LASSO與廣義LASSO選取變數比較

Abstract

在建構模型時，變數的選取是非常重要的，一般使用向前選取、向後刪除、逐步迴歸來挑選變數。\nTibshirani[4]在1996 年提出最小絕對值壓縮挑選運算least absolute\nshrinkage and selection operator；簡稱LASSO），LASSO 方法結合了變數係數的壓縮與變數選取。\n 本研究針對 LASSO 的限制式做修改，另外也將搜尋參數t 的方法改良，評估統計模型優劣則使用貝氏訊息準則，最後，改良的搜尋方法能更精確找到對於反應變數有影響的解釋變數，達到選取變數的效果。

In model construction, variable selection is a very important issue.Typical variable selection tools include\nforward selection, backward selection and stepwise selection. In 1996,Tibshirani proposed a method called LASSO (Least Absolute Shrinkage and Selection Operator), which can be used for variable selection via\ncoefficient shrinkage.\nIn this thesis, a general version of LASSO is proposed to improve the variable selection ability of LASSO. The proposed method is obtained by modifiying the constraints of LASSO. For both LASSO and the proposed method, the constraints depends on a shrinkage parameter that needs to be specified. In this thesis, the shrinkage parameter is selected using Bayesian information criterion. When the optimal parameter is found, the proposed method outperforms LASSO in variable selection. However, the search of the optimal parameter can be computationally intensive.