2024/09/12 by Michael W. Ibrahim, Ibrahim, Michael, Heraldo Rozas +3
Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM
paper · pdf · doi:10.48550/arxiv.2409.08409
openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of multiclass classification for settings where data features x and their labels y are uncertain. We identify that distributionally robust one-vs-all (OVA) classifiers often struggle in settings with imbalanced data. To address this issue, we use Wasserstein distributionally robust optimization to develop a robust version of the multiclass support vector machine (SVM) characterized by the Crammer-Singer (CS) loss. First, we prove that the CS loss is bounded from above by a Lipschitz continuous function for all x ∈ X and y ∈ Y, then we exploit strong duality results to express the dual of the worst-case risk problem, and we show that the worst-case risk minimization problem admits a tractable convex reformulation due to the regularity of the CS loss. Moreover, we develop a kernel version of our proposed model to account for nonlinear class separation, and we show that it admits a tractable convex upper bound. We also propose a projected subgradient method algorithm for a special case of our proposed linear model to improve scalability. Our numerical experiments demonstrate that our model outperforms state-of-the art OVA models in settings where the training data is highly imbalanced. We also show through experiments on popular real-world datasets that our proposed model often outperforms its regularized counterpart as the first accounts for uncertain labels unlike the latter.