Machine learning and geospatial methods for large-scale mining data

The canonical technique for nonlinear modeling of spatial and other point-referenced data is known as kriging in the geostatistics literature, and by Gaussian Process (GP) regression in surrogate modeling and machine learning communities. There are many similarities shared between kriging and GPs, but also some important differences. One is that GPs impose a process on the data-generating mechanism that can be used to automate kernel/variogram inference, thus removing the human from the loop in a conventional semivariogram analysis. 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. Ultimately, we use this discussion as a springboard for an empirics-based advocacy of state-of-the-art GP technology in the geospatial modeling of a large corpus of borehole data involved in mining for gold and other minerals. Our out-of-sample validation exercise quantifies how GP methods (as implemented by open source libraries) can be both more economical (fewer human and compute resources), more accurate and offer better uncertainty quantification than kriging-based alternatives. Once in the GP framework, several possible extensions benefit from a fully generative modeling apparatus. In particular, we showcase a simple imputation scheme that copes with left-censoring of small measurements, which is a common feature in borehole assays.