复杂曲面拟合的相关向量机模型及其泛化能力

Relevance Vector Machine Regression Models for Complex Surface Fitting and Its Generalization Ability

介绍相关向量机回归(RVM,Relevance Vector Machine)的基本原理。分析采用高斯径向基核函数时,核函数参数与模型性能之间的关系,并给出核函数参数选择建议。针对一个复杂非线性函数,采用均匀网格取样,并分别增加正态分布噪声和均匀分布噪声,分析RVM回归分析的拟合和泛化能力并与支持向量机(SVM,Support Vector Machine)回归模型作了比较。结果表明,SVM对样本数据的拟合能力优于RVM。但对于非训练样本,RVM的泛化能力要优于SVM,而且RVM模型更加稀疏,且在给出预测值的同时能够给出预测值的置信区间。

A brief introduction of RVM （Relevance vector machine） Regression models is given firstly. The Gaussian radial basis function is selected as the kernel function in RVM and the relationship between kernel function parameters and model performance is analyzed. With that a parameter selection method is put forward. Then With the equal intervals space filling and a complex nonlinear function, normal-distributed and uniform-distributed noise is added and the fitting and generalization ability of RVM regression is analyzed and the results are compared with support vector machine （SVM） regression models. The results show that for the training samples, the fitting ability of SVM regression models is better than RVM regression models. But for the testing samples, the generalization ability of RVM regression models is much better than SVM regression models, i.e. the RVM regression models are sparser than SVM models. Furthermore, RVM regression models can give not only the predicted values but also their confidence intervals.