IE Integral Neural Network with Monotone Regularization Term

Abstract

The Inclusion-Exclusion integral neural network is a neural network model that uses fuzzy measures, which are non-additive measures, and Inclusion-Exclusion integrals. This makes it possible to measure the contribution of each explanatory variable using statistical indices such as Shapley values and has the advantage of preserving interpretability of the parameters after learning. However, to maintain interpretability, the monotonicity of fuzzy measures should be satisfied. In this study, we propose a regularization term that satisfies the monotonicity of the fuzzy measure for the parameters obtained by training an Inclusion-Exclusion integral neural network, and conduct experiments using regression data. Furthermore, we will verify under what conditions learning can be performed with high accuracy while preserving the monotonicity of the fuzzy measure, compared to the l1 regularization and l2 regularization that are currently widely used.