Information-theoretic Quantification of High-order Feature Effects in Classification Problems

One of the central aspects of model explainability in machine learning is the identification and interpretation of feature importance [1]. Understanding which features drive the predictions, on both local and global levels, not only enhances the user's trust in the automated decision process but also provides valuable insights into the underlying data structure and feature interactions within the prediction process. As a consequence, numerous methods have been proposed for assessing feature contributions in a model-agnostic setting, ranging from simple error-based permutation importance tests [2] and basic information-theoretic approaches [3], to more sophisticated techniques such as SHAP, which relies on the weighted average contribution of features across possible subsets [4]. Despite their success, these methods often fail to isolate true marginal contributions of individual features, particularly in the presence of high-order interactions, cases where the importance of a feature depends not only on its contribution but also on its combined influence with other features. Such interactions can make it difficult to determine whether a feature provides unique information alone or in conjunction with specific feature subsets, leading to synergistic or redundant effects. To address this, König et al. [5] propose a model-agnostic approach to disentangle standalone, interaction, and dependency effects by decomposing the explained variance of a pretrained model's prediction.