In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there is considerable risk of poor performance when deployed in practical measurement scenarios leading to negative patient outcomes. Reliable uncertainties accompanying predictions can provide guidance to clinicians in their interpretation of the trustworthiness of model outputs. It is therefore of interest to compare the effectiveness of different approaches. Here we implement an unprecedented set of eight uncertainty quantification (UQ) techniques to models trained on two clinically relevant prediction tasks: Atrial Fibrillation (AF) detection (classification), and two variants of blood pressure regression. We formulate a comprehensive evaluation procedure to enable a rigorous comparison of these approaches. We observe a complex picture of uncertainty reliability across the different techniques, where the most optimal for a given task depends on the chosen expression of uncertainty, evaluation metric, and scale of reliability assessed. We find that assessing local calibration and adaptivity provides practically relevant insights about model behaviour that otherwise cannot be acquired using more commonly implemented global reliability metrics. We emphasise that criteria for evaluating UQ techniques should cater to the model's practical use case, where the use of a small number of measurements per patient places a premium on achieving small-scale reliability for the chosen expression of uncertainty, while preserving as much predictive performance as possible.

Most existing software lacks accessible Application Programming Interfaces (APIs), requiring agents to operate solely through pixel-based Graphical User Interfaces (GUIs). In this API-free setting, large language model (LLM)-based agents face severe efficiency bottlenecks: limited to local visual experiences, they make myopic decisions and rely on inefficient trial-and-error, hindering both skill acquisition and long-term planning. To address these challenges, we propose KG-Agent, an experience-driven learning framework that structures an agent's raw pixel-level interactions into a persistent State-Action Knowledge Graph (SA-KG). KG-Agent overcomes inefficient exploration by linking functionally similar but visually distinct GUI states, forming a rich neighborhood of experience that enables the agent to generalize from a diverse set of historical strategies. To support long-horizon reasoning, we design a hybrid intrinsic reward mechanism based on the graph topology, combining a state value reward for exploiting known high-value pathways with a novelty reward that encourages targeted exploration. This approach decouples strategic planning from pure discovery, allowing the agent to effectively value setup actions with delayed gratification. We evaluate KG-Agent in two complex, open-ended GUI-based decision-making environments (Civilization V and Slay the Spire), demonstrating significant improvements in exploration efficiency and strategic depth over the state-of-the-art methods.

The bisimulation metric (BSM) is a powerful tool for computing state similarities within a Markov decision process (MDP), revealing that states closer in BSM have more similar optimal value functions. While BSM has been successfully utilized in reinforcement learning (RL) for tasks like state representation learning and policy exploration, its application to multiple-MDP scenarios, such as policy transfer, remains challenging. Prior work has attempted to generalize BSM to pairs of MDPs, but a lack of rigorous analysis of its mathematical properties has limited further theoretical progress. In this work, we formally establish a generalized bisimulation metric (GBSM) between pairs of MDPs, which is rigorously proven with the three fundamental properties: GBSM symmetry, inter-MDP triangle inequality, and the distance bound on identical state spaces. Leveraging these properties, we theoretically analyse policy transfer, state aggregation, and sampling-based estimation in MDPs, obtaining explicit bounds that are strictly tighter than those derived from the standard BSM. Additionally, GBSM provides a closed-form sample complexity for estimation, improving upon existing asymptotic results based on BSM. Numerical results validate our theoretical findings and demonstrate the effectiveness of GBSM in multi-MDP scenarios.

Khiops is an open source machine learning tool designed for mining large multi-table databases. Khiops is based on a unique Bayesian approach that has attracted academic interest with more than 20 publications on topics such as variable selection, classification, decision trees and co-clustering. It provides a predictive measure of variable importance using discretisation models for numerical data and value clustering for categorical data. The proposed classification/regression model is a naive Bayesian classifier incorporating variable selection and weight learning. In the case of multi-table databases, it provides propositionalisation by automatically constructing aggregates. Khiops is adapted to the analysis of large databases with millions of individuals, tens of thousands of variables and hundreds of millions of records in secondary tables. It is available on many environments, both from a Python library and via a user interface.

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural networks (PaTraC BNNs) that enable uncertainty quantification comparable to standard BNNs but use significantly fewer Bayesian parameters. These PaTraC BNNs have computational and statistical advantages over standard Bayesian neural networks in terms of speed and memory requirements. Our proposed methodology therefore facilitates reliable, robust, and scalable uncertainty quantification in neural networks. The three architectures build on trace-class neural network priors which induce an ordering of the neural network parameters, and are thus a natural choice in our framework. In a numerical simulation study, we verify the claimed benefits, and further illustrate the performance of our proposed methodology on a real-world dataset.

Despite remarkable progress in recent years, vision language models (VLMs) remain prone to overconfidence and hallucinations on tasks such as Visual Question Answering (VQA) and Visual Reasoning. Bayesian methods can potentially improve reliability by helping models selectively predict, that is, models respond only when they are sufficiently confident. Unfortunately, Bayesian methods are often assumed to be costly and ineffective for large models, and so far there exists little evidence to show otherwise, especially for multimodal applications. Here, we show the effectiveness and competitive edge of variational Bayes for selective prediction in VQA for the first time. We build on recent advances in variational methods for deep learning and propose an extension called "Variational VQA". This method improves calibration and yields significant gains for selective prediction on VQA and Visual Reasoning, particularly when the error tolerance is low ($\leq 1\%$). Often, just one posterior sample can yield more reliable answers than those obtained by models trained with AdamW. In addition, we propose a new risk-averse selector that outperforms standard sample averaging by considering the variance of predictions. Overall, we present compelling evidence that variational learning is a viable option to make large VLMs safer and more trustworthy.

Data for training structural health monitoring (SHM) systems are often expensive and/or impractical to obtain, particularly for labelled data. Population-based SHM (PBSHM) aims to address this limitation by leveraging data from multiple structures. However, data from different structures will follow distinct distributions, potentially leading to large generalisation errors for models learnt via conventional machine learning methods. To address this issue, transfer learning -- in the form of domain adaptation (DA) -- can be used to align the data distributions. Most previous approaches have only considered \emph{unsupervised} DA, where no labelled target data are available; they do not consider how to incorporate these technologies in an online framework -- updating as labels are obtained throughout the monitoring campaign. This paper proposes a Bayesian framework for DA in PBSHM, that can improve unsupervised DA mappings using a limited quantity of labelled target data. In addition, this model is integrated into an active sampling strategy to guide inspections to select the most informative observations to label -- leading to further reductions in the required labelled data to learn a target classifier. The effectiveness of this methodology is evaluated on a population of experimental bridges. Specifically, this population includes data corresponding to several damage states, as well as, a comprehensive set of environmental conditions. It is found that combining transfer learning and active learning can improve data efficiency when learning classification models in label-scarce scenarios. This result has implications for data-informed operation and maintenance of structures, suggesting a reduction in inspections over the operational lifetime of a structure -- and therefore a reduction in operational costs -- can be achieved.

Modelling pedestrian-driver interactions is critical for understanding human road user behaviour and developing safe autonomous vehicle systems. Existing approaches often rely on rule-based logic, game-theoretic models, or 'black-box' machine learning methods. However, these models typically lack flexibility or overlook the underlying mechanisms, such as sensory and motor constraints, which shape how pedestrians and drivers perceive and act in interactive scenarios. In this study, we propose a multi-agent reinforcement learning (RL) framework that integrates both visual and motor constraints of pedestrian and driver agents. Using a real-world dataset from an unsignalised pedestrian crossing, we evaluate four model variants, one without constraints, two with either motor or visual constraints, and one with both, across behavioural metrics of interaction realism. Results show that the combined model with both visual and motor constraints performs best. Motor constraints lead to smoother movements that resemble human speed adjustments during crossing interactions. The addition of visual constraints introduces perceptual uncertainty and field-of-view limitations, leading the agents to exhibit more cautious and variable behaviour, such as less abrupt deceleration. In this data-limited setting, our model outperforms a supervised behavioural cloning model, demonstrating that our approach can be effective without large training datasets. Finally, our framework accounts for individual differences by modelling parameters controlling the human constraints as population-level distributions, a perspective that has not been explored in previous work on pedestrian-vehicle interaction modelling. Overall, our work demonstrates that multi-agent RL with human constraints is a promising modelling approach for simulating realistic road user interactions.

Harmful fine-tuning poses critical safety risks to fine-tuning-as-a-service for large language models. Existing defense strategies preemptively build robustness via attack simulation but suffer from fundamental limitations: (i) the infeasibility of extending attack simulations beyond bounded threat models due to the inherent difficulty of anticipating unknown attacks, and (ii) limited adaptability to varying attack settings, as simulation fails to capture their variability and complexity. To address these challenges, we propose Bayesian Data Scheduler (BDS), an adaptive tuning-stage defense strategy with no need for attack simulation. BDS formulates harmful fine-tuning defense as a Bayesian inference problem, learning the posterior distribution of each data point's safety attribute, conditioned on the fine-tuning and alignment datasets. The fine-tuning process is then constrained by weighting data with their safety attributes sampled from the posterior, thus mitigating the influence of harmful data. By leveraging the post hoc nature of Bayesian inference, the posterior is conditioned on the fine-tuning dataset, enabling BDS to tailor its defense to the specific dataset, thereby achieving adaptive defense. Furthermore, we introduce a neural scheduler based on amortized Bayesian learning, enabling efficient transfer to new data without retraining. Comprehensive results across diverse attack and defense settings demonstrate the state-of-the-art performance of our approach. Code is available at https://github.com/Egg-Hu/Bayesian-Data-Scheduler.

Generative Adversarial Networks (GANs) are proficient at generating synthetic data but continue to suffer from mode collapse, where the generator produces a narrow range of outputs that fool the discriminator but fail to capture the full data distribution. This limitation is particularly problematic, as generative models are increasingly deployed in real-world applications that demand both diversity and uncertainty awareness. In response, we introduce BI-DCGAN, a Bayesian extension of DCGAN that incorporates model uncertainty into the generative process while maintaining computational efficiency. BI-DCGAN integrates Bayes by Backprop to learn a distribution over network weights and employs mean-field variational inference to efficiently approximate the posterior distribution during GAN training. We establishes the first theoretical proof, based on covariance matrix analysis, that Bayesian modeling enhances sample diversity in GANs. We validate this theoretical result through extensive experiments on standard generative benchmarks, demonstrating that BI-DCGAN produces more diverse and robust outputs than conventional DCGANs, while maintaining training efficiency. These findings position BI-DCGAN as a scalable and timely solution for applications where both diversity and uncertainty are critical, and where modern alternatives like diffusion models remain too resource-intensive.