Optimisation-Based Feature Selection for Regression Neural Networks Towards Explainability

Regression is a fundamental task in machine learning, and neural networks have been successfully employed in many applications to identify underlying regression patterns. However, they are often criticised for their lack of interpretability and commonly referred to as black-box models. Feature selection approaches address this challenge by simplifying datasets through the removal of unimportant features, while improving explainability by revealing feature importance. In this work, we leverage mathematical programming to identify the most important features in a trained deep neural network with a ReLU activation function, providing greater insight into its decision-making process. Unlike traditional feature selection methods, our approach adjusts the weights and biases of the trained neural network via a Mixed-Integer Linear Programming (MILP) model to identify the most important features and thereby uncover underlying relationships. The mathematical formulation is reported, which determines the subset of selected features, and clustering is applied to reduce the complexity of the model. Our results illustrate improved performance in the neural network when feature selection is implemented by the proposed approach, as compared to other feature selection approaches. Finally, analysis of feature selection frequency across each dataset reveals feature contribution in model predictions, thereby addressing the black-box nature of the neural network.