# Enhancing Counterfactual Explanation Search with Diffusion Distance and Directional Coherence

arXiv: https://arxiv.org/abs/2404.12810 · HTML: https://mlsanity.com/paper/2404.12810/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 41 references that are in the map.
- First posted on arXiv 19 Apr 2024.

## Builds on (most cited first, 16 of 16)

- [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)
- [Deep Learning for Medical Image Analysis](https://mlsanity.com/paper/1708.08987/) (2017)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [Explainability Fact Sheets: A Framework for Systematic Assessment of Explainable Approaches](https://mlsanity.com/paper/1912.05100/) (2019)
- [Getting a CLUE: A Method for Explaining Uncertainty Estimates](https://mlsanity.com/paper/2006.06848/) (2020)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [DECE: Decision Explorer with Counterfactual Explanations for Machine Learning Models](https://mlsanity.com/paper/2008.08353/) (2020)
- [Mind the gap: Challenges of deep learning approaches to Theory of Mind](https://mlsanity.com/paper/2203.16540/) (2022)
- [CARE: Coherent Actionable Recourse based on Sound Counterfactual Explanations](https://mlsanity.com/paper/2108.08197/) (2021)
- [Benchmarking Instance-Centric Counterfactual Algorithms for XAI: From White Box to Black Box](https://mlsanity.com/paper/2203.02399/) (2022)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)

## Built on by (most cited first, 4 of 4)

- [Counterfactual Explanations via Riemannian Latent Space Traversal](https://mlsanity.com/paper/2411.02259/) (2024)
- [Towards Unifying Evaluation of Counterfactual Explanations: Leveraging Large Language Models for Human-Centric Assessments](https://mlsanity.com/paper/2410.21131/) (2024)
- [Exploring Energy Landscapes for Minimal Counterfactual Explanations: Applications in Cybersecurity and Beyond](https://mlsanity.com/paper/2503.18185/) (2025)
- [Predicting Satisfaction of Counterfactual Explanations from Human Ratings of Explanatory Qualities](https://mlsanity.com/paper/2504.13899/) (2025)

## Abstract (arXiv)

A pressing issue in the adoption of AI models is the increasing demand for more human-centric explanations of their predictions. To advance towards more human-centric explanations, understanding how humans produce and select explanations has been beneficial. In this work, inspired by insights of human cognition we propose and test the incorporation of two novel biases to enhance the search for effective counterfactual explanations. Central to our methodology is the application of diffusion distance, which emphasizes data connectivity and actionability in the search for feasible counterfactual explanations. In particular, diffusion distance effectively weights more those points that are more interconnected by numerous short-length paths. This approach brings closely connected points nearer to each other, identifying a feasible path between them. We also introduce a directional coherence term that allows the expression of a preference for the alignment between the joint and marginal directional changes in feature space to reach a counterfactual. This term enables the generation of counterfactual explanations that align with a set of marginal predictions based on expectations of how the outcome of the model varies by changing one feature at a time. We evaluate our method, named Coherent Directional Counterfactual Explainer (CoDiCE), and the impact of the two novel biases against existing methods such as DiCE, FACE, Prototypes, and Growing Spheres. Through a series of ablation experiments on both synthetic and real datasets with continuous and mixed-type features, we demonstrate the effectiveness of our method.