Novel Machine Learning Methods for Genomic Data Analysis Open Access
Wang, Shiyu (Spring 2024)
Abstract
Gene-gene interaction networks, such as gene co-expression networks, offer a comprehensive view of biological processes disrupted in disease. Despite its significance, the integration of gene-gene interactions into gene-disease analysis remains under-investigated. In my dissertation, I aim to fill this gap by developing innovative machine learning models to analyze graph-structured data, designing efficient statistical models for genomic data analysis, and finally leveraging techniques in both graph machine learning and statistical genomics to create cutting-edge graph neural network approaches to understand the genetic basis of diseases.
My first objective is to generate graph structures, such as molecular and material structures, that meet various property constraints. This includes ensuring the periodicity of the material structures, optimizing a property's value, and limiting a third property within a range. To accomplish these goals, I create deep generative models for controlled graph generation, including PGD-VAE, which enables the generation of periodic graphs, and CorrVAE, while controls correlated properties in the produced graph structure. Additionally, I contribute to this field by constructing GraphGT, a systematic collection of graph generation and transformation datasets.
The second objective of my research is to determine the spatial arrangement of chromosomes and transcripts in cells and tissues through HiC data and DNA microscopy. Traditional methods have limitations such as high computational demands or insufficient stability for large-scale biomolecular systems. To overcome these challenges, I create a hierarchical Bayesian statistical model. This model uses hierarchical clustering to assign clusters to biomolecules, Poisson regression to infer proximities within and between clusters, and MCMC methods to estimate model parameters and spatial coordinates of biomolecules. This approach offers a more efficient and stable solution for investigating the spatial organization of biological systems.
The third objective of my research is to create novel graph neural networks to analyze genomic data. Variations in gene expression have been found to play a crucial role in elevating the risk of complex diseases, but are usually specific to the tissue type. Hence, the ability to predict gene expression in difficult-to-access target tissues (e.g., brain, lung) from easily obtainable source tissue (e.g., blood, skin) is critical and has many practical uses. Currently, methods used for cross-tissue gene expression prediction mostly rely on linear regression, which cannot account for the potential nonlinear relationships and gene-gene interactions that exist across tissues. To address this gap, I introduce a novel graph-transformation model. The model employs graph attention networks (GATs) to encode gene co-expression networks in both source and target tissues, and a prediction layer to predict target tissue gene expression. I further extend the model to perform multi-source-to-multi-target prediction via hypernetworks that generate GATs guided by tissue-specific meta information.
Table of Contents
1 Controllable data generation by deep learning 1
1.1 Deep generative model for periodic graphs . . . . . . . . . . . . . . . 1
1.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 14
1.1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.1.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.2 Multi-objective deep data generation with correlated property control 26
1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.2.3 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 31
1.2.4 Proposed approach . . . . . . . . . . . . . . . . . . . . . . . . 32
1.2.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
1.2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2 Model-Based Spatial Reconstruction of Large-Scale Biomolecules via Bayesian Inference of a Hierarchical Spatial Model 59
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.2.1 Learning spatial organization via Hi-C . . . . . . . . . . . . . 64
2.2.2 Learning spatial organization via DNA microscopy . . . . . . 66
2.3 Hierarchical Model for Large-Scale Biomolecules . . . . . . . . . . . . 67
2.3.1 A general model for spatial reconstruction of biomolecules . . 67
2.3.2 The hierarchical spatial model . . . . . . . . . . . . . . . . . . 69
2.3.3 Bayesian inference of HiSpa . . . . . . . . . . . . . . . . . . . 75
2.4 Monte Carlo Strategies for Posterior Sampling . . . . . . . . . . . . . 77
2.4.1 Gibbs sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.4.2 Special group moves . . . . . . . . . . . . . . . . . . . . . . . 79
2.5 Efficient Initialization of HiSpa . . . . . . . . . . . . . . . . . . . . . 80
2.5.1 Group partition . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.5.2 Backbone initialization . . . . . . . . . . . . . . . . . . . . . . 82
2.5.3 Local Structure Initialization . . . . . . . . . . . . . . . . . . 83
2.5.4 Assembling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
2.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
2.6.1 Performance evaluation criteria . . . . . . . . . . . . . . . . . 85
2.6.2 Application on Hi-C data analysis . . . . . . . . . . . . . . . . 86
2.6.3 Application on DNA microscopy data analysis . . . . . . . . . 89
2.7 Conclusions and Discussions . . . . . . . . . . . . . . . . . . . . . . . 92
2.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
2.8.1 A Brief Introduction of Hi-C and DNA Microscopy Experiments 93
2.8.2 Algorithm flow of HiSpa . . . . . . . . . . . . . . . . . . . . . 96
2.8.3 Details of the Monte Carlo Computation . . . . . . . . . . . . 97
2.8.4 Derivation of Conditional Distributions for Gibbs Sampling . . 98
2.8.5 Adjustment of UK for Initializing the Backbone . . . . . . . . 100
2.8.6 More Details on Scaling, Rotation and Translation of Recovered Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3 Semi-supervised Gene Expression Prediction 103
3.1 Cross-tissue Graph Attention Networks for Semi-supervised Gene Expression Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.1.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.1.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.2 Domain generalization deep graph transformation . . . . . . . . . . . 132
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
3.2.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.2.3 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . 136
3.2.4 Domain generalization deep graph transformation . . . . . . . 138
3.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
3.3.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
3.3.2 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Bibliography 157
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