Advanced Statistical Learning Methods for Brain Connectome Analysis Restricted; Files Only

Abstract

Recent advances in brain connectome research have significantly enhanced our understanding of brain function, structure, and associated disorders. However, the analysis of neuroimaging-derived connectome data presents major challenges due to its complexity, high dimensionality, and low signal-to-noise ratio. This dissertation addresses these issues through the development of innovative statistical methods designed specifically for brain connectome analysis.

In the first project, we introduce Multi-View LOCUS, a novel blind source separation framework tailored for decomposing multi-view connectome data. This approach identifies both shared and unique neural circuits across different imaging modalities and cognitive states, demonstrated through applications to the multi-modal connectome in Philadelphia Neurodevelopmental Cohort (PNC) study and multi-task connectome in Adolescent Brain Cognitive Development (ABCD) study.

The second project develops locus-CCA, an advanced canonical correlation analysis method coupled with a canonical variant regression (CVR) testing framework. This method robustly identifies and evaluates joint latent structures between functional connectivity and clinical or cognitive outcomes, effectively addressing the dimensionality and interpretability challenges inherent to traditional approaches. Simulations and real-data analyses from the ABCD study confirm the utility of this approach.

The third project proposes a multi-task deep learning framework designed to enhance interpretability in brain connectome analysis. By combining low-rank connectivity traits with task-specific hypernetworks, the method generates individualized, interpretable neural circuit representations. Applied to the ABCD dataset, this approach successfully identifies clinically meaningful neural patterns while maintaining predictive performance. Together, these methodological advances provide powerful tools for extracting interpretable and biologically relevant insights from brain connectome data, facilitating better understanding of brain-behavior relationships in clinical neuroscience.

Table of Contents

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Investigating Neural Circuits Underlying Multi-View Brain Connec-

tome using Multi-View LOCUS 7

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Data and Research Questions . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Multi-modal Connectome from the Philadelphia Neurodevelop-

mental Cohort study . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.2 Multi-task functional Connectome from the Adolescent Brain

Cognitive Development Study . . . . . . . . . . . . . . . . . . 15

2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.2 Multi-View LOCUS . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 Real Data Application . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5.1 Investigation of Multi-modal Connectivity from the Philadel-

phia Neurodevelopmental Cohort (PNC) . . . . . . . . . . . . 30

2.5.2 Investigation of Multi-Task Connectivity Data from Adolescent

Brain Cognitive Development (ABCD) Study . . . . . . . . . 37

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.7 Supplementary Material . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.7.1 Derivation of the Optimization Function . . . . . . . . . . . . 45

2.7.2 The Estimation Algorithm for Multi-View LOCUS . . . . . . 48

2.7.3 Selection of the Number of Components and Tuning Parameters 49

2.7.4 Selection of the Number of Components . . . . . . . . . . . . 49

2.7.5 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . 52

3 Locus-CCA: A Low-Rank Sparse Canonical Correlation Method with

Trait-Level Inference for High-Dimensional Brain Connectome Anal-

ysis 55

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.2 Locus-CCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.3 Subscale informed canonical variate regression (CVR) . . . . . 66

3.2.4 Hypothesis testing for CVR model . . . . . . . . . . . . . . . 67

3.3 Theoretical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.4.1 Locus-CCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.4.2 Subscale-informed CVR . . . . . . . . . . . . . . . . . . . . . 72

3.5 Real data application . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.7 Supplementary Materials . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.7.1 Simulation Study for CVR Testing . . . . . . . . . . . . . . . 82

3.7.2 Additional Canonical Correlation Components . . . . . . . . . 82

4 Adaptive Connectivity Trait Modeling for Interpretable Multi-Task

Brain Connectome Analysis 84

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.2.1 Data and Notations . . . . . . . . . . . . . . . . . . . . . . . . 89

4.2.2 Structured Brain Connectome Masking for Interpretable Multi-

Task Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.2.3 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.3 Application to ABCD Data . . . . . . . . . . . . . . . . . . . . . . . 95

4.3.1 Data and Preprocessing . . . . . . . . . . . . . . . . . . . . . 95

4.3.2 Implementation Details . . . . . . . . . . . . . . . . . . . . . . 97

4.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5 Supplementary Materials . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.5.1 The List of Variables used . . . . . . . . . . . . . . . . . . . . 107

4.5.2 Twenty Connectivity traits learned using ABCD study . . . . 109

5 Conclusion and Future work 112

6 Appendices 114

A Derivation and Proof for the Second Topic . . . . . . . . . . . . . . . 114

A.1 Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

A.2 Proof of Theorem 1 . . . . . . . . . . . . . . . . . . . . . . . . 115

A.3 Proof of Theorem 2 . . . . . . . . . . . . . . . . . . . . . . . . 116

A.4 Technical Lemmas and proof . . . . . . . . . . . . . . . . . . . 119

Bibliography 127

About this Dissertation

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School	Laney Graduate School
Department	Biostatistics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Statistics Biology, Biostatistics Biology, Neuroscience
Keyword	Machine Learning Blind Source Separation Brain Connectome
Committee Chair / Thesis Advisor	Ying Guo, Emory University
Committee Members	Yijian Huang, Emory University Robert Krafty, Emory University Carl Yang, Emory University

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