论文标题
KRYGIG:使用Krylov子空间方法对大规模数据集进行大规模数据集的地理分析
Kryging: Geostatistical analysis of large-scale datasets using Krylov subspace methods
论文作者
论文摘要
使用高斯流程模型分析大量空间数据集会带来计算挑战。这是一个问题,在环境建模,生态学,林业和环境荒地等应用中普遍存在。我们提出了一种新型的近似推理方法,该方法使用特征可能性和Krylov子空间方法来估计空间协方差参数并通过不确定性定量进行空间预测。所提出的方法Kryging既适用于常规网格和不规则间隔的观察结果,以及具有固定协方差函数的任何高斯过程,包括流行的$ \ matern $协方差家庭。我们利用带有协方差矩阵的Toeplitz块的块toeplitz结构,并使用快速的傅立叶变换方法来减轻计算和内存瓶颈。我们进行了广泛的仿真研究,以通过不同的样本大小,空间参数值和采样设计来显示模型的有效性。还在由MODIS卫星采取的土地表面温度读数组成的数据集上执行了真实的数据应用程序。与现有方法相比,所提出的方法在较少的计算时间和更好的可扩展性方面可令人满意。
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a novel approximate inference methodology that uses profile likelihood and Krylov subspace methods to estimate the spatial covariance parameters and makes spatial predictions with uncertainty quantification. The proposed method, Kryging, applies for both observations on regular grid and irregularly-spaced observations, and for any Gaussian process with a stationary covariance function, including the popular $\Matern$ covariance family. We make use of the block Toeplitz structure with Toeplitz blocks of the covariance matrix and use fast Fourier transform methods to alleviate the computational and memory bottlenecks. We perform extensive simulation studies to show the effectiveness of our model by varying sample sizes, spatial parameter values and sampling designs. A real data application is also performed on a dataset consisting of land surface temperature readings taken by the MODIS satellite. Compared to existing methods, the proposed method performs satisfactorily with much less computation time and better scalability.