Joint Distribution-Informed Shapley Values for Sparse Counterfactual Explanations

TL;DR

This paper introduces COLA, a framework that refines counterfactual explanations by minimizing feature edits using optimal transport and Shapley values, improving clarity and actionability across multiple datasets and models.

Contribution

COLA is a novel, model-agnostic framework that refines counterfactual explanations by coupling optimal transport with Shapley-based attribution to reduce unnecessary feature modifications.

Findings

COLA reduces feature edits by 26-45% while maintaining target effects.

Theoretically guarantees minimal deviation from factuals under mild conditions.

Demonstrates near-optimality on a small benchmark.

Abstract

Counterfactual explanations (CE) aim to reveal how small input changes flip a model's prediction, yet many methods modify more features than necessary, reducing clarity and actionability. We introduce \emph{COLA}, a model- and generator-agnostic post-hoc framework that refines any given CE by computing a coupling via optimal transport (OT) between factual and counterfactual sets and using it to drive a Shapley-based attribution (\emph{$p$-SHAP}) that selects a minimal set of edits while preserving the target effect. Theoretically, OT minimizes an upper bound on the $W_1$ divergence between factual and counterfactual outcomes and that, under mild conditions, refined counterfactuals are guaranteed not to move farther from the factuals than the originals. Empirically, across four datasets, twelve models, and five CE generators, COLA achieves the same target effects with only 26--45\% of the original feature edits. On a small-scale benchmark, COLA shows near-optimality.