Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
Permutation and Grouping Methods for Sharpening Gaussian Process Approximations
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DOI：
10.1080/00401706.2018.1437476
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发表时间：
2018-01-01
期刊：
影响因子：
2.5
通讯作者：
Guinness, Joseph
中科院分区：
文献类型：
--
作者：
Guinness, Joseph
Vecchia对高斯过程参数的近似似然依赖于观测结果的排序方式，这被认为是一个缺陷。本文采取了另一种观点，即可以调整顺序以锐化近似。事实上，文章的第一部分包括一个系统的研究如何排序影响韦基亚近似的准确性。我们证明了令人惊讶的结果，随机排序可以提供显着更清晰的近似比默认的基于坐标的排序。额外的排序方案进行了描述和分析，包括能够提高随机排序的排序。本文的第二个贡献是一个新的自动分组计算的近似分量的方法。分组方法同时提高逼近精度和减少计算负担。在常见的设置中，与默认排序的未分组近似值相比，重新排序与分组相结合将目标模型的Kullback-Leibler散度降低了60倍以上。这些主张得到了理论和数值结果的支持，并与其他近似值进行了比较，包括锥形协方差和随机偏微分方程。计算的细节，包括使用的预测和条件模拟的近似。介绍了一种时空卫星数据的应用。
Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which has been cited as a deficiency. This article takes the alternative standpoint that the ordering can be tuned to sharpen the approximations. Indeed, the first part of the article includes a systematic study of how ordering affects the accuracy of Vecchia's approximation. We demonstrate the surprising result that random orderings can give dramatically sharper approximations than default coordinate-based orderings. Additional ordering schemes are described and analyzed numerically, including orderings capable of improving on random orderings. The second contribution of this article is a new automatic method for grouping calculations of components of the approximation. The grouping methods simultaneously improve approximation accuracy and reduce computational burden. In common settings, reordering combined with grouping reduces Kullback-Leibler divergence from the target model by more than a factor of 60 compared to ungrouped approximations with default ordering. The claims are supported by theory and numerical results with comparisons to other approximations, including tapered covariances and stochastic partial differential equations. Computational details are provided, including the use of the approximations for prediction and conditional simulation. An application to space-time satellite data is presented.