Abstract: The dependency relationship between r and the input noise in r-SVR is studied using SVR Bayesian evidence framework.First，focus is paid on the cases of laplacian noise and uniform noise，and the approximately inversely linear dependencies between r and the variances of the two noises are then respectively derived.Second，with the relevant conclusion on r-SVR and experimental study，the more general claim is then proposed that the approximately inversely linear dependency is almost kept between r and the input noise in r-SVR.Such a dependency relationship is useful to determine the optimal choice for r in Norm-r loss function in the existence of unknown input noise.

Key words: Support Vector Machines（SVM）, Support Vector Regression（SVR）, Norm-r function

摘要： 为使r范数SVR更具鲁棒性，深入研究了r范数SVR中参数与输入噪声之间的关系。运用SVR的贝叶斯框架，分别推导出了鲁棒的r范数SVR中参数r与拉斯噪声和均匀噪声之间呈近似的线性反比关系。并结合仿真结果和已有的相关结论，得到了更为一般的结论，即鲁棒的r范数SVR中参数r与输入噪声之间呈近似的线性反比关系。这一结论为输入样本含有分布未知噪声的情况下r范数SVR参数的选择提供了理论依据。

关键词: 支持向量机, 支持向量回归机, r范数损失函数