Machine learning and deep learning methods for density estimation, network estimation, and sample generation in complex biomedical data

다국어 초록 (Multilingual Abstract)

This thesis covers a variety of machine learning and deep learning methods for density estimation, sparse network estimation, and sample generation using Generative Adversarial Network (GAN), in complex and various types of biomedical data. While the density estimation is an essential task for the statistical learning process, the density estimation of multivariate categorical data that have many categorical options for each variable is not straightforward due to the relative sparsity in sample distributions, also known as the curse of dimensionality problem. To solve such a problem, a Bayesian approach that introduces an adaptive partitioning process is proposed in this thesis. In addition, a sparse network estimation method using penalized regression methods are proposed and evaluated with extensive simulations. A two-stage approach using the penalized regressions estimates the skeleton of Directed Acyclic Graphs (DAGs) in the first stage, then finds the directions of the edges. Since various methods can be used for both stages, the methods are compared and assessed in this thesis. Using the sparse network estimation methods, a survival associated gene network estimation method and a survival risk estimation method with the gene network are also proposed. The proposed methods are evaluated with various cancer genome datasets. Furthermore, GAN, a deep learning framework for sample synthesis, and its variants are addressed. Since an ordinary GAN has a limitation that one cannot generated desired samples, the proposed model, called Controllable GAN (ControlGAN), introduces an independent classifier to solve the problem. Evaluated by Inception score, ControlGAN demonstrates superior performance compared to the other conditional variants of GAN.

목차 (Table of Contents)

• Chapter 1. Introduction 1
• 1.1 Machine learning and deep learning 1
• 1.2 Organization of the thesis 4
• Chapter 2. Density estimation of multivariate categorical data 6
• 2.1 Introduction 7
• 2.2 Methods 11
• 2.2.1 Construction of an OPT with factor variables with many categories 11
• 2.2.2 Inference of the probability distribution from an OPT 17
• 2.2.3 Approximating OPT calculations 18
• 2.3 Results 19
• 2.3.1 Simulation Study 19
• 2.3.2 Case Study I 32
• 2.3.3 Case Study II 36
• 2.4 Discussions 38
• Chapter 3. Sparse network estimation of ultrahigh dimensional data 40
• 3.1 Introduction 41
• 3.2 Methods 43
• 3.2.1 Description of two-stage approach for estimating DAGs 43
• 3.2.2 Stage 1: Methods for estimating undirected graphs 44
• 3.2.3 Stage 2: Methods to determine edge directions 48
• 3.3 Simulation Data and Simulation Settings 50
• 3.3.1 Simulation data 50
• 3.3.2 Simulation settings for Stage 1 52
• 3.3.3 Simulation settings for Stage 2 53
• 3.4 Results 54
• 3.4.1 Simulation results for Stage 1: Finding neighborhoods 54
• 3.4.2 Simulation results for Stage 2: Estimating DAGs 64
• 3.4.3 Application: TCGA-BRCA Data 68
• 3.5 Discussions 76
• Chapter 4. Survival outcome estimation through gene networks 77
• 4.1 Introduction 78
• 4.2 Methods 81
• 4.2.1 A risk-gene network 81
• 4.2.2 Gene selection for survival analysis in high dimensional gene expression data 81
• 4.2.3 The construction of risk-gene network by finding neighborhood genes recursively 83
• 4.2.4 The data adjustment and the prediction of survival risk through risk-gene network 85
• 4.3 Results 90
• 4.3.1 Simulation Study 90
• 4.3.1.1 Simulation settings and data generation 90
• 4.3.1.2 Simulation results 93
• 4.3.2 Case Study 96
• 4.3.2.1 Analysis of risk-gene network for low grade glioma 96
• 4.3.2.2 The data adjustment and the prediction of survival risk through risk-gene network 98
• 4.3.2.3 Evaluation of data adjustment method 99
• 4.3.2.4 Additional experiments with other cancer datasets 101
• 4.4 Discussions 103
• Chapter 5. Controllable generative adversarial networks 107
• 5.1 Introduction 108
• 5.2 Background 112
• 5.2.1 A brief review of generative adversarial networks and its conditional variants 112
• 5.2.2 A trade-off between discriminator and classification performance in auxiliary classifier generative adversarial networks 114
• 5.3 Methods 118
• 5.3.1 Controllable generative adversarial networks 118
• 5.3.2 Optimization techniques used for convergence of ControlGAN 122
• 5.4 Results 125
• 5.4.1 Quantitative evaluation of ControlGAN with the CIFAR-10 dataset 125
• 5.4.2 An application to generating multi-label face images 127
• 5.5 Discussions 131
• Chapter 6. Conclusion 133
• Appendix 135
• A.1 Simulation Settings for Section 2 135
• A.2 Comparison of Rules for Asymmetric Edges in MB and Adaptive Lasso 139
• A.3 Other Figures for Section 3 145
• A.4 Supplementary Simulations with Various Network Types 148
• A.5 Comparison of Estimated Networks by each Method for Stages 1 and 2 with TCGA-BRCA Dataset 154
• A.6 Breast Cancer Genes 157
• A.7 Proof of Proposition 1 158
• A.8 Simulation Study of Section 4 161
• A.9 Case Study for Risk-gene Networks 167
• A.10 Repetition of the Risk-gene Networks 173
• A.11 Experimental Settings for ControlGAN 175
• References 178
• 국문초록 (Abstract in Korean) 196
• Curriculum Vitae 197