發(fā)布時間：2018-11-04 10:21

【摘要】：文章基于貝葉斯學習,將正則化方法從貝葉斯分析的角度展開,在響應變量服從正態(tài)分布、回歸系數(shù)服從指數(shù)型先驗分布族的條件下,用貝葉斯準則給出了懲罰因子的取值與響應變量、系數(shù)的方差之間的關系,并將這一結果應用到嶺回歸和lasso回歸中懲罰因子的選擇。實例檢驗結果表明,當響應變量和系數(shù)服從正態(tài)分布,懲罰因子的值取二者方差商的方法比嶺跡法和廣義交叉驗證法(GCV)擬合效果更優(yōu)。
[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.
【作者單位】： 西南交通大學數(shù)學學院;
【基金】：中央高�；究蒲袠I(yè)務費專項資金資助項目(SWJTU11CX155)
【分類號】：O212.8

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