The canonical technique for nonlinear modeling of spatial/point-referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many similarities shared between kriging and GPs, but also highlights some important differences. One is that GPs impose a process that can be used to automate kernel/variogram inference, thus removing the human from the loop. The GP framework also suggests a probabilistically valid means of scaling to handle a large corpus of training data, i.e., an alternative to so-called ordinary kriging. Finally, recent GP implementations are tailored to make the most of modern computing architectures such as multi-core workstations and multi-node supercomputers. We argue that such distinctions are important even in classically geostatistical settings. To back that up, we present out-of-sample validation exercises using two, real, large-scale borehole data sets involved in the mining of gold and other minerals. We pit classic kriging against the modern GPs in several variations and conclude that the latter can more economical (fewer human and compute resources), more accurate and offer better uncertainty quantification. We go on to show how the fully generative modeling apparatus provided by GPs can gracefully accommodate left-censoring of small measurements, as commonly occurs in mining data and other borehole assays.
翻译:用于空间/点参照数据非线性建模的卡通技术被称为地理统计学中的Kriging, 也称为Gausian Process(GP)回归, 用于代理模型和统计学学习。 文章回顾了Kriging和GP之间有许多相似之处, 但也突出了一些重要的差别。 其中之一是GP施加了一个可用于自动内核/变量推断的过程, 从而将人类从环绕中清除出来。 GP框架还提出了一种非常可靠的扩大规模的方法, 用于处理大量的培训数据, 即取代所谓的普通的Kriging。 最后, 最近GP的实施是定制的, 使大多数现代计算结构, 如多核心工作站和多点超级计算机之间具有相似性, 但也突出了一些重要的差别。 我们认为, 即使是在传统的地理统计学环境中, 这样的区分也很重要。 反过来说, 我们用两种真实的大型钻孔数据组, 来容纳大量空洞数据组, 来处理大型金矿和其他矿物开采中的大型培训数据组。 最后,我们用一些典型的精度和精度数据组, 来更精确地展示更精确的精度数据,, 以更精确地展示更精确地显示人类的精度的精度, 。