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Providing a model that achieves a strong predictive performance and at thesame time is interpretable by humans is one of the most difficult challenges inmachine learning research due to the conflicting nature of these twoobjectives. To address this challenge, we propose a modification of the RadialBasis Function Neural Network model by equipping its Gaussian kernel with alearnable precision matrix. We show that precious information is contained inthe spectrum of the precision matrix that can be extracted once the training ofthe model is completed. In particular, the eigenvectors explain the directionsof maximum sensitivity of the model revealing the active subspace andsuggesting potential applications for supervised dimensionality reduction. Atthe same time, the eigenvectors highlight the relationship in terms of absolutevariation between the input and the latent variables, thereby allowing us toextract a ranking of the input variables based on their importance to theprediction task enhancing the model interpretability. We conducted numericalexperiments for regression, classification, and feature selection tasks,comparing our model against popular machine learning models and thestate-of-the-art deep learning-based embedding feature selection techniques.Our results demonstrate that the proposed model does not only yield anattractive prediction performance with respect to the competitors but alsoprovides meaningful and interpretable results that potentially could assist thedecision-making process in real-world applications. A PyTorch implementation ofthe model is available on GitHub at the following link.https://github.com/dannyzx/GRBF-NNs

Learning Active Subspaces and Discovering Important Features with Gaussian Radial Basis Functions Neural Networks