Human social behaviour is governed by complex interactions shaped by uncertainty, causality, and group dynamics. We propose Causal Spherical Hypergraph Networks (Causal-SphHN), a principled framework for socially grounded prediction that jointly models higher-order structure, directional influence, and epistemic uncertainty. Our method represents individuals as hyperspherical embeddings and group contexts as hyperedges, capturing semantic and relational geometry. Uncertainty is quantified via Shannon entropy over von Mises-Fisher distributions, while temporal causal dependencies are identified using Granger-informed subgraphs. Information is propagated through an angular message-passing mechanism that respects belief dispersion and directional semantics. Experiments on SNARE (offline networks), PHEME (online discourse), and AMIGOS (multimodal affect) show that Causal-SphHN improves predictive accuracy, robustness, and calibration over strong baselines. Moreover, it enables interpretable analysis of influence patterns and social ambiguity. This work contributes a unified causal-geometric approach for learning under uncertainty in dynamic social environments.

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/

A reliable evaluation of surgical difficulty can improve the success of the treatment for rectal cancer and the current evaluation method is based on clinical data. However, more data about rectal cancer can be collected with the development of technology. Meanwhile, with the development of artificial intelligence, its application in rectal cancer treatment is becoming possible. In this paper, a multi-view rectal cancer dataset is first constructed to give a more comprehensive view of patients, including the high-resolution MRI image view, pressed-fat MRI image view, and clinical data view. Then, an interpretable incomplete multi-view surgical evaluation model is proposed, considering that it is hard to obtain extensive and complete patient data in real application scenarios. Specifically, a dual representation incomplete multi-view learning model is first proposed to extract the common information between views and specific information in each view. In this model, the missing view imputation is integrated into representation learning, and second-order similarity constraint is also introduced to improve the cooperative learning between these two parts. Then, based on the imputed multi-view data and the learned dual representation, a multi-view surgical evaluation model with the TSK fuzzy system is proposed. In the proposed model, a cooperative learning mechanism is constructed to explore the consistent information between views, and Shannon entropy is also introduced to adapt the view weight. On the MVRC dataset, we compared it with several advanced algorithms and DRIMV_TSK obtained the best results.

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.

Recent advances in flow-based generative modelling have provided scalable methods for computing the Schrödinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The successful Iterative Markovian Fitting (IMF) procedure solves the SB problem via sequential bridge-matching steps, presenting an elegant and practical approach with many favourable properties over the more traditional Iterative Proportional Fitting (IPF) procedure. Beyond the standard setting, optimal transport can be generalised to the multi-marginal case in which the objective is to minimise a cost defined over several marginal distributions. Of particular importance are costs defined over a tree structure, from which Wasserstein barycentres can be recovered as a special case. In this work, we extend the IMF procedure to solve for the tree-structured SB problem. Our resulting algorithm inherits the many advantages of IMF over IPF approaches in the tree-based setting. In the specific case of Wasserstein barycentres, our approach can be viewed as extending fixed-point approaches for barycentre computation to the case of flow-based entropic OT solvers.

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.

Synchronization errors, such as insertions and deletions, present a fundamental challenge in DNA-based data storage systems, arising from both synthesis and sequencing noise. These channels are often modeled as insertion-deletion-substitution (IDS) channels, for which designing maximum-likelihood decoders is computationally expensive. In this work, we propose a data-driven approach based on neural polar decoders (NPDs) to design low-complexity decoders for channels with synchronization errors. The proposed architecture enables decoding over IDS channels with reduced complexity $O(AN log N )$, where $A$ is a tunable parameter independent of the channel. NPDs require only sample access to the channel and can be trained without an explicit channel model. Additionally, NPDs provide mutual information (MI) estimates that can be used to optimize input distributions and code design. We demonstrate the effectiveness of NPDs on both synthetic deletion and IDS channels. For deletion channels, we show that NPDs achieve near-optimal decoding performance and accurate MI estimation, with significantly lower complexity than trellis-based decoders. We also provide numerical estimates of the channel capacity for the deletion channel. We extend our evaluation to realistic DNA storage settings, including channels with multiple noisy reads and real-world Nanopore sequencing data. Our results show that NPDs match or surpass the performance of existing methods while using significantly fewer parameters than the state-of-the-art. These findings highlight the promise of NPDs for robust and efficient decoding in DNA data storage systems.

The rapid adaptation ability of auto-regressive foundation models is often attributed to the diversity of their pre-training data. This is because, from a Bayesian standpoint, minimizing prediction error in such settings requires integrating over all plausible latent hypotheses consistent with observations. While this behavior is desirable in principle, it often proves too ambitious in practice: under high ambiguity, the number of plausible latent alternatives makes Bayes-optimal prediction computationally intractable. Cognitive science has long recognized this limitation, suggesting that under such conditions, heuristics or information-seeking strategies are preferable to exhaustive inference. Translating this insight to next-token prediction, we hypothesize that low- and high-ambiguity predictions pose different computational demands, making ambiguity-agnostic next-token prediction a detrimental inductive bias. To test this, we introduce MetaHMM, a synthetic sequence meta-learning benchmark with rich compositional structure and a tractable Bayesian oracle. We show that Transformers indeed struggle with high-ambiguity predictions across model sizes. Motivated by cognitive theories, we propose a method to convert pre-trained models into Monte Carlo predictors that decouple task inference from token prediction. Preliminary results show substantial gains in ambiguous contexts through improved capacity allocation and test-time scalable inference, though challenges remain.