Title Page

Abstract

국문 초록

Contents

Chapter 1. Introduction 11

Chapter 2. Methodology 14

2.1. Node impurity 14

2.2. An adaptive neural network estimator 16

2.3. Activation function 19

Chapter 3. Implementation 21

3.1. Optimization 21

3.2. Complexity parameter tuning 24

Chapter 4. Numerical Study 26

4.1. Simulation data analysis 26

4.2. Skin of orange data analysis 29

4.3. Real data analysis 30

Chapter 5. Conclusion 35

References 36

Table 4.1. Average test error with standard error in parenthesis and average rate of zero weight of 100 repetitions 29

Figure 2.1. Example of calculating impurity of hidden nodes 16

Figure 2.2. Effects of node impurity on neural network 17

Figure 2.3. Linear B-spline activation function 20

Figure 4.1. True decision boundary and bayes error of generated data 27

Figure 4.2. Plot of true and fitted decision boundary with generated data 28

Figure 4.3. Identified structure with skin of orange data 30

Figure 4.4. Identified structure with wage data (γ＝0.1) 31

Figure 4.5. Identified structure with wage data (γ＝0.8) 32

Figure 4.6. Plot of marital status versus decision function with jittering (1 for never married, 0 for have been married) 33

Figure 4.7. Plot of education level versus decision function with jittering (1 for College graduates and above, 0 for high school diploma or lower) 34

Figure 4.8. Plot of each eliminated predictor versus decision function with jittering 34