Providing a model that achieves a strong predictive performance and at the same time is interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the Radial Basis Function Neural Network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models and the state-of-the-art deep learning-based embedding feature selection techniques. Our results demonstrate that the proposed model does not only yield an attractive prediction performance with respect to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link. https://github.com/dannyzx/GRBF-NNs

翻译：在机器学习研究中，由于预测性能与可解释性这两个目标相互冲突，提供既能实现强大预测性能又同时让人类可解释的模型是最具挑战性的难题之一。为应对这一挑战，我们提出对径向基函数神经网络模型进行改进，为其高斯核配备一个可学习的精度矩阵。我们发现，训练完成后可从精度矩阵的谱中提取出宝贵的信息。具体而言，特征向量揭示了模型最大敏感性的方向，从而展现出活跃子空间，并为监督式降维提供了潜在应用。同时，特征向量凸显了输入与潜变量之间在绝对变化量方面的关系，进而使我们能根据输入变量对预测任务的重要性对其排序，从而增强模型的可解释性。我们针对回归、分类和特征选择任务开展了数值实验，将我们的模型与流行的机器学习模型及基于深度学习的最新嵌入特征选择技术进行了对比。结果表明，所提出的模型不仅在与竞争对手相比时展现出有吸引力的预测性能，还提供了有意义且可解释的结果，这有可能在现实应用中辅助决策过程。模型的PyTorch实现已在GitHub上公开，链接如下：https://github.com/dannyzx/GRBF-NNs。