基于截断Pinball损失的支持向量机多类别概率估计  

SUPPORT VECTOR MACHINE WITH TRUNCATED PINBALL LOSS FOR MULTI-CLASS PROBABILITY ESTIMATION

作　　者：刘恒源 倪中新[1] 陆贵斌[1] Liu Hengyuan;Ni Zhongxin;Lu Guibin(School of Economics,Shanghai University,Shanghai 201800,China)

机构地区：[1]上海大学经济学院,上海201800

出　　处：《计算机应用与软件》2023年第5期297-304,共8页Computer Applications and Software

摘　　要：SVM对训练样本中的噪声非常敏感,因此在概率估计准确性上还存在改进空间。针对这一问题,提出一种稳健非凸的截断Pinball损失,作为Hinge和Pinball损失的广义形式,截断Pinball损失具有稀疏性和噪声鲁棒性,可以有效地降低异常点对损失函数的影响。基于该损失,T-Pin-SVM模型被开发并用于多类别的概率估计。理论研究表明,T-Pin-SVM模型具有Fisher一致性。数值分析表明,相对Hinge和Pinball损失的SVM模型,T-Pin-SVM在概率估计任务中的准确性上具有较强竞争力。另外,概率估计结合分类规则可提供分类结果,因此T-Pin-SVM在分类准确性上也有一定提升。SVM is very sensitive to the outliers in the training samples,there is still room for improvement in the accuracy of probability estimation.Aiming at this problem,this paper proposes a robust and non-convex truncated Pinball loss,which is a generalized form of Hinge and Pinball loss.The truncated Pinball loss had sparsity and noise robustness,therefore could effectively reduce the influence of abnormal points on the loss function.Based on Truncated Pinball loss,a T-Pin-SVM model was developed and used for multi-class probability estimation.Theoretical results show that the proposed T-Pin-SVM model has Fisher consistency.Numerical analysis shows that compared with SVM with Hinge and Pinball loss,T-Pin-SVM is more competitive in the accuracy of probability estimation task.In addition,probability estimation combined with classification rules can provide classification results,so T-Pin-SVM also has a certain improvement in classification accuracy.

关 键 词：SVM 截断Pinball 概率估计 非凸优化 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]