# S-CFE: Simple Counterfactual Explanations

arXiv: https://arxiv.org/abs/2410.15723 · HTML: https://mlsanity.com/paper/2410.15723/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [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)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [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)
- [Sparse and Imperceivable Adversarial Attacks](https://mlsanity.com/paper/1909.05040/) (2019)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [Convex Density Constraints for Computing Plausible Counterfactual Explanations](https://mlsanity.com/paper/2002.04862/) (2020)
- [Towards Robust, Locally Linear Deep Networks](https://mlsanity.com/paper/1907.03207/) (2019)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [Consequence-aware Sequential Counterfactual Generation](https://mlsanity.com/paper/2104.05592/) (2021)
- [Sparse and Imperceptible Adversarial Attack via a Homotopy Algorithm](https://mlsanity.com/paper/2106.06027/) (2021)
- [GSE: Group-wise Sparse and Explainable Adversarial Attacks](https://mlsanity.com/paper/2311.17434/) (2023)
- [CountARFactuals -- Generating plausible model-agnostic counterfactual explanations with adversarial random forests](https://mlsanity.com/paper/2404.03506/) (2024)

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

- [Training on Plausible Counterfactuals Removes Spurious Correlations](https://mlsanity.com/paper/2505.16583/) (2025)

## Abstract (arXiv)

We study the problem of finding optimal sparse, manifold-aligned counterfactual explanations for classifiers. Canonically, this can be formulated as an optimization problem with multiple non-convex components, including classifier loss functions and manifold alignment (or plausibility) metrics. The added complexity of enforcing sparsity, or shorter explanations, complicates the problem further. Existing methods often focus on specific models and plausibility measures, relying on convex ℓ1 regularizers to enforce sparsity. In this paper, we tackle the canonical formulation using the accelerated proximal gradient (APG) method, a simple yet efficient first-order procedure capable of handling smooth non-convex objectives and non-smooth ℓp (where 0 ≤ p < 1) regularizers. This enables our approach to seamlessly incorporate various classifiers and plausibility measures while producing sparser solutions. Our algorithm only requires differentiable data-manifold regularizers and supports box constraints for bounded feature ranges, ensuring the generated counterfactuals remain actionable. Finally, experiments on real-world datasets demonstrate that our approach effectively produces sparse, manifold-aligned counterfactual explanations while maintaining proximity to the factual data and computational efficiency.