基于贝叶斯Lasso处理异常值及重尾数据的研究  

Research on Processing Outliers and Heavy Tails Based on Bayesian Lasso

作　　者：王新军 朱永忠[1] 李佳蓓[1] Wang Xinjun, Zhu Yongzhong, Li Jiabei(College of Science, Hohai University, Nanjing 211100, Chin)

机构地区：[1]河海大学理学院

出　　处：《统计与决策》2018年第6期10-14,共5页Statistics & Decision

摘　　要：在高维数据回归问题中,由于数据中往往存在异常值,特别地在一些领域内会出现数据波动异常激烈甚至呈现出厚尾的特性,所以对于这类问题,传统的最小二乘估计很难处理。文章对上述的问题,改进现有的Bayesian Lasso方法,在Bayesian Lasso的Gibbs抽样过程中引入两组潜变量,来模拟模型的随机误差,通过Gibbs抽样以及边缘极大似然法得出参数及潜变量有效的后验分布,提出了一种稳健有效的处理异常值的方法。通过数据仿真以及实例分析,与现有的方法进行比较,结果表明此方法能很好地处理数据中出现异常值以及呈现厚尾特性的数据。In high dimensional data regression, a fierce fluctuation in the data and even heavy-tailed features will be present particularly in some areas because of a common existence of outliers in the data, so for this kind of problem the traditional least squares estimation is hard to handle. Aiming at the above problems, this paper improves the existing Bayesian Lasso method, and introduces two sets of latent variables into the Gibbs sampling of Bayesian Lasso to simulate the random error of the model. The paper also adopts the Gibbs sampling and marginal maximum likelihood to obtain the effective posterior distribution of the parame- ters and latent variables and propose a robust method of dealing with the outliers effectively. Finally, the results of simulation, real example analysis and the comparison with the existing method show that the improved method is able to dispose outliers and heavy-tails.

关 键 词：贝叶斯Lasso 异常值 重尾 吉布斯抽样 

分 类 号：O212[理学—概率论与数理统计]