應用統計學習方法於響應模型預測與渴望條件分析

Abstract

本論文主要探討如何在滿足響應變數的渴望條件下，找出預測變數的彈性工作範圍，且此範圍愈大愈佳，同時，找出影響工作範圍的重要預測變數排序與權重。相較於許多傳統方法只找出預測變數的最佳工作點，本論文進一步找出預測變數的工作範圍，並以高維長方體來表述此工作範圍，如此，可使得在控制預測變數時能更為彈性。 本實驗以晶圓製程資料為例，希望在滿足良率大於或等於95％的條件下，找出預測變數的彈性工作範圍。首先在資料前置處理上，我們對資料進行特徵選取、濾除冗餘變數與排除歧異值等前置處理。接著，利用經過前置處理過的資料來建立K-最鄰近點、三立方體核心、局部線性迴歸核心、適應K-最鄰近點、適應三立方體核心與適應局部線性迴歸核心等六種記憶基礎模型並進行迴歸。然後，藉由分類樹來分類並決定工作範圍。最後，利用驗證資料來確認所決定的工作範圍。 同樣的方法除了可應用在本論文中所舉的晶圓製程例子之外，也可應用於金融與醫學等領域。

This paper aims to look out for the flexible working region of predictor variable under the condition of meeting the desirability of response variable. The region will be completed as wide as possible. Besides, find out the rank of important predictor variable which will affects working region. Compare to many traditional methods, which merely find out the optimal point, this paper takes one step ahead to look out for the working region of predictor variable and uses hyper rectangular cuboid to state this region. Hence, it will be more flexible when we control predictor variable. This experiment takes wafer manufacturing process data as an example, hoping the yield will be greater than or equal to 95%. Under this situation, we want to find out the flexible working region of predictor variable. Fist, we take data to feature selection, rid of redundancy and outlier in data preprocession. Next, we use the preprocessed data to build up six memory- based models to execute regression. Afterward, we use classification trees to classify and decide the working region. Finally, utilize validation data to confirm the decided working region. The same method can be applied not only to wafer manufacturing process in this paper, but to the fields of finance and medical science, etc….