论文标题
非平稳性高斯流程的可扩展计算
Scalable Computations for Nonstationary Gaussian Processes
论文作者
论文摘要
非平稳的高斯过程模型可以在空间数据集中捕获复杂的空间变化依赖性结构。但是，现代数据集中的大量观察结果使得与常规密集线性代数可在计算上适合这样的模型。另外，在估计许多空间变化的参数时，无衍生物甚至一阶优化方法会降低。我们在这里提出了一个计算框架，该计算框架将代数块 - 基因分子加上低级协方差矩阵近似和随机跟踪估计，以促进二阶求解器的有效利用，以最大程度地估计高斯过程模型的最大可能性估计。我们通过使用107,600个海面温度异常测量值同时将192个参数拟合到Paciorek和Schervish的流行非组织模型中，从而证明了这些方法的有效性。
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be slow to converge when estimating many spatially varying parameters. We present here a computational framework that couples an algebraic block-diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements.
