# BoxRF: A New Machine Learning Algorithm for Grade Estimation
## 1 Introduction  
Grade estimation and orebody modeling are important elements of mining, whether it is at the exploration/mine development stage or at the operational stage. While geostatistics has traditionally been the key technique used for orebody modeling, artificial intelligence (AI) methods have been examined by researchers in the last two or three decades in a wide variety of deposits [1, 2, 3, 4, 5, 6]. Documented AI performances have been all over the place, from marginal to inferior to geostatistics, to better than geostatistics [7, 8, 9, 10]. The appeal for AI has always been that specialized skills are less important than in geostatistics [1]. Therefore, from the very beginning, researchers tested this assumption. Issues such as sparseness in data, the effect of data aggregation, and subdivision methods for training/testing were investigated [11, 12] to understand how these components affected prediction performance. As research on the use of AI in mining has matured, researchers have focused on addressing the limitations of geostatistics by manipulating AI modeling methods or using geostatistics to gain insights into AI performance [13]. Variogram ranges were found to be insightful concerning hyperparameter selection in AI modeling, as well as serving as indicators of AI model performance [14]. A method that combined kriging and randomforests (RFs) was reported to have performance that was superior to both methods in modeling aboveground biomass [15]. The researchers did not change the methods themselves; the two methods were applied sequentially, though not like an ensemble. Some researchers combined SVM with heuristic reasoning to create geologically realistic domain boundaries [5], while others just combined geostatistics and machine learning models using an ensemble approach [16]. None of the geostatistics-AI combinations involved changing AI methods structurally, however. The researchers were simply creative about what data were fed to the methods [17]. This is also true of other (non-grade estimation) AI geospatial applications [18; 19; 20] where the focus was on the importance of applications and the use of big data. \"Big data\" applies to the broader geospatial sector, as data are typically generated by sensors (satellite, aerial campaigns), whereas it does not apply to mining drillhole datasets, as they are limited in quantity, as drilling is expensive. Therefore, some geospatial modelers modify AI methods by imposing the use of important covariates as inputs along with distances [21]. Some also suggested transfer learning, where knowledge from one area was used to model another [17; 22]. Those not involving image processing focused on neural networks, random forests, support vector machines, and boosted methods [23]. A recently published approach, GeoRF, however, has made structural changes to the RF method by modifying how samples are split [24]. This research, which reported superior results to the typical RF, was contemporaneous with the work being performed for this paper. Rather than a split based on a single variable, they based the split based on multiple variables. In a step that significantly advances the enmeshing of geostatistical methods and AI, this paper announces a new AI method that is created through structural changes made to the RF method. This method is called BoxRF to acknowledge that the proposed RF type method was developed by applying the concept of search boxes typical in orebody modeling. There are several differences between GeoRF and BoxRF. The biggest differences are that BoxRF splits are in 3D boxes, and directions are very important. BoxRF actively looks for trends. BoxRF also makes multivariate splits, but the split criteria are different. BoxRF also incorporates strategies to improve predictions by accommodating the challenges of mining industry drillhole datasets. The method of prediction from a split is also different.