# DISCOVER: A Solver for Distributional Counterfactual Explanations

arXiv: https://arxiv.org/abs/2603.16436 · HTML: https://mlsanity.com/paper/2603.16436/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (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)
- [TabArena: A Living Benchmark for Machine Learning on Tabular Data](https://mlsanity.com/paper/2506.16791/) (2025)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (2021)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [GLOBE-CE: A Translation-Based Approach for Global Counterfactual Explanations](https://mlsanity.com/paper/2305.17021/) (2023)
- [Explaining Groups of Points in Low-Dimensional Representations](https://mlsanity.com/paper/2003.01640/) (2020)
- [Model-agnostic and Scalable Counterfactual Explanations via Reinforcement Learning](https://mlsanity.com/paper/2106.02597/) (2021)
- [MACE: An Efficient Model-Agnostic Framework for Counterfactual Explanation](https://mlsanity.com/paper/2205.15540/) (2022)
- [Distributional Counterfactual Explanations With Optimal Transport](https://mlsanity.com/paper/2401.13112/) (2024)
- [A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations](https://mlsanity.com/paper/2403.01221/) (2024)
- [CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forests](https://mlsanity.com/paper/2404.03506/) (2024)
- [Joint Distribution-Informed Shapley Values for Sparse Counterfactual Explanations](https://mlsanity.com/paper/2410.05419/) (2024)
- [MC3G: Model Agnostic Causally Constrained Counterfactual Generation](https://mlsanity.com/paper/2508.17221/) (2025)

## Built on by (most cited first, 1 of 1)

- [Decomposition of Evidence, Contradiction, and Fragility in Perturbation Responses](https://mlsanity.com/paper/2608.12935/) (2026)

## Abstract (arXiv)

Counterfactual explanations (CE) explain model decisions by identifying input modifications that lead to different predictions. Most existing methods operate at the instance level. Distributional Counterfactual Explanations (DCE) extend this setting by optimizing an optimal transport objective that balances proximity to a factual input distribution and alignment to a target output distribution, with statistical certification via chance constrained bounds. However, DCE relies on gradient based optimization, while many real-world tabular pipelines are dominated by non-differentiable models. We propose DISCOVER, a model-agnostic solver for distributional counterfactual explanations. DISCOVER preserves the original DCE objective and certification while replacing gradient descent with a budgeted propose-and-select search paradigm. It exploits a sample-wise decomposition of the transport objective to compute per-row impact scores and enforce a top-k intervention budget, focusing edits on the most influential samples. To guide candidate generation without predictor gradients, DISCOVER introduces an OT-guided cone sampling primitive driven by input-side transport geometry. Experiments on multiple tabular datasets demonstrate strong joint alignment of input and output distributions, extending distributional counterfactual reasoning to modern black box learning pipelines. A code repository is available at: https://github.com/VALHALLA9/Discover.