Using logistic regression model selection towards interpretable machine learning in mineral prospectivity modeling

Regression or regression-like models are often employed in mineral prospectivity modeling, i.e., for the targeting of resources, either based on 2D map images or 3D geomodels both in raster mode or based on spatial point processes. Machine learning techniques like artificial neural networks are often applied and give decent results in the prediction of target events. However, they typically provide little insight into the problem regarding the importance, or relevance, of covariables. On the other hand, logistic regression has a well understood statistical foundation and uses an explicit model from which knowledge can be gained about the underlying phenomenon. Establishing such an explicit model is rather difficult for real world problems. In the context of mineral prospectivity modeling additional challenges arise, such as rare events, i.e. only a small fraction of data instances describes a positive target event, which is the event of interest. In this paper, we propose a model selection procedure applied to logistic regression incorporating explicit nonlinearities. The model selection procedure, based on the Wald test and the Bayes' information criterion (BIC), as proposed in this paper is new. The performance regarding the predictive power of the obtained model is comparable to logistic regression using a stepwise model selection and to neural networks on several real world datasets, one of them a dataset for the detection of gold mineralizations in Ghana. However, our new method is significantly faster than standard stepwise selection, while selecting fewer variables for the final model. In our numerical experiments, the prediction accuracy is also comparable to a neural network, which is currently in use in industry. In applications, the method can aid the model building process through an explicit model. Furthermore, it may be used as preprocessing step for other machine learning algorithms such as neural networks. In this paper, we intend to present mathematics of prospectivity modeling with the potential to contribute to bridging the gap between statistical and machine learning. Big Data and Artificial Intelligence are of increasing importance in mineral exploration. At the same time there is a growing demand for mathematically rigorous machine learning methods, which can still be interpreted by experts. This paper is a contribution to this field.

Automated summary

Regression models are commonly used in mineral prospectivity modeling, with logistic regression providing a well understood statistical foundation and newly proposed model selection procedures. The comparison shows performance similar to neural networks but with faster speed and fewer variables selected. The explicit model in logistic regression can aid in the model building process and bridge the gap between statistical and machine learning methods.