基于非对称RoBoSS损失函数的稀疏鲁棒几何孪生支持向量机

中文摘要 AI 辅助

在实际场景中，训练数据通常包含冗余特征、标签噪声和特征噪声，这对机器学习方法的效率构成了严峻挑战。标准支持向量机（SVM）采用$l_2$-范数惩罚和铰链损失函数，因此缺乏选择重要特征的能力，且对噪声敏感。为解决这些问题，本文提出一种新颖的非对称、鲁棒、有界、稀疏且平滑的（aR）损失函数，用于$l_1$-范数惩罚的几何孪生支持向量机（aRSGTSVM），以处理分类和回归任务。$l_1$-范数惩罚可实现特征选择。所提出的aR损失函数不仅能有效减轻标签噪声的影响，还能显著增强对重采样噪声的稳定性，即边界超平面周围的零均值特征噪声。此外，本文还使用影响函数对aRSGTSVM的鲁棒性进行了统计分析。由于aRSGTSVM涉及非凸且非平滑的优化问题，我们开发了一种快速且稳定的基于近端梯度下降的求解算法。与相关的最先进方法相比，实验结果表明，所提出的aRSGTSVM在合成数据集和UCI数据集上均具有优越性。此外，我们将aRSGTSVM应用于指数跟踪任务，其在中国股市跟踪不同指数的结果表明，该方法可取得令人满意的性能。

英文摘要

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.

发表机构

• Chongqing Normal University（重庆师范大学）
• School of Mathematical Sciences, Chongqing Normal University（重庆师范大学数学科学学院）

机构由 AI 辅助整理，请以论文原文为准。