贝叶斯支持向量回归及其应用  

Bayesian Support Vector Regression and Its Application

作　　者：林芳逗 赵为华[1] 张日权 Lin Fangdou;Zhao Weihua;Zhang Riquan(School of Science,Nantong University,Nantong Jiangsu 226019,China;School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai 201620,China)

机构地区：[1]南通大学理学院,江苏南通226019 [2]上海对外经贸大学统计与信息学院,上海201620

出　　处：《统计与决策》2023年第3期49-54,共6页Statistics & Decision

基　　金：国家社会科学基金资助项目(22BTJ025);国家自然科学基金资助项目(11971171)。

摘　　要：支持向量回归(SVR)是机器学习中重要的数据挖掘方法,当前关于SVR的研究大多基于二次规划理论,同时,利用交叉验证或一些智能算法选取模型中的超参数,然而,基于二次规划理论的SVR估计方法不仅计算量较大,而且不能进行后续的统计推断分析。文章基于贝叶斯方法研究SVR,通过引入两个潜在变量将SVR的ϵ不敏感损失函数表示为双重正态-尺度混合模型并构建似然函数,通过选取适当的先验分布获得兴趣参数和超参数的Gibbs抽样算法。为筛选重要变量和最优模型,引入0-1指示变量并选取回归参数的Spike and Slab先验来获得贝叶斯变量选择算法。数值模拟证明了所提算法的有效性,并在非正态误差下表现出很好的稳健性。最后将所提方法应用于房价数据分析,得到了有意义的结果。Support vector regression(SVR)is an important data mining method in machine learning.Current researches about SVR are mostly based on the theory of quadratic programming,and the hyperparameters in the model are selected by cross-validation or some intelligent algorithms.However,the SVR estimation method based on quadratic programming theory not only requires a large amount of computation,but also cannot carry out subsequent statistical inference analysis.This paper is based on Bayesian method to study SVR.By introducing two potential variables,the ϵ insensitive loss function of SVR is ex⁃pressed as a double normal-scale mixed model and the likelihood function is constructed.By selecting appropriate prior distribu⁃tions,the Gibbs sampling algorithm of interest parameters and hyperparameters is obtained.In order to screen important variables and optimal models,0-1 indicator variables are introduced and Spike and Slab priors of regression parameters are selected to ob⁃tain Bayesian variable selection algorithm.Numerical simulation proves the effectiveness of the proposed algorithm,and shows good robustness under the non-normal error.Finally,the proposed method is applied to the analysis of housing price data,and the meaningful results are obtained.

关 键 词：支持向量回归 贝叶斯变量选择 GIBBS抽样 Spike and Slab先验 

分 类 号：O212.8[理学—概率论与数理统计]