High-quality training data is critical to the performance of machine learning models, particularly Large Language Models (LLMs). However, obtaining real, high-quality data can be challenging, especially for smaller organizations and early-stage startups. Synthetic data generators provide a promising solution by replicating the statistical and structural properties of real data while preserving privacy and scalability. This study evaluates the performance of six tabular synthetic data generators from two widely used open-source libraries: SDV (Gaussian Copula, CTGAN, TVAE) and Synthicity (Bayesian Network, CTGAN, TVAE). Using a real-world dataset from the UCI Machine Learning Repository, comprising energy consumption and environmental variables from Belgium, we simulate a low-data regime by training models on only 1,000 rows. Each generator is then tasked with producing synthetic datasets under two conditions: a 1:1 (1,000 rows) and a 1:10 (10,000 rows) input-output ratio. Evaluation is conducted using two criteria: statistical similarity, measured via classical statistics and distributional metrics; and predictive utility, assessed using a "Train on Synthetic, Test on Real" approach with four regression models. While statistical similarity remained consistent across models in both scenarios, predictive utility declined notably in the 1:10 case. The Bayesian Network from Synthicity achieved the highest fidelity in both scenarios, while TVAE from SDV performed best in predictive tasks under the 1:10 setting. Although no significant performance gap was found between the two libraries, SDV stands out for its superior documentation and ease of use, making it more accessible for practitioners.

Software-intensive systems, such as software product lines and robotics, utilise Markov decision processes (MDPs) to capture uncertainty and analyse sequential decision-making problems. Despite the usefulness of conventional policy synthesis methods, they fail to scale to large state spaces. Our approach addresses this issue and accelerates policy synthesis in large MDPs by dynamically refining the MDP and iteratively selecting the most fragile MDP regions for refinement. This iterative procedure offers a balance between accuracy and efficiency, as refinement occurs only when necessary. Through a comprehensive empirical evaluation comprising diverse case studies and MDPs up to 1M states, we demonstrate significant performance improvements yielded by our approach compared to the leading probabilistic model checker PRISM (up to 2x), thus offering a very competitive solution for real-world policy synthesis tasks in larger MDPs.

Social reasoning - inferring unobservable beliefs and intentions from partial observations of other agents - remains a challenging task for large language models (LLMs). We evaluate the limits of current reasoning language models in the social deduction game Avalon and find that while the largest models demonstrate strong performance, they require extensive test-time inference and degrade sharply when distilled to smaller, real-time-capable variants. To address this, we introduce a hybrid reasoning framework that externalizes belief inference to a structured probabilistic model, while using an LLM for language understanding and interaction. Our approach achieves competitive performance with much larger models in Agent-Agent play and, notably, is the first language agent to defeat human players in a controlled study - achieving a 67% win rate and receiving higher qualitative ratings than both reasoning baselines and human teammates. We release code, models, and a dataset to support future work on social reasoning in LLM agents, which can be found at https://camp-lab-purdue.github.io/bayesian-social-deduction/

Large language models (LLMs) have shown significant potential to change how we write, communicate, and create, leading to rapid adoption across society. This dissertation examines how individuals and institutions are adapting to and engaging with this emerging technology through three research directions. First, I demonstrate how the institutional adoption of AI detectors introduces systematic biases, particularly disadvantaging writers of non-dominant language varieties, highlighting critical equity concerns in AI governance. Second, I present novel population-level algorithmic approaches that measure the increasing adoption of LLMs across writing domains, revealing consistent patterns of AI-assisted content in academic peer reviews, scientific publications, consumer complaints, corporate communications, job postings, and international organization press releases. Finally, I investigate LLMs' capability to provide feedback on research manuscripts through a large-scale empirical analysis, offering insights into their potential to support researchers who face barriers in accessing timely manuscript feedback, particularly early-career researchers and those from under-resourced settings.

Semiparametric Bayesian networks (SPBNs) integrate parametric and non-parametric probabilistic models, offering flexibility in learning complex data distributions from samples. In particular, kernel density estimators (KDEs) are employed for the non-parametric component. Under the assumption of data normality, the normal rule is used to learn the bandwidth matrix for the KDEs in SPBNs. This matrix is the key hyperparameter that controls the trade-off between bias and variance. However, real-world data often deviates from normality, potentially leading to suboptimal density estimation and reduced predictive performance. This paper first establishes the theoretical framework for the application of state-of-the-art bandwidth selectors and subsequently evaluates their impact on SPBN performance. We explore the approaches of cross-validation and plug-in selectors, assessing their effectiveness in enhancing the learning capability and applicability of SPBNs. To support this investigation, we have extended the open-source package PyBNesian for SPBNs with the additional bandwidth selection techniques and conducted extensive experimental analyses. Our results demonstrate that the proposed bandwidth selectors leverage increasing information more effectively than the normal rule, which, despite its robustness, stagnates with more data. In particular, unbiased cross-validation generally outperforms the normal rule, highlighting its advantage in high sample size scenarios.

Modern industrial systems are often subject to multiple failure modes, and their conditions are monitored by multiple sensors, generating multiple time-series signals. Additionally, time-to-failure data are commonly available. Accurately predicting a system's remaining useful life (RUL) requires effectively leveraging multi-sensor time-series data alongside multi-mode failure event data. In most existing models, failure modes and RUL prediction are performed independently, ignoring the inherent relationship between these two tasks. Some models integrate multiple failure modes and event prediction using black-box machine learning approaches, which lack statistical rigor and cannot characterize the inherent uncertainty in the model and data. This paper introduces a unified approach to jointly model the multi-sensor time-series data and failure time concerning multiple failure modes. This proposed model integrate a Cox proportional hazards model, a Convolved Multi-output Gaussian Process, and multinomial failure mode distributions in a hierarchical Bayesian framework with corresponding priors, enabling accurate prediction with robust uncertainty quantification. Posterior distributions are effectively obtained by Variational Bayes, and prediction is performed with Monte Carlo sampling. The advantages of the proposed model is validated through extensive numerical and case studies with jet-engine dataset.

We address the problem of detecting an anomalous process among a large number of processes. At each time t, normal processes are in state zero (normal state), while the abnormal process may be in either state zero (normal state) or state one (abnormal state), with the states being hidden. The transition between states for the abnormal process is governed by a Markov chain over time. At each time step, observations can be drawn from a selected subset of processes. Each probed process generates an observation depending on its hidden state, either a typical distribution under state zero or an abnormal distribution under state one. The objective is to design a sequential search strategy that minimizes the expected detection time, subject to an error probability constraint. In contrast to prior works that assume i.i.d. observations, we address a new setting where anomalies evolve according to a hidden Markov model. To this end, we propose a novel algorithm, dubbed Anomaly Detection under Hidden Markov model (ADHM), which dynamically adapts the probing strategy based on accumulated statistical evidence and predictive belief updates over hidden states. ADHM effectively leverages temporal correlations to focus sensing resources on the most informative processes. The algorithm is supported by an asymptotic theoretical foundation, grounded in an oracle analysis that characterizes the fundamental limits of detection under the assumption of a known distribution of the hidden states. In addition, the algorithm demonstrates strong empirical performance, consistently outperforming existing methods in extensive simulations.

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.

We introduce CIfly, a framework for efficient algorithmic primitives in graphical causal inference that isolates reachability as a reusable core operation. It builds on the insight that many causal reasoning tasks can be reduced to reachability in purpose-built state-space graphs that can be constructed on the fly during traversal. We formalize a rule table schema for specifying such algorithms and prove they run in linear time. We establish CIfly as a more efficient alternative to the common primitives moralization and latent projection, which we show are computationally equivalent to Boolean matrix multiplication. Our open-source Rust implementation parses rule table text files and runs the specified CIfly algorithms providing high-performance execution accessible from Python and R. We demonstrate CIfly's utility by re-implementing a range of established causal inference tasks within the framework and by developing new algorithms for instrumental variables.

-- Trust prediction is a key issue in human-robot collaboration, especially in construction scenarios where maintaining appropriate trust calibration is critical for safety and efficiency. This paper introduces the Performance-guided Physiological signal-based Trust Prediction (PPTP), a novel framework designed to improve trust assessment. We designed a human-robot construction scenario with three difficulty levels to induce different trust states. Our approach integrates synchronized multimodal physiological signals (ECG, GSR, and EMG) with collaboration performance evaluation to predict human trust levels. Individual physiological signals are processed using collaboration performance information as guiding cues, leveraging the standardized nature of collaboration performance to compensate for individual variations in physiological responses. Extensive experiments demonstrate the efficacy of our cross-modality fusion method in significantly improving trust classification performance. Our model achieves over 81% accuracy in three-level trust classification, outperforming the best baseline method by 6.7%, and notably reaches 74.3% accuracy in high-resolution seven-level classification, which is a first in trust prediction research. Ablation experiments further validate the superiority of physiological signal processing guided by collaboration performance assessment.