臺灣博碩士論文加值系統

目標:由於醫療技術的進展，我們能夠獲得越來越豐富的生物標記醫療數據，透過結合這些生物標記，我們可以對病人的疾病有更全盤的評估。梯度提升法是機器學習中集成學習的方法之一，不僅是各大機器學習競賽的常勝軍，而且有良好的模型解釋能力。約登指數可以對診斷之切點進行量化評估，進而利用此指數最佳化整體的準確率。因此本論文利用梯度提升法為演算法，結合約登指數為目標函數，提出新的統計方法。
方法:由S函數推導出新的平滑函數來近似約登指數中的符號函數，由此得到平滑之約登指數；再將目標函數對輸出函數做偏微分，得到目標函數的梯度。我們藉由目標函數的反向梯度對輸出函數進行優化，透過疊代不斷重複優化的過程，此步驟即為梯度提升法並且以約登指數為目標函數進行最佳化。
結果:經由多筆實際資料(包含小樣本及高維度資料)及模擬資料(包含線性及非線性)來評估模型的診斷正確率，新方法在線性及高維度資料中表現較佳。
結論:藉由優化約登指數的梯度提升法求得之生物標記組合在高維度資料中甚為實用，不僅有良好的模型解釋能力更在分類預測中具有優勢。

Objective: With the development of medical technology, we have more and more biomarker information recorded to evaluate the clinical situation of a patient. Combining the related biomarkers can help us to have a general picture of the disease. With the reasons above, we proposed a strategy to combine biomarkers. Gradient boosting is one of the ensemble learning methods in machine learning. Gradient boosting not only always being one of the winning solutions in machine learning competitions but also has a good interpretability of models. Youden Index is able to evaluate the cutoff point with quantity of the diagnostic test and we further apply it on the overall accuracy optimization. Hence, we proposed a new method with choosing gradient boosting as our algorithm and combining with the Youden Index as the target function as optimization.
Methods: A new smooth function is derived via modified the sigmoid function. Surrogating the sign function with the new smooth function in the Youden Index target function, a new smooth Youden Index was set as the target function. Gradient of the target function is the partial derivative of the Youden Index with respect to the output function. Optimize the output function with negative gradient and repeat the optimization process by iteration time.
Results: The performance in diagnostic accuracy was demonstrated in real data (including high dimension data and small sample data) and simulation data (including linear data and non-linear data). Our methods have a competitive outcome in linear data and high dimension data.
Conclusions: The biomarker combination derived from the new strategy, gradient boosting the Youden Index, may provide not only a good interpretability in a high dimension data structure but also a competitive perdition prediction accuracy.

Chapter 1 Introduction 1
1.1 Study Background 1
1.2 Study purpose 3
Chapter 2 Literature Review 4
2.1 Youden Index 4
2.1.1 An Introduction of Youden Index 4
2.1.2 The Objection Function of Youden Index 7
2.2 Gradient Boosting 9
2.2.1 Ensemble Methods 9
2.2.2 Bagging 10
2.2.3 The Beginning Concept of Boosting 11
2.2.4 The First Boosting Algorithm – Adaboost 11
2.2.5 From Machine Learning to Statistical Modeling – Gradient Boosting 13
2.2.6 Gradient Boosting Algorithm 13
2.2.7 Flow Chart of Gradient Boosting 15
Chapter 3 Proposed a New Method – Gradient Boosting the Youden Index 17
3.1 Applied the Youden Index as the target function in gradient boosting 17
3.2 The proposed new smooth function 18
3.3 Surrogate the sign function with new smooth function 19
3.4 The proposed new negative gradient 19
3.5 Parameter Setting 20
3.6 Programming approach 20
Chapter 4 Result 21
4.1 Simulation Result 21
4.2 Bupa Liver Disease Data 26
4.2.1 Data Description 26
4.2.2 Cross Validation and Model 27
4.2.3 Result 28
4.3 Leukemia Data 29
4.3.1 Data Description 29
4.3.2 Cross Validation and Model 30
4.3.3 Result 30
4.4 Tuberculosis(TB) Data 31
4.3.1 Data Description 31
4.3.2 Cross Validation and Model 31
4.3.3 Result 32
Chapter 5 Discussion 33
References 35
Attachment 38

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