An approach to the interpretation of backpropagation neural network models in QSAR studies

An approach to the interpretation of backpropagation neural network models for quantitative structure-activity and structure-property relationships (QSAR/QSPR) studies is proposed. The method is based on analyzing the first and second moments of distribution of the values of the first and the second partial derivatives of neural network outputs with respect to inputs calculated at data points. The use of such statistics makes it possible not only to obtain actually the same characteristics as for the case of traditional "interpretable" statistical methods, such as the linear regression analysis, but also to reveal important additional information regarding the non-linear character of QSAR/QSPR relationships. The approach is illustrated by an example of interpreting a backpropagation neural network model for predicting position of the long-wave absorption band of cyane dyes.