LICON: A linear weighting scheme for the contribution of input variables in deep artificial neural networks

In recent years artificial neural networks have become the method of choice for many pattern recognition tasks. Despite their overwhelming success, a rigorous and easy to interpret mathematical explanation of the influence of input variables on a output produced by a neural network is still missing. We propose a generic framework as well as a concrete method for quantifying the influence of individual input signals on the output computed by a deep neural network. Inspired by the variable weighting scheme in the log-linear combination of variables in logistic regression, the proposed method provides linear models for specific observations of the input variables. This linear model locally approximates the behaviour of the neural network and can be used to quantify the influence of input variables in a principled way. We demonstrate the effectiveness of the proposed method in experiments on various synthetic and real-world datasets.