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In this work we study binary classification problems where we assume that ourtraining data is subject to uncertainty, i.e. the precise data points are notknown. To tackle this issue in the field of robust machine learning the aim isto develop models which are robust against small perturbations in the trainingdata. We study robust support vector machines (SVM) and extend the classicalapproach by an ensemble method which iteratively solves a non-robust SVM ondifferent perturbations of the dataset, where the perturbations are derived byan adversarial problem. Afterwards for classification of an unknown data pointwe perform a majority vote of all calculated SVM solutions. We study threedifferent variants for the adversarial problem, the exact problem, a relaxedvariant and an efficient heuristic variant. While the exact and the relaxedvariant can be modeled using integer programming formulations, the heuristicone can be implemented by an easy and efficient algorithm. All derived methodsare tested on random and realistic datasets and the results indicate that thederived ensemble methods have a much more stable behaviour when changing theprotection level compared to the classical robust SVM model.

Ensemble Methods for Robust Support Vector Machines using Integer Programming