Variance-Based Feature Importance in Neural Networks

Abstract

This paper proposes a new method to measure the relative importance of features in Artificial Neural Networks (ANN) models. Its underlying principle assumes that the more important a feature is, the more the weights, connected to the respective input neuron, will change during the training of the model. To capture this behavior, a running variance of every weight connected to the input layer is measured during training. For that, an adaptation of Welford’s online algorithm for computing the online variance is proposed. When the training is finished, for each input, the variances of the weights are combined with the final weights to obtain the measure of relative importance for each feature. This method was tested with shallow and deep neural network architectures on several well-known classification and regression problems. The results obtained confirm that this approach is making meaningful measurements. Moreover, results showed that the importance scores are highly correlated with the variable importance method from Random Forests (RF).