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 \textbf{MinShap}, a general framework for identifying \emph{important} or \emph{non-redundant} features through conditional importance functionals $VI_j^S$.

Rather than averaging feature contributions across conditioning sets, MinShap aggregates them using the \emph{minimum}, thereby testing whether a feature remains relevant under every conditioning context.

We show that, under a simple \emph{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.