Cornell Theses and Dissertations
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The theses and dissertations of graduate students at Cornell University have been deposited in Cornell's institutional repository (eCommons) since about 2004. This collection also includes a few earlier Cornell theses.
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Item Scalable Gaussian Processes and Bayesian Optimization with Application to Hyperparameter TuningZhu, Xinran (2024-05)This dissertation delves into the advanced realms of Gaussian Processes (GPs) and Bayesian Optimization (BO), presenting novel methodologies that enhance their performance and applicability. GPs, as a principled probabilistic approach, are powerful in modeling complex and noisy functions due to their non-parametric nature and capability for uncertainty quantification. However, exact GPs become intractable for large datasets since the computational cost scales cubically with the size of the dataset. In particular, this dissertation focuses on improving variational GPs, which is able to handle large-scale data by sparsifying the model via inducing points and approximating the posterior. Despite advances, variational GPs still may require many inducing points (and significant computational costs) to achieve good accuracy, a gap this dissertation aims to bridge.This dissertation also studies efficient computational methods for Bayesian transformed GPs (BTG), which is particularly useful when the Gaussian assumption is not satisfied and data is limited. Furthermore, the dissertation explores BO as a method for optimizing complex and expensive objective functions, with an emphasis on its application in hyperparameter tuning. By leveraging the probabilistic modeling strengths of GPs, BO can efficiently traverse the hyperparameter space, thus reducing the need for extensive model evaluations. Through the introduction of novel algorithms and methodologies, this research not only enhances the performance of BTG and variational GPs but also broadens the scope of BO in hyperparameter tuning.Item Essays on China’s Economic DevelopmentZhao, Zihui (2024-05)This dissertation investigates the effects of policy interventions in China’s education, taxation, and labor markets, utilizing three studies to analyze their impacts and consequences. The first study assesses the gendered impacts of mandated education in patrilocal societies, highlighting the importance of taking traditional institutions into consideration when evaluating government interventions. The second examines the labor market following state-owned enterprise (SOE) reform-induced layoffs, revealing temporary adverse effects on less educated workers and an eventual increase in high school completion rates. The third evaluates the shift from a regressive poll tax to a progressive land tax in 18th-century Imperial China and its impact on peasant revolts, underscoring potential mechanisms of such a causal relationship.Item Ordered Consensus with Equal OpportunityZhang, Yunhao (2024-05)The specific total order of commands agreed upon when running state machine replication (SMR) is immaterial to fault tolerance: all that is required is for all correct nodes to follow the same order. In SMR-based blockchains, however, correct nodes should be responsible for being unbiased when choosing the total order, and for preventing malicious parties from manipulating the order to their advantage. The traditional specification of SMR correctness, however, has no language to express such responsibilities. This dissertation thus extends SMR as ordered consensus by introducing the language of ordering preferences and relevant features, which lead to the following contributions. With ordering preferences, the two notions of Byzantine democracy and Byzantine oligarchy are specified, which capture the minimum and maximum degree of power that Byzantine (e.g., malicious) nodes would have over the order. We prove that the minimum degree of Byzantine power is in general inevitable, but the maximum degree, a Byzantine oligarchy, can be avoided. To remove Byzantine oligarchies, this dissertation introduces Pompē, an SMR protocol that is guaranteed to order commands in a way analogous to linearizability. The evaluation shows that Pompē can achieve competitive performance compared to state-of-the-art SMR protocols in which Byzantine nodes dictate the total order. With relevant features, two principles are specified capturing the notion of equal opportunity, i.e., how correct nodes should treat clients equally instead of being biased toward certain clients. These principles are inspired by social sciences and law, leading to the notion of a point system. In a point system, system designers specify a set of relevant features and a function that maps a vector of feature values into a score. The total order is thus decided by scores and ties are broken randomly. To achieve equal opportunity, this dissertation introduces a secret random oracle (SRO), a system component that generates random numbers in a fault-tolerant manner, and Pompē-SRO, an extension of Pompē that is guaranteed to order commands in a way analogous to a point system. The evaluation shows that Pompē-SRO could mitigate real-world concerns about ordering in blockchains, including front-running and sandwich attacks.Item PRACTICAL AND THEORETICAL ADVANCES IN CONSTRAINED BAYESIAN OPTIMIZATION AND BAYESIAN OPTIMIZATION FOR MACHINE LEARNING SYSTEMSZhang, Duke (2024-05)Recent advances in computationally efficient non-myopic Bayesian optimization (BO) improve query efficiency over traditional myopic methods like expected improvement while only modestly increasing computational cost. These advances have been largely limited, however, to unconstrained optimization. For constrained optimization, the few existing non-myopic BO methods require heavy computation. For instance, one existing non-myopic constrained BO method [1] relies on computationally expensive unreliable brute-force derivative-free optimization of a Monte Carlo rollout acquisition function. Methods that use the reparameterization trick for more efficient derivative-based optimization of non-myopic acquisition functions in the unconstrained setting, like sample average approximation and infinitesimal perturbation analysis, do not extend: constraints introduce discontinuities in the sampled acquisition function surface that hinder its optimization. Moreover, we argue here that being non-myopic is even more important in constrained problems because fear of violating constraints pushes myopic methods away from sampling the boundary between feasible and infeasible regions, slowing the discovery of optimal solutions with tight constraints. In this work, we propose a computationally efficient two-step lookahead constrained Bayesian optimization acquisition function (2-OPT-C) supporting both sequential and batch settings. To enable fast acquisition function optimization, we develop a novel likelihood-ratio-based unbiased estimator of the gradient of the two-step optimal acquisition function that does not use the reparameterization trick. In numerical experiments, 2-OPT-C typically improves query efficiency by 2x or more over previous methods, and in some cases by 10x or more. Recent advances in Bayesian optimization with constraints (CBO) have significantly improved the sample query efficiency compared to the standard CBO algorithm, constrained expected improvement (EIC). Although the EIC is first proposed by [2] and rediscovered by [3], which is more than twenty years ago, there is no work focusing on the theoretical aspect of the EIC algorithm, especially regarding its consistency property. In this work, we show that EIC is inconsistent. In detail, we construct a counterexample where both the objective and constraint functions are piece-wise linear, and the Gaussian process priors are Wiener processes. Moreover, to overcome the inconsistency of EIC, we propose a new algorithm named Constrained Expected Improvement with Perturbation (EIC-P). We prove that EIC-P is consistent in the setting of reproducing kernel Hilbert space. Machine learning systems, consisting of various models, have shown superiority over single-model approaches in both academia and industry. However, tuning the hyperparameters of these systems is challenging. First, machine learning systems usually have numerous hyperparameters. Moreover, due to the interaction between models in the system, the hyperparameters of upstream models might also affect the downstream models. In this paper, we first provide a formal mathematical definition of a machine learning (ML) system. Also, we formulate the evaluation of an ML system and its components as a network of evaluation functions. Moreover, we provide extensive guidance on building effective Bayesian optimization function networks (BOFN) for the evaluation function network including evaluation metric design. Then, we investigate the efficacy of standard and grey-box [4] Bayesian optimization (BO) algorithms for tuning hyperparameters for machine learning systems. The experiment results demonstrate that even if we utilize BOFN with simple structures to leverage partial information within ML systems regarding models' qualities, BOFN can still improve sample efficiency or compare favorably to standard BO methods.Item Rigidity Theory of Circles, Polygons, and PolyhedraZhang, Zhen (2024-05)Rigidity theory is the study of the uniqueness of structures. In most cases, a structure is defined by a set of variables with constraints, ideally polynomial, that come from geometry. A constraint can be an equality or an inequality. There are various types of rigidity. Intuitively, local rigidity means uniqueness in a small neighborhood, global rigidity means uniqueness in a much larger space at the given dimension, and universal rigidity means uniqueness in all higher dimensions. This thesis explores the rigidity of several common structures that are slightly more complex than a set of points with fixed distance constraints, known as the bar-joint frameworks. These structures include circle packings, polyhedra, and various special sets of points with inequality constraints, known as tensegrities. They are natural extensions of the bar-joint frameworks that occur in many studies. The rigidity of circles with a given tangency pattern and fixed radii has been well studied. This is known as sticky disks, as the disks that are required to be tangent must ``stick together''. It is natural to ask if the rigidity results for sticky disks still hold with flexible radii. Another problem arises from the study of polytopes as regards the rigidity of a polyhedron with fixed edge lengths and vertices of each facet staying in the same plane. To solve these problems, we extend the methods used for bar-joint frameworks so that the algebra behaves analogously. Several examples of structures with interesting results on rigidity are given in each chapter. Often, rigidity is done in a ``generic'' sense where singularities are ignored. An ambitious attempt is made to replace the assumption ``generic'' with the assumption ``convex'' for several classes of bar-joint frameworks. Some examples of resolved cases and an open case are given in the last chapter.
Item DECIPHERING MULTI-LAYER FUNCTIONAL EFFECTS OF GENOMIC VARIANTS IN HUMAN DISEASESZhang, Yingying (2024-05)Every individual has millions of genomic variants compared to a reference genome. Only a small fraction of these variants can have significant impacts on human diseases. The challenge in human genomics research lies in identifying these large-effect variants and understanding how subtle changes in the DNA translate into disease phenotypes. This involves unraveling complex intermediate layers of how these genetic alterations exert their functional effects across multiple scales. In this dissertation, I present my research on bridging the gap between genetic variation and disease phenotypes, which is fundamental to advancing personalized medicine and targeted therapies. In Chapter 2, I present several computational approaches to identify functional disease-associated variants, leveraging genomic background mutability models, 3D protein structural information, transcription-based enhancer identification strategies, and enhancer-gene linkage mapping approaches. In Chapter 3, I developed a unified, end-to-end 3D structurally-informed protein interaction network propagation framework, NetFlow3D, that systematically maps the multiscale mechanistic effects of somatic mutations in cancer. NetFlow3D anisotropically propagates the impacts of spatial clusters of mutations on 3D protein structures across the protein interaction network, with propagation guided by the specific 3D structural interfaces involved, to identify significantly interconnected network “modules”, thereby uncovering key biological processes driving cancer. In Chapter 4, I established an integrative framework to delve into the etiology underlying autism spectrum disorder (ASD), which combines: (i) a gene-centric statistical model integrating coding and noncoding evidence of rare variant association, (ii) likely altered PPIs–as revealed by the presence of damaging de novo missense variants on their 3D structural interfaces, and (iii) the topology of the PPI network. The integration of noncoding data has nearly doubled the analytical power of gene discovery, and has uncovered an emerging class of potential ASD pathways. In summary, the theme of my thesis is identifying disease-associated variants by leveraging various biological data, and combining their complementary insights to decipher the complex mechanisms underlying in human diseases. The core principle of my approach is to strategically integrate these separate insights into unified framework architectures that closely aligns with the underlying biological nature, thereby effectively converging relevant signals while filtering out noise, and at the same time, systematically unraveling the complex intermediate layers that illustrate how subtle genetic changes translate into observable disease phenotypes.Item Safe University Instruction During COVID-19: Simulation, Statistics, and Uncertainty QuantificationZhang, Yujia (2024-05)The COVID-19 pandemic has inflicted significant losses and disruptions on the society since its emergence in 2020. During this difficult time, colleges and universities faced numerous operational decisions that needed to balance safety, educational quality, and cost. This dissertation focuses on a few projects that partly supported safe in-person instruction at Cornell University during COVID-19 and hold great promise for broader applications. First, we study the risk of returning to pre-pandemic level in-person instruction through mathematical modeling and agent-based simulation. We estimate the risk associated with different policies and recommend that fully masked in-person classrooms would be safe without needing to assign seats or update the rooms for better ventilation. This result supported the university's decision to return to regular in-person instruction in Fall 2021. Second, we conduct survival analysis to evaluate the risk of infection associated with attending classes in person. Using data on surveillance testing, class schedules, and class enrollments in Fall 2021 and Spring 2022, we construct a novel feature to quantify the amount of exposure that a student has in the classroom. Using extended Cox regression and logistic regression, we find that attending classes was associated with minimal increase in the risk of infection. Third, we investigate group testing under the presence of correlation among samples. In large-scale screenings, correlation between samples in the same pool is naturally induced through human behavior and the process of sample collection. By realistically modeling network contagion, viral load progression, and the dilution effect in pooled testing, we show that such correlation improves the sensitivity and resource efficiency of population-wide testing. Thus, policy-makers envisioning using group testing for large-scale screening should take correlation into account and intentionally maximize it when possible. Fourth, we present an approach for uncertainty quantification of simulation models with a large number of parameters. Using a linear approximation, we quantify the sensitivity of simulation output to each parameter. Furthermore, we adapt ideas from robust optimization and identify a one-dimensional family of parameter configurations associated with different pessimism levels. This method provides insight into the uncertainty of the compartmental simulation developed by the Cornell COVID-19 modeling team, and can be broadly used for sensitivity analysis and scenario analysis in an interpretable way for various simulation models.Item Computational Approaches to Frustrated Many-Body SystemsZhang, Kevin (2024-05)Computational tools are ubiquitous in condensed matter physics, providing essential insights into many-body physics when analytical techniques fall short. This dissertation focuses on the application and interpretation of these tools, applied to the realm of frustrated systems, where competing interactions prevent the system from settling into simply ordered states. Frustrated systems often host exotic phenomena such as spin liquids, which make them an intriguing topic of study despite their inherent complexity. To tackle these challenges, a variety of computational techniques have been developed and refined over the years, such as density matrix renormalization group, quantum Monte Carlo, or projected entangled pair states. In the first part of this dissertation, we introduce a method to analyze improve variational numerical methods.Although recent developments in variational techniques have greatly expanded our ability to explore many-body Hilbert spaces, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. To tackle this, we propose a new way to evaluate variational ansatze using a method called Hamiltonian reconstruction by looking at the bias between original and reconstructed Hamiltonians. We apply the method to neural network wavefunctions for the J1-J2 model on a square lattice, which is a frustrated model long-standing open problem. From this method, we diagnose specific regions of poor performance of the variational ansatz and gain insight into specific directions for improvement. In the second part, we develop an approach for finding signatures of exotic and nonconventional phases by combining wavefunction snapshots with interpretable machine learning. Obtaining a ground state approximation of a Hamiltonian is only half the battle, since wavefunction amplitudes by themselves do not represent physically meaningful quantities. Thus, gaining insight into states can be just as formidable a task, especially when their true nature is unclear. We introduce a quantum-classical hybrid method of analyzing numerical results and apply it to a mysterious gapless phase of the honeycomb Kitaev model under external field. Using our method, we find that the machine learning procedure discovers features which we interpret as signatures and evidence of a spinon Fermi surface, guiding both theoretical and experimental searches for spin liquids. In the last part, we explore a new paradigm of frustration called orbital geometric frustration through the lens of twisted bilayer graphene. By introducing a new geometric framework for thinking about the extended flat-band Wannier states in twisted bilayer graphene, we connect the problem to the broader study of constrained plaquette models. From this framework arises the enticing possibility of fractional correlated insulating states with fractionalized quasiparticles, which we also approach with a numerical Monte Carlo study. Our investigations reveal a liquid state characterized by algebraic correlations with multi-flavored defects, a direct consequence of the unique form of frustration introduced by the extended Wannier orbitals' peculiar geometry. This finding not only enriches the theoretical framework of frustration in condensed matter physics but also opens up new avenues for experimental exploration in moire and flat-band materials.Item Essays on AI, Digitization, and InnovationZakerinia, Saleh (2024-05)This dissertation includes three chapters that study pressing issues in today's economy, focusing on artificial intelligence (AI), digitization, and innovation. The first chapter studies the impact of accumulated experience in innovation on improving additional innovations in terms of scope, scale, and cost. It studies this concept in the context of AI innovations. This is done by introducing a dynamic structural model and underpinning the underlying mechanisms of accumulated experience in innovation. The second chapter looks deeper into the impact of accumulated experience and studies the impact of accumulated experience in AI innovations on firms' profitability. This chapter applies dynamic structural modeling to examine how firms leverage their accumulated experience in AI innovations to improve their profitability. The first two chapters study how firms strategically use accumulated experience to gain competitive advantage from different aspects. The last chapter shifts the attention from technological advancements at the firm level to consumer interactions. This chapter examines how consumers' purchasing behaviors changed with the introduction of a two-hour delivery service by a major online retailer. This study highlights how online retailers could use technological advancements to increase their consumers. These chapters collectively give a comprehensive view of the impacts of the accumulation of innovation within a firm and how firms leverage innovative strategies, such as reduced delivery time, to increase their revenue. The developed models in this dissertation can be used to examine the impacts of various policies and how they may impact the market and firms' competitive position.Item REAL EARNINGS MANAGEMENT AND INNOVATION EXTERNALIZATION: EVIDENCE FROM CORPORATE VENTURE CAPITALYu, Elisha (2024-05)This study examines whether firms increase their investment in startups using Corporate Venture Capital (CVC) when they reduce internal research and development (R&D) spending to meet short-term earnings targets. My findings suggest that firms are more likely to make CVC investments when they just meet or beat analysts’ earnings forecasts and have lower than predicted R&D expenses. The effect is particularly concentrated in firms with lower transient investor ownership, firms with long-term oriented CEOs, and firms with more exploitative innovation strategies. Subsequently, firms that make CVC investments during R&D-cutting and benchmark-beating years have superior innovation outcomes and better long-term performance than those that cut R&D but do not make CVC investments. My findings suggest that managers utilize CVC investments to mitigate the negative impacts of cutting internal R&D and highlight the importance of considering external innovation efforts in addition to internal R&D in future studies.