# MCCE: Monte Carlo sampling of realistic counterfactual explanations

arXiv: https://arxiv.org/abs/2111.09790 · HTML: https://mlsanity.com/paper/2111.09790/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 18 Nov 2021.

## Builds on (most cited first, 23 of 23)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [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)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [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)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [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)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (2021)
- [ViCE: Visual Counterfactual Explanations for Machine Learning Models](https://mlsanity.com/paper/2003.02428/) (2020)
- [Counterfactual Explanations for Machine Learning: Challenges Revisited](https://mlsanity.com/paper/2106.07756/) (2021)
- [CARE: Coherent Actionable Recourse based on Sound Counterfactual Explanations](https://mlsanity.com/paper/2108.08197/) (2021)

## Built on by (most cited first, 7 of 7)

- [Feature-based Learning for Diverse and Privacy-Preserving Counterfactual Explanations](https://mlsanity.com/paper/2209.13446/) (2022)
- [Achieving Diversity in Counterfactual Explanations: a Review and Discussion](https://mlsanity.com/paper/2305.05840/) (2023)
- [DiCoFlex: Model-agnostic diverse counterfactuals with flexible control](https://mlsanity.com/paper/2505.23700/) (2025)
- [What's Wrong with Your Synthetic Tabular Data? Using Explainable AI to Evaluate Generative Models](https://mlsanity.com/paper/2504.20687/) (2025)
- [BELLA: Black box model Explanations by Local Linear Approximations](https://mlsanity.com/paper/2305.11311/) (2023)
- [RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations](https://mlsanity.com/paper/2508.10455/) (2025)
- [CounterFlowNet: From Minimal Changes to Meaningful Counterfactual Explanations](https://mlsanity.com/paper/2602.17244/) (2026)

## Abstract (arXiv)

We introduce MCCE: Monte Carlo sampling of valid and realistic Counterfactual Explanations for tabular data, a novel counterfactual explanation method that generates on-manifold, actionable and valid counterfactuals by modeling the joint distribution of the mutable features given the immutable features and the decision. Unlike other on-manifold methods that tend to rely on variational autoencoders and have strict prediction model and data requirements, MCCE handles any type of prediction model and categorical features with more than two levels. MCCE first models the joint distribution of the features and the decision with an autoregressive generative model where the conditionals are estimated using decision trees. Then, it samples a large set of observations from this model, and finally, it removes the samples that do not obey certain criteria. We compare MCCE with a range of state-of-the-art on-manifold counterfactual methods using four well-known data sets and show that MCCE outperforms these methods on all common performance metrics and speed. In particular, including the decision in the modeling process improves the efficiency of the method substantially.