基于贝叶斯学习的惩罚因子的选择
发布时间：2018-11-04 10:21
【摘要】：文章基于贝叶斯学习,将正则化方法从贝叶斯分析的角度展开,在响应变量服从正态分布、回归系数服从指数型先验分布族的条件下,用贝叶斯准则给出了惩罚因子的取值与响应变量、系数的方差之间的关系,并将这一结果应用到岭回归和lasso回归中惩罚因子的选择。实例检验结果表明,当响应变量和系数服从正态分布,惩罚因子的值取二者方差商的方法比岭迹法和广义交叉验证法(GCV)拟合效果更优。
[Abstract]:Based on Bayesian learning, the regularization method is developed from the perspective of Bayesian analysis. Under the condition that the response variable is normally distributed, the regression coefficient is assumed to be an exponential prior distribution family, the regularization method is developed from the point of view of Bayesian analysis. The relation between the value of penalty factor and the variance of response variable and coefficient is given by using Bayesian criterion, and the result is applied to the choice of penalty factor in ridge regression and lasso regression. The results show that when the response variables and coefficients are from normal distribution, the method of taking the variance quotient of the penalty factor from the value of the two factors is better than the ridge trace method and the generalized cross validation method in (GCV) fitting.
【作者单位】： 西南交通大学数学学院;
【基金】：中央高校基本科研业务费专项资金资助项目(SWJTU11CX155)
【分类号】：O212.8
本文编号：2309535
[Abstract]:Based on Bayesian learning, the regularization method is developed from the perspective of Bayesian analysis. Under the condition that the response variable is normally distributed, the regression coefficient is assumed to be an exponential prior distribution family, the regularization method is developed from the point of view of Bayesian analysis. The relation between the value of penalty factor and the variance of response variable and coefficient is given by using Bayesian criterion, and the result is applied to the choice of penalty factor in ridge regression and lasso regression. The results show that when the response variables and coefficients are from normal distribution, the method of taking the variance quotient of the penalty factor from the value of the two factors is better than the ridge trace method and the generalized cross validation method in (GCV) fitting.
【作者单位】： 西南交通大学数学学院;
【基金】：中央高校基本科研业务费专项资金资助项目(SWJTU11CX155)
【分类号】：O212.8
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