在本論文裡，針對一般非線性回歸問題，我們提出一個新的學習機：加法幅基函數網路。此學習機結合了經常使用在一般機器學習問題的幅基函數網路和半參數回歸問題裡使用的加法模型。
在統計回歸理論裡，於線性模型和非參數模型之間加法模型是一個好的折衷模型。為能處理更一般化的資料，我們將加法模型崁入幅基函數網路的輸出層而形成加法幅基函數網路。在本論文中，我們也將會提出簡單的權重更新規則。
我們會提出一些範例用來比較一般幅基函數網路和我們所提出的加法幅基函數網路的模擬結果。由模擬結果顯示，在加法輸出層中，適當選擇隱藏節點和核平滑器的頻寬，加法幅基函數網路會表現得比一般幅基函數網路好。此外，在所給定的學習問題中，我們發現在同樣準確度的標準下，加法幅基函數網路通常比幅基函數網路需要較少的隱藏節點。

In this thesis, we propose a new class of learning models, namely the additive generalized radial basis function networks (AGRBFNs), for general nonlinear regression problems. This class of learning machines combines the generalized radial basis function networks (GRBFNs) commonly used in general machine learning problems and the additive models (AMs) frequently encountered in semiparametric regression problems. In statistical regression theory, AM is a good compromise between the linear model and the nonparametric model. In order for more general network structure hoping to address more general data sets, the AMs are embedded in the output layer of the GRBFNs to form the AGRBFNs. Simple weights updating rules based on incremental gradient descent will be derived. Several illustrative examples are provided to compare the performances for the classical GRBFNs and the proposed AGRBFNs. Simulation results show that upon proper selection of the hidden nodes and the bandwidth of the kernel smoother used in additive output layer, AGRBFNs can give better fits than the classical GRBFNs. Furthermore, for the given learning problem, AGRBFNs usually need fewer hidden nodes than those of GRBFNs for the same level of accuracy.

誌謝 i
摘要 ii
Abstract iii
List of Figures and Tables iv
Glossary of Symbols vi
Glossary of Abbreviations vii
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Brief Sketch of the Contents 4
Chapter 2 Generalized Radial Basis Function Networks 7
2.1 Introduction 8
2.2 Training by Incremental Gradient Descent Algorithm 11
2.3 Subset Selection by K-means Algorithm 13
Chapter 3 Additive Models 16
3.1 Introduction 17
3.2 Backfitting Method for Additive Models 20
3.3 Univariate Nadaraya-Watson Estimators 21
3.4 Degrees of Freedom of a Smoother 25
Chapter 4 Additive Generalized Radial Basis Function Networks 27
4.1 Introduction 28
4.2 Training by Steepest Descent Algorithm 31
4.3 Bandwidth Selection 34
4.4 Degrees of Freedom 36
Chapter 5 Illustrative Examples 38
Chapter 6 Conclusion and Discussion 53
References 56

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