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    Functional Causal Mediation Analysis with Zero-inflated Count Data
    (University of Waterloo, 2026-04-01) Xu, Henan
    Causal mediation analysis decomposes the effect of an exposure on an outcome into a component operating directly and a component operating through an intermediate variable. In many biomedical and behavioural studies, the mediator evolves over time and is naturally represented as a function, while the outcome is a count with excess zeros. These features create methodological challenges for identification, estimation, and robustness assessment, particularly when mediator processes are sparsely and irregularly observed, and the outcome model is nonlinear due to zero inflation. This thesis develops a functional causal mediation framework for zero-inflated count outcomes, together with estimation procedures and robustness tools tailored to the functional setting. Chapter 2 lays the conceptual and methodological foundations for functional mediation with zero-inflated counts. Within the potential outcomes framework, it defines the total effect, natural direct and indirect effects when the mediator is a time-varying process observed sparsely and irregularly, and clarifies the identifying assumptions required for natural-effect decompositions. The chapter develops a simulation-based implementation of the mediation formula under function-on-scalar regression models for the mediator and functional zero-inflated count models for the outcome. The proposed framework is illustrated in a MIMIC-IV application among patients undergoing coronary artery bypass grafting, where the use of sex as a non-manipulable treatment is discussed, and a principal stratification framework is adopted to handle post-treatment selection into the surgical cohort. Postoperative processes of physiological measurements are studied as candidate mechanisms relating sex to subsequent rehospitalisation outcomes within the always-CABG principal stratum. Chapter 3 addresses computational and inferential limitations of simulation-based mediation implementations by developing a marginal functional mediation approach built on the functional marginalised zero-inflated Poisson model. By modelling the marginal mean of the zero-inflated count outcome directly, the resulting framework yields closed-form expressions for total, natural direct, and natural indirect effects on both incidence-rate-ratio and risk-difference scales. This analytic structure supports fast computation, transparent decomposition of time-local contributions through inner-product representations, and delta-method standard error estimation. Extensive simulation studies across multiple sample sizes and mediator complexities demonstrate that the proposed estimators exhibit good performance in moderate to large samples. The methodology is applied to the Wisconsin Smokers' Health Study 2, evaluating whether time-varying craving during the first two weeks after cessation mediates the effect of varenicline versus nicotine patch on subsequent cigarette use, which is highly concentrated at zero. Chapter 4 revisits causal interpretation and robustness when natural-effect identification assumptions are vulnerable in realistic observational settings. In particular, it addresses concerns about unmeasured baseline mediator--outcome confounding, and exposure-induced mediator--outcome confounding. To assess the robustness of natural effect estimates under potential unmeasured baseline mediator--outcome confounding, we explore both a simulation-based Gaussian copula approach and a closed-form characterisation approach to sensitivity analysis. As natural effects are generally unidentifiable in the presence of post-treatment confounding, the chapter further develops interventional estimands that avoid cross-world potential outcomes and are more directly connected to policy-relevant mediator-distribution interventions. These ideas are illustrated through the MIMIC-IV CABG analysis, providing a robustness-oriented perspective on conclusions drawn from functional mediators and zero-inflated rehospitalisation outcomes. Collectively, the thesis contributes a set of causal estimands, modelling tools, and inferential procedures for mediation problems in which mediators evolve over time and outcomes display zero inflation, and it demonstrates their practical value through simulation evidence and applications to large-scale electronic health records and intensive longitudinal trial data.
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    Scalable Deep Learning for Individual Tree Species Classification from Cross-Platform LiDAR Point Clouds
    (University of Waterloo, 2026-04-01) Wang, Lanying
    Accurate individual tree species classification from point cloud data are essential tasks with significant implications for forest inventory, biomass estimation, and carbon monitoring. Recent advancements in Light Detection and Ranging (LiDAR) technologies, such as airborne LiDAR, Unmanned Aerial Vehicle (UAV)-based LiDAR, and handheld mobile LiDAR, provide rich data sources for these applications. Additionally, the rapid rise of deep learning techniques has demonstrated considerable potential for enhancing the accuracy and efficiency of data interpretation tasks. However, effectively leveraging deep learning to utilize diverse LiDAR datasets for individual tree segmentation and species classification remains challenging. However, deep learning methods typically require extensive annotated data, posing a critical challenge in forestry applications, where labelling individual trees in point clouds is particularly difficult, unlike the abundant large-scale datasets available in image-based domains. This issue leads to three primary research questions: Firstly, how can individual tree segmentation be achieved more efficiently and reliably in complex forest environments characterized by crown overlap, occlusion, and varying point cloud densities? Secondly, can deep learning models effectively classify individual tree species using low-density LiDAR point clouds? Lastly, how can we enhance cross-platform generalization and enable efficient adaptation to newly introduced tree species with limited labelled samples? To address these questions, this thesis presents three main contributions. First, it develops an interactive deep learning pipeline for individual tree segmentation from cross platform laser-scanning data. By integrating user-guided prompts, such as bounding boxes or point clicks, with point cloud-based instance segmentation, the pipeline produces accurate and flexible tree delineations while reducing manual delineation time, thereby supporting the efficient preparation of tree-level training samples. Second, it proposes the Attribute-Aware Cross-Branch Transformer, tailored for tree species classification from low density LiDAR data. The model jointly exploits geometric and radiometric attributes and is designed to learn discriminative, species-specific features under sparse, and uneven point cloud conditions. Third, it investigates a transfer learning framework to enhance the generalization of tree species classification models across heterogeneous LiDAR platforms and to support rapid fine tuning for unseen species. By pretraining on multi platform datasets and adapting to new domains with limited labels, the framework improves scalability and data efficiency. These contributions provide a unified and scalable framework that integrates interactive segmentation, tree species classification, and transfer learning for forestry LiDAR applications, enabling automated, data-efficient forest monitoring in support of operational inventory and carbon-related assessment.
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    Sovereignty, Rhetoric, and World Order: Woodrow Wilson’s Self- Determination
    (University of Waterloo, 2026-03-31) Lauer, Caleb
    This thesis elucidates Woodrow Wilson’s unique rendering of the concept of “self-determination,” examining how Wilson made the concept his own, and how this unique rendering has been obscured by certain conventions and characterizations that predominate in the scholarly literature. I demonstrate that Wilson’s self-determination was less sensational, more limited, and more instrumentalist than is typically acknowledged in the literature—while also being richer in articulation than prevailing interpretations suggest. I situate Wilson’s self-determination within Wilson’s larger persuasive project, a broader rhetorical and political framework which reflected who he was trying to persuade of what, showing that Wilson’s conceptualization of self-determination was inseparable from his efforts to persuade people of his interpretation of the First World War, of the peace settlement that followed, and of the League of Nations as the institutional embodiment of a new world order. This framework was prior to, superordinate to, and much more important to Wilson than was any standalone notion of self-determination. In this way, and contrary to standard accounts, I argue for an image of Wilson’s self-determination that was neither Wilson’s priority, nor summative of his worldview, and neither intrinsically democratic, nor, in its essence, about nationality. And yet in the way Wilson deployed the concept within his larger persuasive project, I argue for an image of Wilson’s self-determination that remains a key to understanding the basis of his vision of a new world order—an order constructed upon the limitations intrinsic to the concept of sovereignty. In this regard, I show that Wilson’s largely unexamined theory of sovereignty is essential to understanding better the significance of his conceptualization of self-determination—not only did Wilson here employ the phrase “self-determination” much earlier than is recognized in the literature, but this earlier usage also offers a corrective to the often-misunderstood distinction between self-determination and the closely associated notions of “the consent of the governed” and “self-government,” and it illuminates his later views on sovereignty in relation to the League of Nations and his vision of world order.
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    Robust optimisation for sequential investment problems: an application to climate adaptation in the Mississippi River Basin
    (Taylor & Francis, 2026-03) Wu, Zhenggao; Dimitrov, Stanko; Pavlin, Michael
    Effectively adapting to climate change requires long-term investment strategies informed by climate forecasts. This paper presents methods and a case study assessing how an investor would approach sequential land investments in the Mississippi River Basin (MRB) using 32 climate models under two emission scenarios (RCP4.5 and RCP8.5). Each model produces projected farmland values, which are used in a robust optimisation framework to identify optimal investment policies under varying levels of conservatism-reflecting the degree to which worst-case outcomes are considered. The model is linearised and scalable across long horizons and asset sets. The case study spans 2023-2090 and uses regression-based projections of land values. Robust investment strategies are derived for each climate model and scenario. Results show that as conservatism increases, investment becomes more geographically constrained, with significant variation in optimal regions. While all climate forecasts predict warming, the regions benefiting from such changes vary by model and scenario. Investment patterns range from concentration in specific areas to broad diversification or complete withdrawal. The analysis underscores substantial disagreements among climate models, which critically affect spatial investment decisions and highlight the importance of robust planning under climate uncertainty.
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    Analysis of Neural Networks with Physics Applications
    (University of Waterloo, 2026-03-30) Mohamed, Ahmed
    This thesis investigates core aspects of machine learning, spanning foundational studies on generalization phenomena in neural networks, novel architectural strategies for enhancing representation learning and classification performance, and high accuracy predictive and inverse modeling of emerging nanoelectronic devices. Together, these studies highlight the significance of data and model structure, the impact of nonlinearity, and the potential of interpretable, generalizable machine learning methods for scientific and engineering applications. For generalization in neural networks, the thesis focuses on the phenomenon of grokking, a delayed generalization effect where models initially overfit but eventually learn to generalize well after extended training. Through a series of interconnected studies, this work proposes insights and practical tools to diagnose, forecast, and enhance generalization in modern machine learning systems. The first part of the thesis examines grokking in modular arithmetic tasks, revealing how dropout induced variance, embedding similarity, activation sparsity, and weight entropy evolve across training, and hence introduces diagnostic metrics to capture phase transitions between memorization and generalization. Further analysis shows that nonlinearity, network depth, and symmetry in data collectively modulate grokking behavior, linking model architecture to its capacity for structured generalization. Next, the thesis introduces a Branched Variational Autoencoder (BVAE), a hybrid architecture that integrates generative and discriminative objectives. By shaping latent representations through a supervised branch, the BVAE achieves improved class separability and interpretability on benchmark datasets, illustrating the potential of structured latent shaping for semi-supervised learning. Finally, the research extends to scientific machine learning, demonstrating how neural and ensemble models as Random Forests can accelerate the modeling and inverse design of Carbon Nanotube Tunnel Field-Effect Transistors (CNT TFETs). By coupling physical insights with machine learning interpretability techniques, this work bridges the gap between theoretical ML and real-world scientific applications.