Providing a model that achieves a strong predictive performance and is simultaneously 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, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared 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/Gaussian-RBFNN

翻译：提供兼具强预测性能与人类可解释性的模型是机器学习研究中最具挑战性的难题之一，原因在于这两个目标本质上的冲突性。为应对这一挑战，我们提出了一种径向基函数神经网络模型的改进方案，通过为其高斯核配备可学习的精度矩阵。研究表明，在模型训练完成后，可从精度矩阵的谱中提取宝贵信息。具体而言，特征向量揭示了模型最大敏感性的方向，从而呈现出主动子空间，并为监督式降维提供了潜在应用前景。与此同时，特征向量还凸显了输入变量与潜在变量之间基于绝对变化量的关联关系，使我们能够根据输入变量对预测任务的重要性提取其排序，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，将所提模型与主流机器学习模型、基于深度学习的先进嵌入特征选择技术以及面向表格数据的Transformer模型进行了对比。结果表明，所提模型不仅在预测性能上具有竞争力，还能提供有意义的可解释结果，有望在实际应用中辅助决策过程。模型的PyTorch实现在GitHub上公开可用，链接如下：https://github.com/dannyzx/Gaussian-RBFNN