Assessing high-order effects in feature importance via predictability decomposition

Building on recent advances in describing redundancy and synergy in multivariate interactions among random variables, we propose an approach to quantify cooperative effects in feature importance, a key technique in explainable artificial intelligence. Specifically, we introduce an adaptive version of the widely used metric Leave One Covariate Out (LOCO), designed to disentangle high-order effects involving a particular input feature in regression problems. LOCO measures the reduction in prediction error when the feature of interest is added to the set of features used in regression. Unlike the standard approach that computes LOCO using all available features, our method identifies the subsets of features that maximize and minimize LOCO. This results in a decomposition of LOCO into a two-body component and higher-order components (redundant and synergistic), while also identifying the features that contribute to these high-order effects in conjunction with the driving feature. We demonstrate the effectiveness of the proposed method in a benchmark dataset related to wine quality and to proton versus pion discrimination using simulated detector measurements generated by LEANT.