# Rethinking Distance Metrics for Counterfactual Explainability

arXiv: https://arxiv.org/abs/2410.14522 · HTML: https://mlsanity.com/paper/2410.14522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 49 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 30 of 35)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [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)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Sanity Checks for Saliency Metrics](https://mlsanity.com/paper/1912.01451/) (2019)
- [Do Concept Bottleneck Models Learn as Intended?](https://mlsanity.com/paper/2105.04289/) (2021)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Algorithms to estimate Shapley value feature attributions](https://mlsanity.com/paper/2207.07605/) (2022)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [CXPlain: Causal Explanations for Model Interpretation under Uncertainty](https://mlsanity.com/paper/1910.12336/) (2019)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Inverse Classification for Comparison-based Interpretability in Machine Learning](https://mlsanity.com/paper/1712.08443/) (2017)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)
- [Generating Counterfactual Explanations with Natural Language](https://mlsanity.com/paper/1806.09809/) (2018)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [Towards Understanding In-Context Learning with Contrastive Demonstrations and Saliency Maps](https://mlsanity.com/paper/2307.05052/) (2023)

## Built on by (most cited first, 1 of 1)

- [GlyTwin: Digital Twin for Glucose Control in Type 1 Diabetes Through Optimal Behavioral Modifications Using Patient-Centric Counterfactuals](https://mlsanity.com/paper/2504.09846/) (2025)

## Abstract (arXiv)

Counterfactual explanations have been a popular method of post-hoc explainability for a variety of settings in Machine Learning. Such methods focus on explaining classifiers by generating new data points that are similar to a given reference, while receiving a more desirable prediction. In this work, we investigate a framing for counterfactual generation methods that considers counterfactuals not as independent draws from a region around the reference, but as jointly sampled with the reference from the underlying data distribution. Through this framing, we derive a distance metric, tailored for counterfactual similarity that can be applied to a broad range of settings. Through both quantitative and qualitative analyses of counterfactual generation methods, we show that this framing allows us to express more nuanced dependencies among the covariates.