# Robust Explanations for Private Support Vector Machines

arXiv: https://arxiv.org/abs/2102.03785 · HTML: https://mlsanity.com/paper/2102.03785/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 7 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)

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

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [SoK: Taming the Triangle -- On the Interplays between Fairness, Interpretability and Privacy in Machine Learning](https://mlsanity.com/paper/2312.16191/) (2023)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)

## Abstract (arXiv)

We consider counterfactual explanations for private support vector machines (SVM), where the privacy mechanism that publicly releases the classifier guarantees differential privacy. While privacy preservation is essential when dealing with sensitive data, there is a consequent degradation in the classification accuracy due to the introduced perturbations in the classifier weights. For such classifiers, counterfactual explanations need to be robust against the uncertainties in the SVM weights in order to ensure, with high confidence, that the classification of the data instance to be explained is different than its explanation. We model the uncertainties in the SVM weights through a random vector, and formulate the explanation problem as an optimization problem with probabilistic constraint. Subsequently, we characterize the problem's deterministic equivalent and study its solution. For linear SVMs, the problem is a convex second-order cone program. For non-linear SVMs, the problem is non-convex. Thus, we propose a sub-optimal solution that is based on the bisection method. The results show that, contrary to non-robust explanations, the quality of explanations from the robust solution degrades with increasing privacy in order to guarantee a prespecified confidence level for correct classifications.