# Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity

arXiv: https://arxiv.org/abs/2605.30901 · HTML: https://mlsanity.com/paper/2605.30901/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 25 of 25)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [TabNet: Attentive Interpretable Tabular Learning](https://mlsanity.com/paper/1908.07442/) (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)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (2021)
- [Optimal Counterfactual Explanations in Tree Ensembles](https://mlsanity.com/paper/2106.06631/) (2021)
- [Latent Diffusion Counterfactual Explanations](https://mlsanity.com/paper/2310.06668/) (2023)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Towards Fixing Clever-Hans Predictors with Counterfactual Knowledge Distillation](https://mlsanity.com/paper/2310.01011/) (2023)
- [Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization](https://mlsanity.com/paper/2012.11782/) (2020)
- [Probabilistically Plausible Counterfactual Explanations with Normalizing Flows](https://mlsanity.com/paper/2405.17640/) (2024)
- [Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Change](https://mlsanity.com/paper/2408.04842/) (2024)
- [CeFlow: A Robust and Efficient Counterfactual Explanation Framework for Tabular Data using Normalizing Flows](https://mlsanity.com/paper/2303.14668/) (2023)
- [TABCF: Counterfactual Explanations for Tabular Data Using a Transformer-Based VAE](https://mlsanity.com/paper/2410.10463/) (2024)
- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [TabRep: Training Tabular Diffusion Models with a Simple and Effective Continuous Representation](https://mlsanity.com/paper/2504.04798/) (2025)

## Abstract (arXiv)

Counterfactual explanations (CEs) are essential for actionable recourse, yet their reliability is often compromised in low-density regions, where classifiers exhibit high variance. Unlike existing methods that rely on expensive ensemble intersections to define stability, we propose textitDensityFlow, a generative framework that constructs robust CEs by adhering to the high-confidence data manifold. Specifically, we model the counterfactual generation as continuous-time dynamics parameterized by Neural ODE, guided by a differentiable density score to actively avoid uncertain, low-density areas. This density score is learned via Noise Contrastive Estimation, effectively leveraging a (K+1)-way discriminator to estimate density ratios. For black-box settings, we introduce a local proxy distillation mechanism that aligns a lightweight surrogate with the target model strictly within the trajectory of CE generation, enabling efficient gradient-based optimization with minimal queries. Experiments demonstrate that textitDensityFlow achieves superior validity under model multiplicity while significantly reducing query costs compared to ensemble-based baselines. Our implementation is available at https://github.com/G-AILab/DensityFlow.