In this work, we develop a hypothesis testing framework to determine whether pairwise comparison data is generated by an underlying \emph{generalized Thurstone model} $\mathcal{T}_F$ for a given choice function $F$. While prior work has predominantly focused on parameter estimation and uncertainty quantification for such models, we address the fundamental problem of minimax hypothesis testing for $\mathcal{T}_F$ models. We formulate this testing problem by introducing a notion of separation distance between general pairwise comparison models and the class of $\mathcal{T}_F$ models. We then derive upper and lower bounds on the critical threshold for testing that depend on the topology of the observation graph. For the special case of complete observation graphs, this threshold scales as $Θ((nk)^{-1/2})$, where $n$ is the number of agents and $k$ is the number of comparisons per pair. Furthermore, we propose a hypothesis test based on our separation distance, construct confidence intervals, establish time-uniform bounds on the probabilities of type I and II errors using reverse martingale techniques, and derive minimax lower bounds using information-theoretic methods. Finally, we validate our results through experiments on synthetic and real-world datasets.

Many modern datasets consist of multiple related matrices measured on a common set of units, where the goal is to recover the shared low-dimensional subspace. While the Angle-based Joint and Individual Variation Explained (AJIVE) framework provides a solution, it relies on equal-weight aggregation, which can be strictly suboptimal when views exhibit significant statistical heterogeneity (arising from varying SNR and dimensions) and structural heterogeneity (arising from individual components). In this paper, we propose HeteroJIVE, a weighted two-stage spectral algorithm tailored to such heterogeneity. Theoretically, we first revisit the ``non-diminishing" error barrier with respect to the number of views $K$ identified in recent literature for the equal-weight case. We demonstrate that this barrier is not universal: under generic geometric conditions, the bias term vanishes and our estimator achieves the $O(K^{-1/2})$ rate without the need for iterative refinement. Extending this to the general-weight case, we establish error bounds that explicitly disentangle the two layers of heterogeneity. Based on this, we derive an oracle-optimal weighting scheme implemented via a data-driven procedure. Extensive simulations corroborate our theoretical findings, and an application to TCGA-BRCA multi-omics data validates the superiority of HeteroJIVE in practice.

Zero-shot anomaly classification and segmentation (AC/AS) aim to detect anomalous samples and regions without any training data, a capability increasingly crucial in industrial inspection and medical imaging. This dissertation aims to investigate the core challenges of zero-shot AC/AS and presents principled solutions rooted in theory and algorithmic design. We first formalize the problem of consistent anomalies, a failure mode in which recurring similar anomalies systematically bias distance-based methods. By analyzing the statistical and geometric behavior of patch representations from pre-trained Vision Transformers, we identify two key phenomena - similarity scaling and neighbor-burnout - that describe how relationships among normal patches change with and without consistent anomalies in settings characterized by highly similar objects. We then introduce CoDeGraph, a graph-based framework for filtering consistent anomalies built on the similarity scaling and neighbor-burnout phenomena. Through multi-stage graph construction, community detection, and structured refinement, CoDeGraph effectively suppresses the influence of consistent anomalies. Next, we extend this framework to 3D medical imaging by proposing a training-free, computationally efficient volumetric tokenization strategy for MRI data. This enables a genuinely zero-shot 3D anomaly detection pipeline and shows that volumetric anomaly segmentation is achievable without any 3D training samples. Finally, we bridge batch-based and text-based zero-shot methods by demonstrating that CoDeGraph-derived pseudo-masks can supervise prompt-driven vision-language models. Together, this dissertation provides theoretical understanding and practical solutions for the zero-shot AC/AS problem.

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Increasing climate change and habitat loss are driving unprecedented shifts in species distributions. Conservation professionals urgently need timely, high-resolution predictions of biodiversity risks, especially in ecologically diverse regions like Africa. We propose EcoCast, a spatio-temporal model designed for continual biodiversity and climate risk forecasting. Utilizing multisource satellite imagery, climate data, and citizen science occurrence records, EcoCast predicts near-term (monthly to seasonal) shifts in species distributions through sequence-based transformers that model spatio-temporal environmental dependencies. The architecture is designed with support for continual learning to enable future operational deployment with new data streams. Our pilot study in Africa shows promising improvements in forecasting distributions of selected bird species compared to a Random Forest baseline, highlighting EcoCast's potential to inform targeted conservation policies. By demonstrating an end-to-end pipeline from multi-modal data ingestion to operational forecasting, EcoCast bridges the gap between cutting-edge machine learning and biodiversity management, ultimately guiding data-driven strategies for climate resilience and ecosystem conservation throughout Africa.

The analysis of non-real-valued data, such as binary time series, has attracted great interest in recent years. This manuscript proposes a post-selection estimator for estimating the coefficient matrices of a high-dimensional generalized binary vector autoregressive process and establishes a Gaussian approximation theorem for the proposed estimator. Furthermore, it introduces a second-order wild bootstrap algorithm to enable statistical inference on the coefficient matrices. Numerical studies and empirical applications demonstrate the good finite-sample performance of the proposed method.

Artificial intelligence (AI) is increasingly integrated into modern healthcare, offering powerful support for clinical decision-making. However, in real-world settings, AI systems may experience performance degradation over time, due to factors such as shifting data distributions, changes in patient characteristics, evolving clinical protocols, and variations in data quality. These factors can compromise model reliability, posing safety concerns and increasing the likelihood of inaccurate predictions or adverse outcomes. This review presents a forward-looking perspective on monitoring and maintaining the "health" of AI systems in healthcare. We highlight the urgent need for continuous performance monitoring, early degradation detection, and effective self-correction mechanisms. The paper begins by reviewing common causes of performance degradation at both data and model levels. We then summarize key techniques for detecting data and model drift, followed by an in-depth look at root cause analysis. Correction strategies are further reviewed, ranging from model retraining to test-time adaptation. Our survey spans both traditional machine learning models and state-of-the-art large language models (LLMs), offering insights into their strengths and limitations. Finally, we discuss ongoing technical challenges and propose future research directions. This work aims to guide the development of reliable, robust medical AI systems capable of sustaining safe, long-term deployment in dynamic clinical settings.

Reasoning models are large language models that emit a long chain-of-thought before answering, providing both higher accuracy and explicit reasoning for their response. A major question has been whether language model reasoning generalizes beyond mathematics, programming, and logic, where most previous work has focused. We demonstrate that reasoning models can be post-trained for chemistry without additional domain pretraining, and require substantially less data compared to contemporary domain-specific models. We report ether0, a 24B parameter LLM (based on Mistral-Small-24B) that can reason in natural language and respond with chemical structures. This reasoning model was trained with reinforcement learning on 640,730 experimentally-grounded chemistry problems across 375 tasks ranging from synthesizability, to blood-brain barrier permeability, to human receptor activity, to scent. Our model exceeds general-purpose chemistry models, frontier models, and human experts on molecular design tasks. It is also more data efficient relative to specialized models. We anticipate that this method can be applied to train data-efficient language models specialized for tasks across a wide variety of scientific domains.

Large language model-powered chatbots have transformed how people seek information, especially in high-stakes contexts like mental health. Despite their support capabilities, safe detection and response to crises such as suicidal ideation and self-harm are still unclear, hindered by the lack of unified crisis taxonomies and clinical evaluation standards. We address this by creating: (1) a taxonomy of six crisis categories; (2) a dataset of over 2,000 inputs from 12 mental health datasets, classified into these categories; and (3) a clinical response assessment protocol. We also use LLMs to identify crisis inputs and audit five models for response safety and appropriateness. First, we built a clinical-informed crisis taxonomy and evaluation protocol. Next, we curated 2,252 relevant examples from over 239,000 user inputs, then tested three LLMs for automatic classification. In addition, we evaluated five models for the appropriateness of their responses to a user's crisis, graded on a 5-point Likert scale from harmful (1) to appropriate (5). While some models respond reliably to explicit crises, risks still exist. Many outputs, especially in self-harm and suicidal categories, are inappropriate or unsafe. Different models perform variably; some, like gpt-5-nano and deepseek-v3.2-exp, have low harm rates, but others, such as gpt-4o-mini and grok-4-fast, generate more unsafe responses. All models struggle with indirect signals, default replies, and context misalignment. These results highlight the urgent need for better safeguards, crisis detection, and context-aware responses in LLMs. They also show that alignment and safety practices, beyond scale, are crucial for reliable crisis support. Our taxonomy, datasets, and evaluation methods support ongoing AI mental health research, aiming to reduce harm and protect vulnerable users.

Brownfield engineering work involving legacy systems, incomplete documentation, and fragmented architectural knowledge poses unique challenges for the effective use of large language models (LLMs). Prior research has largely focused on greenfield or synthetic tasks, leaving a gap in structured workflows for complex, context-heavy environments. This paper introduces the Discover-Define-Deliver (D3) Framework, a disciplined LLM-assisted workflow that combines role-separated prompting strategies with applied best practices for navigating ambiguity in brownfield systems. The framework incorporates a dual-agent prompting architecture in which a Builder model generates candidate outputs and a Reviewer model provides structured critique to improve reliability. I conducted an exploratory survey study with 52 software practitioners who applied the D3 workflow to real-world engineering tasks such as legacy system exploration, documentation reconstruction, and architectural refactoring. Respondents reported perceived improvements in task clarity, documentation quality, and cognitive load, along with self-estimated productivity gains. In this exploratory study, participants reported a weighted average productivity improvement of 26.9%, reduced cognitive load for approximately 77% of participants, and 83% of participants spent less time fixing or rewriting code due to better initial planning with AI. As these findings are self-reported and not derived from controlled experiments, they should be interpreted as preliminary evidence of practitioner sentiment rather than causal effects. The results highlight both the potential and limitations of structured LLM workflows for legacy engineering systems and motivate future controlled evaluations.