论文标题
基于广义近似消息传递的惩罚回归的预测错误
Prediction Errors for Penalized Regressions based on Generalized Approximate Message Passing
论文作者
论文摘要
我们讨论了假定的统计模型的预测准确性，从广义线性模型的预测误差和惩罚最大似然方法方面的预测准确性。我们使用通用的近似消息传递（GAMP）算法和副本方法来得出预测错误的估计量形式，例如$ C_P $标准，信息标准和剩余的交叉验证（LOOCV）错误。当模型参数的数量足够小时，这些估计器相互重合。但是，它们之间的差异尤其是模型参数数量大于数据维度的参数区域中。在本文中，我们回顾了预测错误和相应的估计器，并讨论了它们的差异。在GAMP的框架中，我们表明信息标准可以使用估计值的方差来表示。此外，我们通过利用GAMP提供的表达方式来说明如何从信息标准中解决LOOCV误差。
We discuss the prediction accuracy of assumed statistical models in terms of prediction errors for the generalized linear model and penalized maximum likelihood methods. We derive the forms of estimators for the prediction errors, such as $C_p$ criterion, information criteria, and leave-one-out cross validation (LOOCV) error, using the generalized approximate message passing (GAMP) algorithm and replica method. These estimators coincide with each other when the number of model parameters is sufficiently small; however, there is a discrepancy between them in particular in the parameter region where the number of model parameters is larger than the data dimension. In this paper, we review the prediction errors and corresponding estimators, and discuss their differences. In the framework of GAMP, we show that the information criteria can be expressed by using the variance of the estimates. Further, we demonstrate how to approach LOOCV error from the information criteria by utilizing the expression provided by GAMP.
