# MACE: An Efficient Model-Agnostic Framework for Counterfactual Explanation

arXiv: https://arxiv.org/abs/2205.15540 · HTML: https://mlsanity.com/paper/2205.15540/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Causal Interpretability for Machine Learning -- Problems, Methods and Evaluation](https://mlsanity.com/paper/2003.03934/) (2020)
- [Interpretable Credit Application Predictions With Counterfactual Explanations](https://mlsanity.com/paper/1811.05245/) (2018)
- [Gradientless Descent: High-Dimensional Zeroth-Order Optimization](https://mlsanity.com/paper/1911.06317/) (2019)
- [Model Agnostic Contrastive Explanations for Structured Data](https://mlsanity.com/paper/1906.00117/) (2019)
- [Generating Counterfactual Explanations with Natural Language](https://mlsanity.com/paper/1806.09809/) (2018)
- [Generative Counterfactual Introspection for Explainable Deep Learning](https://mlsanity.com/paper/1907.03077/) (2019)
- [Contrastive Explanations with Local Foil Trees](https://mlsanity.com/paper/1806.07470/) (2018)
- [Generating Counterfactual and Contrastive Explanations using SHAP](https://mlsanity.com/paper/1906.09293/) (2019)

## Built on by (most cited first, 12 of 12)

- [Is Conversational XAI All You Need? Human-AI Decision Making With a Conversational XAI Assistant](https://mlsanity.com/paper/2501.17546/) (2025)
- [OmniXAI: A Library for Explainable AI](https://mlsanity.com/paper/2206.01612/) (2022)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [Exploring Energy Landscapes for Minimal Counterfactual Explanations: Applications in Cybersecurity and Beyond](https://mlsanity.com/paper/2503.18185/) (2025)
- [Navigating the Structured What-If Spaces: Counterfactual Generation via Structured Diffusion](https://mlsanity.com/paper/2312.13616/) (2023)
- ["What is Different Between These Datasets?" A Framework for Explaining Data Distribution Shifts](https://mlsanity.com/paper/2403.05652/) (2024)
- [On Minimizing the Impact of Dataset Shifts on Actionable Explanations](https://mlsanity.com/paper/2306.06716/) (2023)
- [Flexible Counterfactual Explanations with Generative Models](https://mlsanity.com/paper/2502.17613/) (2025)
- [EndToEndML: An Open-Source End-to-End Pipeline for Machine Learning Applications](https://mlsanity.com/paper/2403.18203/) (2024)
- [DISCOVER: A Solver for Distributional Counterfactual Explanations](https://mlsanity.com/paper/2603.16436/) (2026)
- [What's meant by explainable model: A Scoping Review](https://mlsanity.com/paper/2307.09673/) (2023)
- [ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material](https://mlsanity.com/paper/2605.30225/) (2026)

## Abstract (arXiv)

Counterfactual explanation is an important Explainable AI technique to explain machine learning predictions. Despite being studied actively, existing optimization-based methods often assume that the underlying machine-learning model is differentiable and treat categorical attributes as continuous ones, which restricts their real-world applications when categorical attributes have many different values or the model is non-differentiable. To make counterfactual explanation suitable for real-world applications, we propose a novel framework of Model-Agnostic Counterfactual Explanation (MACE), which adopts a newly designed pipeline that can efficiently handle non-differentiable machine-learning models on a large number of feature values. in our MACE approach, we propose a novel RL-based method for finding good counterfactual examples and a gradient-less descent method for improving proximity. Experiments on public datasets validate the effectiveness with better validity, sparsity and proximity.