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    Towards Trustworthy Federated Learning: Security, Privacy, and Verifiability
    (University of Waterloo, 2026-06-24) Deressa, Biniyam
    Federated learning enables collaborative model training across institutions that cannot share raw data, but practical deployments rely on trust assumptions that do not hold in adversarial environments. Malicious clients may omit or falsify computation, inject poisoned updates, or free-ride on collective training with negligible detection risk. Existing defenses address security, privacy, and verifiability in isolation: privacy mechanisms obscure the signals required for robustness, while general-purpose zero-knowledge proof systems incur costs that scale with circuit size and are impractical for neural network workloads. The result is a structural \emph{trust deficit} that no single existing mechanism resolves. This thesis argues that the security--privacy--verifiability tension in federated learning is \emph{architectural rather than fundamental}. By decomposing trust into \emph{four separable research problems}, namely, adversarial client selection, privacy-compatible robust aggregation, cryptographic training verification, and compositional architecture, and by exploiting the algebraic structure of learning workloads, each property can be enforced by a mechanism with explicit assumptions and well-defined interfaces. These mechanisms are independently deployable and compose via defined interfaces without requiring cross-mechanism security re-analysis, yielding a \emph{modular trust architecture} for trustworthy federated learning. \textsc{TrustBandit} addresses the security dimension by formulating client selection as an adversarial multi-armed bandit under partial observability. Importance-weighted reputation estimation with adaptive exploration achieves a provable regret bound $O(\sqrt{T N \ln N})$, where $T$ is the number of training rounds and $N$ is the number of clients, and, in evaluation, identifies trustworthy clients with $94$--$99\%$ success in low-adversary settings (up to $20\%$ adversaries) and maintains $67$--$69\%$ selection success under $50\%$ adversarial participation, while sustaining $70.97\%$ test accuracy at $50\%$ adversarial participation and improving robustness by up to $5.5\times$ over standard selection baselines. \textsc{PROFILE} addresses the privacy--robustness tension through architectural separation rather than algorithmic compromise: anomaly detection is relocated from centralized plaintext inspection to server-side predictive detection over bucket-wise homomorphically encrypted aggregates with semantic client assignment. The framework enforces IND-CPA computational privacy for individual updates under Ring-LWE hardness, with LDP-protected metadata, while preserving Byzantine robustness under poisoning and backdoor attacks; empirically it achieves accuracy within 2--3\,pp of the best plaintext baseline (FLTrust) while operating under full RLWE encryption, with detection rates from $0.87$ to $0.99$ across all datasets and non-adaptive attack types; adaptive adversaries that suppress per-round statistical signals fall outside this bound, as characterised by the leakage--detectability frontier. \textsc{zkMaP} and \textsc{zkExp} address verifiability by specializing to the dominant computational kernels in training. \textsc{zkMaP} gives succinct verification for matrix multiplication via polynomial identities over pairing groups, achieving $O(n^2)$ prover complexity for matrix dimension $n$, constant-size proofs (320 bytes), and constant-time verification (3.68\,ms), yielding up to $19.07\times$ verification speedup over prior specialized matrix multiplication protocols at comparable security. \textsc{zkExp} provides a succinct proof system for exponentiation with constant-time verification and constant-size proofs (160 bytes for single proofs; 256 bytes in batched mode), with low amortized batch overhead (1.35$\times$). \textsc{RIV} composes these primitives into an end-to-end proof-of-training protocol. Training transcripts are committed prior to challenge selection, preventing selective honest computation. Stochastic Interval Commitments certify native IEEE-754 floating-point computation within backward-error-derived bounds while preserving cryptographic binding. The resulting protocol provides parameterized detection guarantees: for an adversary corrupting a $q_{\mathrm{adv}}$-fraction of challenged layers, the per-round acceptance probability is bounded by $(1-q_{\mathrm{adv}})^k + k\varepsilon_{\mathrm{crypto}} + \delta_{\mathrm{fp}}$ (where $\varepsilon_{\mathrm{crypto}} \le 2m/|\mathbb{F}_p| + \mathsf{negl} \lambda)$ per challenged layer), yielding explicit trade-offs between challenge rate, overhead, and adversarial detectability (e.g., $>99.99\%$ cumulative detection at $k=3$ over 50 rounds). Collectively, these results demonstrate that cryptographically grounded trust in federated learning is achievable through specialized, composable mechanisms rather than monolithic designs.
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    Sustainability Management in Private Capital Markets: Important and Distinct, yet Underexplored-Institutional Pressures, Legitimacy, and ESG Disclosure
    (University of Waterloo, 2026-06-24) Mirza, Majid
    The rapid expansion of sustainable finance has intensified demands for consistent sustainability disclosure across global capital markets. While public market actors and listed corporations have received significant scholarly attention, private capital markets, particularly private equity, remain comparatively underexamined despite their growing influence in global investment flows. This dissertation investigates how sustainability management and disclosure practices are emerging within private capital markets and how private equity actors respond to evolving institutional pressures shaping environmental, social, and governance (ESG) reporting. Drawing on institutional theory, legitimacy theory, and sustainability management literature, the dissertation explores three interconnected dimensions of sustainability integration in private capital. The first paper presents a systematic literature review of sustainability research within private capital investing, identifying a substantial gap between the rapid growth of ESG practices in industry and the limited academic attention devoted to sustainability within private equity and venture capital research. The review reveals that sustainability-related scholarship constitutes a very small proportion of the broader private capital literature and highlights several emerging thematic areas requiring further investigation. Building on this foundation, the second paper examines ESG reporting practices among leading global private equity firms through a comparative analysis of ESG reports and Sustainable Development Goal (SDG) integration strategies. The findings suggest that while sustainability commitments are increasingly communicated within ESG disclosures, much of the integration appears to function as legitimacy signaling rather than deeply embedded investment decision-making processes. The third paper extends the analysis to the evolving institutional landscape of global sustainability disclosure by examining comment letters submitted by financial institutions and private equity firms in response to the International Sustainability Standards Board’s (ISSB) consultation on agenda priorities. Using a mixed-method approach combining thematic interpretation and structured content analysis, the study identifies patterns of institutional isomorphism and dissonance within the consultation process. While financial institutions and private equity actors demonstrate convergence around biodiversity and climate–nature disclosure priorities, significant divergence emerges regarding the role of integration in sustainability reporting, reflecting distinct institutional logics within the financial sector. Taken together, the findings illustrate how private capital actors both conform to and shape emerging sustainability management frameworks in the form of selective institutionalization. The dissertation contributes to scholarship by expanding understanding of sustainability integration within private capital markets, highlighting the role of institutional pressures in shaping ESG disclosure practices, and introducing private equity as an important and distinct, yet underexplored actor in global sustainability reporting debates.
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    Quantifying Structural Uncertainty in Hydrologic Models
    (University of Waterloo, 2026-06-23) Arabzadeh, Rezgar
    Hydrologic models are essential tools for understanding watershed processes and supporting water resource management. However, their predictions are inherently uncertain due to imperfect model structures (structural uncertainty), parameter estimation challenges (parameter uncertainty), and limitations in observational data and model forcings (input uncertainty). Bayesian inference has become a widely used framework for quantifying these uncertainties because it enables probabilistic parameter estimation and prediction while formally incorporating prior information and observational evidence. Despite these advantages, the application of Bayesian methods to complex hydrologic models remains computationally demanding, and the resulting predictive uncertainty often represents a combination of multiple uncertainty sources (including input, parameter, and structural uncertainties) that are difficult to interpret individually. These limitations reduce the effectiveness of Bayesian uncertainty analysis as a diagnostic tool for improving hydrologic models. This thesis develops methodological advances to improve the efficiency and interpretability of Bayesian uncertainty quantification in hydrologic modeling. The research focuses on two challenges: improving the computational feasibility of Bayesian inference for complex models and separating the sources of uncertainty represented within Bayesian predictive distributions. To address these challenges, new methods are developed and evaluated using both regional and continental-scale hydrologic datasets. 1. A machine learning–assisted framework is developed to improve the efficiency of Bayesian joint inference for hydrologic models. The proposed approach integrates machine learning techniques with Bayesian calibration to facilitate exploration of complex posterior parameter distributions and reduce the computational burden associated with traditional sampling methods. The framework is evaluated using twelve watersheds from the MOPEX dataset and demonstrates improved inference performance while maintaining reliable uncertainty quantification. 2. A variance decomposition methodology is introduced to identify and quantify the sources of uncertainty embedded within Bayesian predictions. While Bayesian calibration provides probabilistic estimates of model outputs, it does not directly attribute predictive uncertainty to individual components of the modeling framework. The proposed method decomposes posterior predictive uncertainty into interpretable components, enabling a clearer understanding of how different aspects of the modeling process contribute to overall uncertainty. 3. The proposed uncertainty decomposition framework is applied to a large-scale hydrologic analysis across approximately 3,000 watersheds in North America. This continental-scale application enables the systematic evaluation of spatial patterns in hydrologic model uncertainty and reveals how dominant uncertainty sources vary across hydroclimatic and physiographic regions. Together, the contributions of this thesis improve both the computational efficiency and the interpretability of Bayesian uncertainty estimates in hydrologic modeling. The proposed approaches provide tools for diagnosing uncertainty sources and evaluating model reliability, which can support more transparent hydrological predictions across a range of environmental and water resource applications.
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    Contributions to the model theory of algebraic differential equations
    (University of Waterloo, 2026-06-23) Eagles, Christine
    This thesis deals with semiminimal analyses of finite rank types, primarily in the stable theory of differentially closed fields of characteristic zero (DCF0). The two main themes considered in this thesis are determining when a type is minimal or semiminimal, and understanding what invariants of finite rank types are captured by a semiminimal analysis. In DCF0, a central concern of this thesis is determining when a type is almost internal to the field of constants. Partially generalising a result of Rosenlicht, algebraic criteria are provided in two different contexts: rational vector fields on affine n-space, and pullbacks under the logarithmic derivative of certain types which are internal to the constants. The criteria in the former case answers a question posed by Freitag, Jaoui, Marker and Nagloo about when the Poizat equations are internal to the constants. In both cases, the theory of binding groups in stable theories plays a significant role. Results of Duan and Nagloo are improved upon to completely classify when the generic types of Lotka-Volterra systems are minimal. In the minimal case, a characterization of the possible relations that may exist between solutions of distinct Lotka-Volterra systems is given. In the general setting of a totally transcendental theory, it is shown that the multiplicity with which a minimal type arises in a semiminimal analysis of a finite rank type is invariant, i.e., it is independent of the semiminimal analysis. A conjecture is proposed for the possible ways for two semiminimal analyses of the same finite rank type to differ. Along the way, the connection between semiminimal analyses and domination decompositions, is clarified.
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    Parameter Inference and Model Selection for Differential Equation Models with Applications
    (University of Waterloo, 2026-06-23) Zhao, Yuxuan
    Dynamic systems are commonly modelled by differential equations (DEs) in epidemiology and biology, among other fields. The parameters in the DEs are often of scientific interest and required for estimation, given a set of noisy observations. The first and oldest general class of methods for the parameter inference problem in DEs is based on numerical solvers. As a preliminary study, we conduct a comparative study of compartmental models for COVID-19 transmission using such numerical solver-based methods. However, this class of methods can be computationally intensive and may only converge to the local optima due to the sensitivity of the numerical solution to the parameters and initial conditions. This thesis begins by presenting this study, which highlights these limitations and motivates the methodological developments that follow. To address these challenges, Gaussian process-based methods serve as an alternative that bypass the need for numerical solvers. In particular, the recent manifold-constrained Gaussian process inference (MAGI) method demonstrated accurate estimation and fast computational speed. However, the original MAGI method is limited to ordinary differential equations (ODEs), which are inadequate for some dynamic systems, calling for more complex or flexible structures in the specification of the DE model. Motivated by this, this thesis extends the framework of MAGI to facilitate inference for three common but challenging contexts, including (i) delayed differential equations, where system components exhibit time delays in their responses, (ii) mixed-effects ODEs, where experimental data consist of time-course observations on multiple subjects from a population, and (iii) selection of the most appropriate ODE model from a set of candidate models, where there is no true underlying model. The complex structures of these DEs introduce inferential and computational burdens and we address them in this thesis, along with computational and theoretical justifications. We illustrate the efficacy of our methodologies through simulated and real-world applications.