. Supplementary materials for this article are available online.

搭载于卫星与航空器的自动化传感仪器，使得研究人员能够在广阔空间区域内采集海量高分辨率的空间场观测数据。若能对这些数据集进行高效开发利用，即可为诸多研究领域提供全新认知视角。然而，诸如克里金法（kriging）这类传统空间统计技术，在处理大规模数据集时不具备计算可行性。针对空间不规则点位处的高斯过程（Gaussian process）观测数据，本文提出一种多分辨率近似（multi-resolution approximation，M-RA）方法。该M-RA过程被定义为多空间分辨率层级下基函数的线性组合，可捕捉从极精细到极宏观尺度的空间结构特征。基函数可自动选取以拟合给定的协方差函数（covariance function），该协方差函数可为非平稳形式。所有涉及M-RA的计算流程（包括参数推断与预测），针对大规模数据集均具备极强的可扩展性。尤为关键的是，该推断算法还支持并行化处理，可充分利用大规模分布式内存计算环境的算力资源。在基于模拟数据与大型卫星数据集的对比实验中，M-RA的表现优于当前同类顶尖方法。本文的补充材料可在线获取。