Functional relevance based on the continuous Shapley value

Abstract: The presence of AI in our society is increasing, which brings with it the need to understand the behavior of AI mechanisms, including machine learning predictive algorithms fed with tabular data, text or images, among others. This work focuses on interpretability of predictive models based on functional data. Designing interpretability methods for functional data models implies working with a set of features whose size is infinite. In the context of scalar on function regression, we propose an interpretability method based on the Shapley value for continuous games, a mathematical formulation that allows for the fair distribution of a global payoff among a continuous set of players. The method is illustrated through a set of experiments with simulated and real data sets. The open source Python package ShapleyFDA is also presented.