Mineral Potential Mapping Using Bayesian Learning for Multilayer Perceptrons

Abstract

Multilayer perceptrons (MLPs) can be used to discover a function which can be used to map from a set of input variables onto a value representing the conditional probability of mineralization. The standard approach to training MLPs is gradient descent, in which the error between the network output and the target output is reduced in each iteration of the training algorithm. In order to prevent overfitting, a split-sample validation procedure is used, in which the data is partitioned into two sets: a training set, which is used for weight optimization, and a validation set, which is used to optimize various parameters that can be used to prevent overfitting. One of the problems with this approach is that the resulting maps can display significant variability which stems from (i) the (randomly initialized) starting weights and (ii) the particular training/validation set partition (also determined randomly). This problem is especially pertinent on mineral potential mapping tasks, in which the number of deposit cells is a very small proportion of the total number of cells in the study area. In contrast to gradient descent methods, Bayesian learning techniques do not find a single weight vector; rather, they infer the posterior distribution of the weights given the data. Predictions are then made by integrating over this distribution. An important advantage of the Bayesian approach is that the optimization of parameters such as the weight decay regularization coefficient can be performed using training data alone, thus avoiding the noise introduced through split-sample validation. This paper reports results of applying Bayesian learning techniques to the production of maps representing gold mineralization potential over the Castlemaine region of Victoria, Australia. Maps produced using the Bayesian approach display significantly less variability than those produced using gradient descent training. They are also more reliable at predicting the presence of unknown deposits.