# Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals

arXiv: https://arxiv.org/abs/2312.10648 · HTML: https://mlsanity.com/paper/2312.10648/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 17 Dec 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["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)
- [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)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [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)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Preserving Causal Constraints in Counterfactual Explanations for Machine Learning Classifiers](https://mlsanity.com/paper/1912.03277/) (2019)
- [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)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [The Case for Bayesian Deep Learning](https://mlsanity.com/paper/2001.10995/) (2020)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertainties](https://mlsanity.com/paper/2103.08951/) (2021)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Counterfactual Explanations for Arbitrary Regression Models](https://mlsanity.com/paper/2106.15212/) (2021)
- [Explaining Black-Box Models through Counterfactuals](https://mlsanity.com/paper/2308.07198/) (2023)

## Built on by (most cited first, 5 of 5)

- [Looking in the mirror: A faithful counterfactual explanation method for interpreting deep image classification models](https://mlsanity.com/paper/2509.16822/) (2025)
- [Individualised Counterfactual Examples Using Conformal Prediction Intervals](https://mlsanity.com/paper/2505.22326/) (2025)
- [Provably Robust Bayesian Counterfactual Explanations under Model Changes](https://mlsanity.com/paper/2601.16659/) (2026)
- [CONFEX: Uncertainty-Aware Counterfactual Explanations with Conformal Guarantees](https://mlsanity.com/paper/2510.19754/) (2025)
- [Counterfactual Training: Teaching Models Plausible and Actionable Explanations](https://mlsanity.com/paper/2601.16205/) (2026)

## Abstract (arXiv)

Counterfactual explanations offer an intuitive and straightforward way to explain black-box models and offer algorithmic recourse to individuals. To address the need for plausible explanations, existing work has primarily relied on surrogate models to learn how the input data is distributed. This effectively reallocates the task of learning realistic explanations for the data from the model itself to the surrogate. Consequently, the generated explanations may seem plausible to humans but need not necessarily describe the behaviour of the black-box model faithfully. We formalise this notion of faithfulness through the introduction of a tailored evaluation metric and propose a novel algorithmic framework for generating Energy-Constrained Conformal Counterfactuals that are only as plausible as the model permits. Through extensive empirical studies, we demonstrate that ECCCo reconciles the need for faithfulness and plausibility. In particular, we show that for models with gradient access, it is possible to achieve state-of-the-art performance without the need for surrogate models. To do so, our framework relies solely on properties defining the black-box model itself by leveraging recent advances in energy-based modelling and conformal prediction. To our knowledge, this is the first venture in this direction for generating faithful counterfactual explanations. Thus, we anticipate that ECCCo can serve as a baseline for future research. We believe that our work opens avenues for researchers and practitioners seeking tools to better distinguish trustworthy from unreliable models.