Illuminating the ‘‘black box’’: a randomization approach for understanding variable contributions in artificial neural networks

With the growth of statistical modeling in the ecological sciences, researchers are using more complex methods, such as artificial neural networks (ANNs), to address problems associated with pattern recognition and prediction. Although in many studies ANNs have been shown to exhibit superior predictive power compared to traditional approaches, they have also been labeled a ‘‘black box’’ because they provide little explanatory insight into the relative influence of the independent variables in the prediction process. This lack of explanatory power is a major concern to ecologists since the interpretation of statistical models is desirable for gaining knowledge of the causal relationships driving ecological phenomena. In this study, we describe a number of methods for understanding the mechanics of ANNs (e.g. Neural Interpretation Diagram, Garson’s algorithm, sensitivity analysis). Next, we propose and demonstrate a randomization approach for statistically assessing the importance of axon connection weights and the contribution of input variables in the neural network. This approach provides researchers with the ability to eliminate null-connections between neurons whose weights do not significantly influence the network output (i.e. predicted response variable), thus facilitating the interpretation of individual and interacting contributions of the input variables in the network. Furthermore, the randomization approach can identify variables that significantly contribute to network predictions, thereby providing a variable selection method for ANNs. We show that by extending randomization approaches to ANNs, the ‘‘black box’’ mechanics of ANNs can be greatly illuminated. Thus, by coupling this new explanatory power of neural networks with its strong predictive abilities, ANNs promise to be a valuable quantitative tool to evaluate, understand, and predict ecological phenomena. © 2002 Elsevier Science B.V. All rights reserved.