MinShap: A Shapley-Based Framework for Feature Redundancy

Shapley values provide a flexible framework for attributing feature contributions to model predictions, but they are not naturally suited for feature selection: a feature may receive a positive attribution even when it is redundant given the remaining variables. In this paper, we introduce MinShap, a general framework for identifying important or non-redundant features through conditional importance functionals VIjS. Rather than averaging feature contributions across conditioning sets, MinShap aggregates them using the minimum, thereby testing whether a feature remains relevant under every conditioning context. We show that, under a simple null monotonicity condition, the minimum aggregation exactly characterizes feature redundancy and yields a principled feature selection criterion. This perspective provides a unified framework for statistical feature selection and representation-based interpretability while retaining the stability advantages of Shapley-style aggregation. We develop scalable algorithms with statistical guarantees, establish connections to multiple-testing procedures, and demonstrate through theory and experiments that MinShap produces more accurate and stable feature selection than existing model-agnostic approaches.