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.

This study proposes the novel Bayesian and inverse Bayesian (BIB) inference framework that incorporates symmetry bias into the Bayesian updating process to perform both conventional and inverse Bayesian updates concurrently. Conventional Bayesian inference is constrained by a fundamental trade-off between adaptability to abrupt environmental changes and accuracy during stable periods. The BIB framework addresses this limitation by dynamically modulating the learning rate via inverse Bayesian updates, thereby enhancing adaptive flexibility. The BIB model was evaluated in a sequential estimation task involving observations drawn from a Gaussian distribution with a stochastically time-varying mean, where it exhibited spontaneous bursts in the learning rate during environmental transitions, transiently entering high-sensitivity states that facilitated rapid adaptation. This burst-relaxation dynamic serves as a mechanism for balancing adaptability and accuracy. Furthermore, avalanche analysis, detrended fluctuation analysis, and power spectral analysis revealed that the BIB system likely operates near a critical state-a property not observed in standard Bayesian inference. This suggests that the BIB model uniquely achieves a coexistence of computational efficiency and critical dynamics, resolving the adaptability-accuracy trade-off while maintaining scale-free behavior. These findings offer a new computational perspective on scale-free dynamics in natural systems and provide valuable insights for the design of adaptive inference systems in nonstationary environments.

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is unavailable, with a focus on model selection and misspecification diagnosis. Existing unsupervised model evaluation methods are often unsuitable for computational imaging due to their high computational cost and incompatibility with modern image priors defined implicitly via machine learning models. We herein propose a general methodology for unsupervised model selection and misspecification detection in Bayesian imaging sciences, based on a novel combination of Bayesian cross-validation and data fission, a randomized measurement splitting technique. The approach is compatible with any Bayesian imaging sampler, including diffusion and plug-and-play samplers. We demonstrate the methodology through experiments involving various scoring rules and types of model misspecification, where we achieve excellent selection and detection accuracy with a low computational cost.

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Matérn Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Matérn prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.

This note introduces a unified theory for causal inference that integrates Riesz regression, covariate balancing, density-ratio estimation (DRE), targeted maximum likelihood estimation (TMLE), and the matching estimator in average treatment effect (ATE) estimation. In ATE estimation, the balancing weights and the regression functions of the outcome play important roles, where the balancing weights are referred to as the Riesz representer, bias-correction term, and clever covariates, depending on the context. Riesz regression, covariate balancing, DRE, and the matching estimator are methods for estimating the balancing weights, where Riesz regression is essentially equivalent to DRE in the ATE context, the matching estimator is a special case of DRE, and DRE is in a dual relationship with covariate balancing. TMLE is a method for constructing regression function estimators such that the leading bias term becomes zero. Nearest Neighbor Matching is equivalent to Least Squares Density Ratio Estimation and Riesz Regression.

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted maximum likelihood estimation (TMLE), and density-ratio estimation. In many problems involving causal effects or structural models, the parameters of interest depend on regression functions. Plugging regression functions estimated by machine learning methods into the identifying equations can yield poor performance because of first-stage bias. To reduce such bias, debiased machine learning employs Neyman orthogonal estimating equations. Debiased machine learning typically requires estimation of the Riesz representer and the regression function. For this problem, we develop a direct debiased machine learning framework with an end-to-end algorithm. We formulate estimation of the nuisance parameters, the regression function and the Riesz representer, as minimizing the discrepancy between Neyman orthogonal scores computed with known and unknown nuisance parameters, which we refer to as Neyman targeted estimation. Neyman targeted estimation includes Riesz representer estimation, and we measure discrepancies using the Bregman divergence. The Bregman divergence encompasses various loss functions as special cases, where the squared loss yields Riesz regression and the Kullback-Leibler divergence yields entropy balancing. We refer to this Riesz representer estimation as generalized Riesz regression. Neyman targeted estimation also yields TMLE as a special case for regression function estimation. Furthermore, for specific pairs of models and Riesz representer estimation methods, we can automatically obtain the covariate balancing property without explicitly solving the covariate balancing objective.