A Fast Summation Tree Code for Matérn Kernel
A Fast Summation Tree Code for Matérn Kernel
复制标题
Matérn内核的快速求和树代码
DOI：
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复制
发表时间：
2014
影响因子：
3.1
通讯作者：
M. Anitescu
中科院分区：
文献类型：
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作者：
Jie Chen;Lei Wang;M. Anitescu
Matern函数族是高斯过程建模的空间统计中广泛使用的协方差核，在许多情况下需要使用协方差矩阵进行计算。在本文中，我们设计了一个快速求和算法的Matern内核，以有效地执行矩阵向量乘法。该算法是基于Barnes-Hut树代码框架，并解决了几个实际问题：核的各向异性，点集的非均匀分布，和一个严格的近似误差估计。尽管算法细节在几个方面与标准树代码不同，但根据经验，我们算法的计算成本为O（n log n）。综合数值实验表明，该设计的实用性。
The Matern family of functions is a widely used covariance kernel in spatial statistics for Gaussian process modeling, which in many instances requires calculations with a covariance matrix. In this paper, we design a fast summation algorithm for the Matern kernel in order to efficiently perform matrix-vector multiplications. This algorithm is based on the Barnes-Hut tree code framework and addresses several practical issues: the anisotropy of the kernel, the nonuniform distribution of the point set, and a tight error estimate of the approximation. Even though the algorithmic details differ from the standard tree code in several aspects, empirically the computational cost of our algorithm scales as O(n log n )f orn points. Comprehensive numerical experiments are shown to demonstrate the practicality of the design.