# FCx: An algorithm for finding Feasible Counterfactual Explanations

arXiv: https://arxiv.org/abs/2609.19383 · HTML: https://mlsanity.com/paper/2609.19383/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 16 Sep 2026.

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

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [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)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [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)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Benchmarking and Survey of Explanation Methods for Black Box Models](https://mlsanity.com/paper/2102.13076/) (2021)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [Counterfactual Explanations as Interventions in Latent Space](https://mlsanity.com/paper/2106.07754/) (2021)
- [Counterfactual Explanations for Time Series Forecasting](https://mlsanity.com/paper/2310.08137/) (2023)
- [FACEGroup: Feasible and Actionable Counterfactual Explanations for Group Fairness](https://mlsanity.com/paper/2410.22591/) (2024)
- [Towards Feasible Counterfactual Explanations: A Taxonomy Guided Template-based NLG Method](https://mlsanity.com/paper/2310.02019/) (2023)
- [Flexible Counterfactual Explanations with Generative Models](https://mlsanity.com/paper/2502.17613/) (2025)

## Abstract (arXiv)

Counterfactual (CF) explanations identify changes that alter an input's classification. While existing methods produce realistic and low-cost CFs, they often fail to ensure feasibility, by suggesting non-constructive modifications or incompatible with future changes (e.g., changing an individual's race to secure a job offer). We introduce a refinement of CF explanations that explicitly enforces feasibility. Our approach is the first to efficiently generate CFs that are realistic, low-cost and feasible. We accommodate both hard feasible constraints, specified by domain knowledge users, and soft feasible constraints, inferred automatically via causal inference from the dataset. Our method, Feasible Counterfactual Explanations (FCx), is based on a modified Variational Autoencoder (VAE) optimized with a multi-factor loss function. We measure the cost of a change based on the absolute change in values (proximity) as well as the number of features changed (sparsity) while realism is measured based on the LOF for density estimation, guaranteeing that CFs reside in densely populated regions. Extensive experiments on four public datasets show that our approach matches state-of-the-art performance across multiple metrics while guaranteeing feasibility.