廣義線性模型下之距離相關係數篩選模型平均法

Abstract

這篇文章主要在探討廣義線性模型中，變數數量相當多且樣本數相當少的資料(大p小n資料)該如何處理。然而，我們並非關注於模型中變數的顯著性與否，我們更著重於結果的精確度。因此，我們採用了模型平均法基於 Kullback-Leibler 損失函數 (KL loss) 加上一個特別的懲罰項。緊接著，我們透過配合隨機切割與距離相關係數兩種方法來做為模型的篩選的方法。所以，我們的方法大致有兩個步驟。第一步 : 先透過隨機切割與距離相關係數法來篩選模型。第二步 : 將第一步篩選出的模型運用模型平均法得出最佳的平均模型。總而言之，在大p小n資料中，這個方法有較穩定的精確度且花費較少的時間。

This article sorts out the problem of high-dimension generalized linear regression models (GLM), especially for the number of predictors far more than the sample size (large-p-small-n problem). However, our method does not focus on seeking those true predictors, we concentrates on the accuracy of the results. Therefore, the Model Averaging method based on the Kullback-Leibler loss (KL loss) with a penalty term is constructed. Moreover, we apply random-partition and distance correlation method in order to obtain the comparatively outstanding candidate model set which does not produce a heavy computational burden as traditional model screening method. Our method consists of two steps. Firstly, we can obtain the candidate model set by using random-partition and distance correlation method. Secondly, compute the optimal weights of those models in candidate set above, and finally gain the best averaging model. To sum up, this method is good at better accuracy with comparatively less time for us to solve large-p-small-n GLM problems.