Resampling in neural networks with application to spatial analysis

In developing Artificial Neural Networks (ANNs), the available dataset is split into three categories: training, validation and testing. However, an important problem arises: How to trust the prediction provided by a particular ANN? Due to the randomness related to the network itself (architecture, initialization and learning procedure), there is usually no best choice. Considering this issue, we provide a framework, which captures the randomness related to the network itself. The idea is to perform several training and test trials based on the Jackknife resampling method. Jackknife consists of iteratively deleting a single observation each time from the sample and recomputing the ANN on the rest of the sample data. Consequently, interval prediction is available instead of point prediction. The proposed method was applied and tested using pH, Ca and P data obtained by analyzing 118 georeferenced soil points. The results, based on the dataset size simulation, showed that 60% reduction in available dataset offers compatible accuracy in relation to full dataset, and therefore a higher cost of sampling in the field would not be necessary. The re-sampling method spatially characterizes the points of greater or lesser accuracy and uncertainty. The re-sampling method increased the success rate by using interval prediction instead of using the mean as the most probable value. Although we restrict it to the regression neural network model, the resampling method proposed can also be extended to other modern statistical tools, such as Kriging, Least Squares Collocation (LSC), Convolutional Neural Network (CNN), and so on.