# Axiomatic Aggregations of Abductive Explanations

arXiv: https://arxiv.org/abs/2310.03131 · HTML: https://mlsanity.com/paper/2310.03131/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## Builds on (most cited first, 22 of 22)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Asymmetric Shapley values: incorporating causal knowledge into model-agnostic explainability](https://mlsanity.com/paper/1910.06358/) (2019)
- [Deep Learning for Financial Applications : A Survey](https://mlsanity.com/paper/2002.05786/) (2020)
- [Secure and Robust Machine Learning for Healthcare: A Survey](https://mlsanity.com/paper/2001.08103/) (2020)
- [Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay](https://mlsanity.com/paper/2008.05803/) (2020)
- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Explanations for Monotonic Classifiers](https://mlsanity.com/paper/2106.00154/) (2021)
- [On Computing Probabilistic Explanations for Decision Trees](https://mlsanity.com/paper/2207.12213/) (2022)
- [On Validating, Repairing and Refining Heuristic ML Explanations](https://mlsanity.com/paper/1907.02509/) (2019)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [On Computing Probabilistic Abductive Explanations](https://mlsanity.com/paper/2212.05990/) (2022)
- [High Dimensional Model Explanations: an Axiomatic Approach](https://mlsanity.com/paper/2006.08969/) (2020)
- [On Formal Feature Attribution and Its Approximation](https://mlsanity.com/paper/2307.03380/) (2023)
- [A Unifying Formal Approach to Importance Values in Boolean Functions](https://mlsanity.com/paper/2305.08103/) (2023)

## Built on by (most cited first, 10 of 10)

- [SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelism](https://mlsanity.com/paper/2510.21599/) (2025)
- [Most General Explanations of Tree Ensembles (Extended Version)](https://mlsanity.com/paper/2505.10991/) (2025)
- [Logic-Based Explainability: Past, Present & Future](https://mlsanity.com/paper/2406.11873/) (2024)
- [SHAP scores fail pervasively even when Lipschitz succeeds](https://mlsanity.com/paper/2412.13866/) (2024)
- [CAGE: Causality-Aware Shapley Value for Global Explanations](https://mlsanity.com/paper/2404.11208/) (2024)
- [Sufficient Explanations in Databases and their Connections to Database Repairs](https://mlsanity.com/paper/2511.15623/) (2025)
- [Multi-criteria Rank-based Aggregation for Explainable AI](https://mlsanity.com/paper/2505.24612/) (2025)
- [Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index](https://mlsanity.com/paper/2508.11959/) (2025)
- [Efficient & Correct Predictive Equivalence for Decision Trees](https://mlsanity.com/paper/2509.17774/) (2025)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)

## Abstract (arXiv)

The recent criticisms of the robustness of post hoc model approximation explanation methods (like LIME and SHAP) have led to the rise of model-precise abductive explanations. For each data point, abductive explanations provide a minimal subset of features that are sufficient to generate the outcome. While theoretically sound and rigorous, abductive explanations suffer from a major issue -- there can be several valid abductive explanations for the same data point. In such cases, providing a single abductive explanation can be insufficient; on the other hand, providing all valid abductive explanations can be incomprehensible due to their size. In this work, we solve this issue by aggregating the many possible abductive explanations into feature importance scores. We propose three aggregation methods: two based on power indices from cooperative game theory and a third based on a well-known measure of causal strength. We characterize these three methods axiomatically, showing that each of them uniquely satisfies a set of desirable properties. We also evaluate them on multiple datasets and show that these explanations are robust to the attacks that fool SHAP and LIME.