# Computing Rule-Based Explanations by Leveraging Counterfactuals

arXiv: https://arxiv.org/abs/2210.17071 · HTML: https://mlsanity.com/paper/2210.17071/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 31 Oct 2022.

## Builds on (most cited first, 15 of 15)

- [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)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [An Interpretable Model with Globally Consistent Explanations for Credit Risk](https://mlsanity.com/paper/1811.12615/) (2018)
- [GeCo: Quality Counterfactual Explanations in Real Time](https://mlsanity.com/paper/2101.01292/) (2021)

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

- [On the Complexity of Global Necessary Reasons to Explain Classification](https://mlsanity.com/paper/2501.06766/) (2025)
- [RUBEN: Rule-Based Explanations for Retrieval-Augmented LLM Systems](https://mlsanity.com/paper/2605.10862/) (2026)
- [Rule-Based Explanations for Retrieval-Augmented LLM Systems](https://mlsanity.com/paper/2510.22689/) (2025)
- [Assessing Alignment and Stability of Feature Importance Explanations via Weight of Evidence](https://mlsanity.com/paper/2609.00090/) (2026)

## Abstract (arXiv)

Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for high-stake decisions like loan applications, because they increase the users' trust in the decision. However, rule-based explanations are very inefficient to compute, and existing systems sacrifice their quality in order to achieve reasonable performance. We propose a novel approach to compute rule-based explanations, by using a different type of explanation, Counterfactual Explanations, for which several efficient systems have already been developed. We prove a Duality Theorem, showing that rule-based and counterfactual-based explanations are dual to each other, then use this observation to develop an efficient algorithm for computing rule-based explanations, which uses the counterfactual-based explanation as an oracle. We conduct extensive experiments showing that our system computes rule-based explanations of higher quality, and with the same or better performance, than two previous systems, MinSetCover and Anchor.