# Counterfactual Plans under Distributional Ambiguity

arXiv: https://arxiv.org/abs/2201.12487 · HTML: https://mlsanity.com/paper/2201.12487/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 29 Jan 2022.

## Builds on (most cited first, 18 of 18)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [Contrastive Explanation: A Structural-Model Approach](https://mlsanity.com/paper/1811.03163/) (2018)
- [BayLIME: Bayesian Local Interpretable Model-Agnostic Explanations](https://mlsanity.com/paper/2012.03058/) (2020)
- [Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts](https://mlsanity.com/paper/2106.00322/) (2021)
- [Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/1911.03539/) (2019)
- [Mean-Covariance Robust Risk Measurement](https://mlsanity.com/paper/2112.09959/) (2021)
- [Robust Bayesian Classification Using an Optimistic Score Ratio](https://mlsanity.com/paper/2007.04458/) (2020)

## Built on by (most cited first, 19 of 19)

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Distributionally Robust Recourse Action](https://mlsanity.com/paper/2302.11211/) (2023)
- [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)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)
- [Feasible Recourse Plan via Diverse Interpolation](https://mlsanity.com/paper/2302.11213/) (2023)
- [On Minimizing the Impact of Dataset Shifts on Actionable Explanations](https://mlsanity.com/paper/2306.06716/) (2023)
- [Don't Explain Noise: Robust Counterfactuals for Randomized Ensembles](https://mlsanity.com/paper/2205.14116/) (2022)
- [Verified Training for Counterfactual Explanation Robustness under Data Shift](https://mlsanity.com/paper/2403.03773/) (2024)
- [Leveraging Contextual Counterfactuals Toward Belief Calibration](https://mlsanity.com/paper/2307.06513/) (2023)
- [BELLA: Black box model Explanations by Local Linear Approximations](https://mlsanity.com/paper/2305.11311/) (2023)
- [Estimation of Counterfactual Interventions under Uncertainties](https://mlsanity.com/paper/2309.08332/) (2023)
- [Model-Free Counterfactual Subset Selection at Scale](https://mlsanity.com/paper/2502.08326/) (2025)
- [CounterFlowNet: From Minimal Changes to Meaningful Counterfactual Explanations](https://mlsanity.com/paper/2602.17244/) (2026)

## Abstract (arXiv)

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.