# Joint Distribution-Informed Shapley Values for Sparse Counterfactual Explanations

arXiv: https://arxiv.org/abs/2410.05419 · HTML: https://mlsanity.com/paper/2410.05419/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2024.

## Built on by (most cited first, 4 of 4)

- [DISCOVER: A Solver for Distributional Counterfactual Explanations](https://mlsanity.com/paper/2603.16436/) (2026)
- [FairSHAP: Preprocessing for Fairness Through Attribution-Based Data Augmentation](https://mlsanity.com/paper/2505.11111/) (2025)
- [xai-cola: A Python library for sparsifying counterfactual explanations](https://mlsanity.com/paper/2602.21845/) (2026)
- [Decomposition of Evidence, Contradiction, and Fragility in Perturbation Responses](https://mlsanity.com/paper/2608.12935/) (2026)

## Abstract (arXiv)

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 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 (p-SHAP) that selects a minimal set of edits while preserving the target effect. Theoretically, OT minimizes an upper bound on the W1 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.