arXiv:2603.25221cs.LGmath.OC2026-03被引 1

提出安全筛选规则,加速鲁棒支持向量机训练。

Gap Safe Screening Rules for Fast Training of Robust Support Vector Machines under Feature Noise

  • 基于拉格朗日对偶性设计筛选规则,识别可排除的样本。
  • 实验显示训练时间大幅降低,分类准确率不变。
  • 适合处理带特征噪声的监督学习任务。

鲁棒支持向量机(R-SVM)通过引入不确定性集来应对特征噪声,采用最坏情况建模提升可靠性,但计算成本更高。本文首次将安全样本筛选技术应用于最坏情况鲁棒模型,提出针对R-SVM的安全筛选规则,可在不改变最优解的前提下减少训练规模。通过拉格朗日对偶性分析,构建理想筛选规则,并进一步基于GAP安全区域适应到鲁棒设置中,实现有效样本筛选。实验表明,该方法显著缩短训练时间,同时保持分类精度,适用于存在特征噪声的场景。

原文摘要 · Abstract (English)

Robust Support Vector Machines (R-SVMs) address feature noise by adopting a worst-case robust formulation that explicitly incorporates uncertainty sets into training. While this robustness improves reliability, it also leads to increased computational cost. In this work, we develop safe sample screening rules for R-SVMs that reduce the training complexity without affecting the optimal solution. To the best of our knowledge, this is the first study to apply safe screening techniques to worst-case robust models in supervised machine learning. Our approach safely identifies training samples whose uncertainty sets are guaranteed to lie entirely on either side of the margin hyperplane, thereby reducing the problem size and accelerating optimization. Owing to the nonstandard structure of R-SVMs, the proposed screening rules are derived from the Lagrangian duality rather than the Fenchel-Rockafellar duality commonly used in recent methods. Based on this analysis, we first establish an ideal screening rule, and then derive a practical rule by adapting GAP-based safe regions to the robust setting. Experiments demonstrate that the proposed method significantly reduces training time while preserving classification accuracy.

鲁棒学习支持向量机筛选规则

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