# Ensemble Methods for Robust Support Vector Machines using Integer Programming

arXiv: https://arxiv.org/abs/2203.01606 · HTML: https://mlsanity.com/paper/2203.01606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Understanding and Mitigating the Tradeoff Between Robustness and Accuracy](https://mlsanity.com/paper/2002.10716/) (2020)
- [Provable tradeoffs in adversarially robust classification](https://mlsanity.com/paper/2006.05161/) (2020)
- [A Practical Guide to Robust Optimization](https://mlsanity.com/paper/1501.02634/) (2015)

## Abstract (arXiv)

In this work we study binary classification problems where we assume that our training data is subject to uncertainty, i.e. the precise data points are not known. To tackle this issue in the field of robust machine learning the aim is to develop models which are robust against small perturbations in the training data. We study robust support vector machines (SVM) and extend the classical approach by an ensemble method which iteratively solves a non-robust SVM on different perturbations of the dataset, where the perturbations are derived by an adversarial problem. Afterwards for classification of an unknown data point we perform a majority vote of all calculated SVM solutions. We study three different variants for the adversarial problem, the exact problem, a relaxed variant and an efficient heuristic variant. While the exact and the relaxed variant can be modeled using integer programming formulations, the heuristic one can be implemented by an easy and efficient algorithm. All derived methods are tested on random and realistic datasets and the results indicate that the derived ensemble methods have a much more stable behaviour when changing the protection level compared to the classical robust SVM model.