论文标题
CDC提交第1461号的补充材料
Supplementary Material for CDC Submission No. 1461
论文作者
论文摘要
在本文中，我们将重点放在两种超参数估计方法之间的比较时，回归矩阵的条件数量的影响：与输出预测相关的均方误差（MSE）相对于均方误差（MSE），经验贝叶斯（EB）（EB）和Stein的无偏估计量。我们首先表明，Surey成本函数收敛速率上限的回归矩阵的条件数中最大的功率始终比EB成本函数收敛速率上限大于一个。同时，事实证明，EB和Surey高参数估计量在适当的条件下均非正态分布。此外，进一步研究了一个脊回归案例，以表明当回归矩阵的状况数量到Infinity时，Surey估计器的渐近方差往往大于EB估计器的渐近方差。
In this paper, we focus on the influences of the condition number of the regression matrix upon the comparison between two hyper-parameter estimation methods: the empirical Bayes (EB) and the Stein's unbiased estimator with respect to the mean square error (MSE) related to output prediction (SUREy). We firstly show that the greatest power of the condition number of the regression matrix of SUREy cost function convergence rate upper bound is always one larger than that of EB cost function convergence rate upper bound. Meanwhile, EB and SUREy hyper-parameter estimators are both proved to be asymptotically normally distributed under suitable conditions. In addition, one ridge regression case is further investigated to show that when the condition number of the regression matrix goes to infinity, the asymptotic variance of SUREy estimator tends to be larger than that of EB estimator.
