# CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows

arXiv: https://arxiv.org/abs/2303.14668 · HTML: https://mlsanity.com/paper/2303.14668/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 26 Mar 2023.

## Builds on (most cited first, 22 of 22)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (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)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Inverse Classification for Comparison-based Interpretability in Machine Learning](https://mlsanity.com/paper/1712.08443/) (2017)
- [Interpretable Credit Application Predictions With Counterfactual Explanations](https://mlsanity.com/paper/1811.05245/) (2018)
- [Model Agnostic Contrastive Explanations for Structured Data](https://mlsanity.com/paper/1906.00117/) (2019)
- [Convex Density Constraints for Computing Plausible Counterfactual Explanations](https://mlsanity.com/paper/2002.04862/) (2020)
- [Causality Learning: A New Perspective for Interpretable Machine Learning](https://mlsanity.com/paper/2006.16789/) (2020)
- [ECINN: Efficient Counterfactuals from Invertible Neural Networks](https://mlsanity.com/paper/2103.13701/) (2021)
- [Generalized Inverse Classification](https://mlsanity.com/paper/1610.01675/) (2016)
- [Learning Discrete Distributions by Dequantization](https://mlsanity.com/paper/2001.11235/) (2020)

## Built on by (most cited first, 8 of 8)

- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [Counterfactual Explanations via Riemannian Latent Space Traversal](https://mlsanity.com/paper/2411.02259/) (2024)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [Graph Counterfactual Explainable AI via Latent Space Traversal](https://mlsanity.com/paper/2501.08850/) (2025)
- [Counterfactual Explanations on Robust Perceptual Geodesics](https://mlsanity.com/paper/2601.18678/) (2026)
- [Model-Based Counterfactual Explanations Incorporating Feature Space Attributes for Tabular Data](https://mlsanity.com/paper/2404.13224/) (2024)
- [CounterFlowNet: From Minimal Changes to Meaningful Counterfactual Explanations](https://mlsanity.com/paper/2602.17244/) (2026)
- [Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity](https://mlsanity.com/paper/2605.30901/) (2026)

## Abstract (arXiv)

Counterfactual explanation is a form of interpretable machine learning that generates perturbations on a sample to achieve the desired outcome. The generated samples can act as instructions to guide end users on how to observe the desired results by altering samples. Although state-of-the-art counterfactual explanation methods are proposed to use variational autoencoder (VAE) to achieve promising improvements, they suffer from two major limitations: 1) the counterfactuals generation is prohibitively slow, which prevents algorithms from being deployed in interactive environments; 2) the counterfactual explanation algorithms produce unstable results due to the randomness in the sampling procedure of variational autoencoder. In this work, to address the above limitations, we design a robust and efficient counterfactual explanation framework, namely CeFlow, which utilizes normalizing flows for the mixed-type of continuous and categorical features. Numerical experiments demonstrate that our technique compares favorably to state-of-the-art methods. We release our source at https://github.com/tridungduong16/fairCE.git for reproducing the results.