提出新型鲁棒损失函数，提升分类回归模型对噪声和冗余特征的抗性。
Sparse and robust geometric twin support vector machine via asymmetric RoBoSS loss function
- 设计非对称鲁棒损失函数，结合l1正则实现特征选择与噪声抑制。
- 在合成数据与UCI数据集上优于主流方法，且对标签噪声和特征扰动更稳定。
- 适合高噪声、高维数据场景，尤其适用于金融指数追踪等实际任务。
真实场景中训练数据常含冗余特征、标签噪声和特征噪声，严重制约机器学习效率。标准支持向量机（SVM）采用l2范数惩罚和合页损失，难以筛选关键特征且对噪声敏感。本文提出一种新颖的非对称、鲁棒、有界、稀疏和平滑（aR）损失函数，用于l1范数正则化的几何孪生支持向量机（aRSGTSVM），以应对分类与回归任务。l1范数惩罚可实现特征选择；所提aR损失函数不仅能有效缓解标签噪声影响，还可显著增强对重采样噪声（即边界超平面附近的零均值特征噪声）的稳定性。此外，通过影响函数进行了aRSGTSVM鲁棒性的统计分析。由于aRSGTSVM涉及非凸与非光滑优化，本文开发了一种快速稳定的基于近端梯度下降的求解算法。实验结果表明，在合成数据与UCI数据集上，该方法优于现有先进方法。进一步应用于中国股市指数追踪任务，结果显示其在跟踪不同指数时表现优异。
原文摘要 · Abstract (English)
In real-world scenarios, the training data usually contains redundant features, label noise and feature noise, which provide severe challenges for the efficiency of machine learning methods. Since standard support vector machine (SVM) adopts $l_2$-norm penalty and hinge loss function, it lacks the ability of selecting significant features and is sensitive to noise. To address these issues, this paper proposes a novel asymmetric, robust, bounded, sparse and smooth (aR) loss function for $l_1$-norm penalized geometric twin SVM (aRSGTSVM) to handle classification and regression tasks. The $l_1$-norm penalty can achieve the feature selection. The proposed aR loss function can not only effectively mitigate the impact of label noise, but also significantly enhance the stability to resampling noise, i.e., the zero-mean feature noise around the boundary hyperplanes. Furthermore, a statistical analysis of the robustness of aRSGTSVM was also conducted using the influence function. Since aRSGTSVM involves nonconvex and nonsmooth optimization, we develop a fast and stable proximal gradient descent based solving algorithm. Compared with related state-of-the-art methods, experimental results demonstrate the superiority of the proposed aRSGTSVM on both synthetic and UCI datasets. Furthermore, we apply aRSGTSVM to index tracking tasks, where results for tracking the different indices in the China stock market show that it can achieve satisfactory performance.
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