Federated learning (FL) demonstrates its advantages in integrating distributed infrastructure, communication, computing and learning in a privacy-preserving manner. However, the robustness and capabilities of existing FL methods are challenged by limited and dynamic data and conditions, complexities including heterogeneities and uncertainties, and analytical explainability. Bayesian federated learning (BFL) has emerged as a promising approach to address these issues. This survey presents a critical overview of BFL, including its basic concepts, its relations to Bayesian learning in the context of FL, and a taxonomy of BFL from both Bayesian and federated perspectives. We categorize and discuss client- and server-side and FL-based BFL methods and their pros and cons. The limitations of the existing BFL methods and the future directions of BFL research further address the intricate requirements of real-life FL applications.

A digital twin (DT) leverages a virtual representation of the physical world, along with communication (e.g., 6G), computing (e.g., edge computing), and artificial intelligence (AI) technologies to enable many connected intelligence services. In order to handle the large amounts of network data based on digital twins (DTs), wireless systems can exploit the paradigm of semantic communication (SC) for facilitating informed decision-making under strict communication constraints by utilizing AI techniques such as causal reasoning. In this paper, a novel framework called causal semantic communication (CSC) is proposed for DT-based wireless systems. The CSC system is posed as an imitation learning (IL) problem, where the transmitter, with access to optimal network control policies using a DT, teaches the receiver using SC over a bandwidth limited wireless channel how to improve its knowledge to perform optimal control actions. The causal structure in the source data is extracted using novel approaches from the framework of deep end-to-end causal inference, thereby enabling the creation of a semantic representation that is causally invariant, which in turn helps generalize the learned knowledge of the system to unseen scenarios. The CSC decoder at the receiver is designed to extract and estimate semantic information while ensuring high semantic reliability. The receiver control policies, semantic decoder, and causal inference are formulated as a bi-level optimization problem within a variational inference framework. This problem is solved using a novel concept called network state models, inspired from world models in generative AI, that faithfully represents the environment dynamics leading to data generation. Simulation results demonstrate that the proposed CSC system outperforms state-of-the-art SC systems by achieving better semantic reliability and reduced semantic representation.

While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest in recent years. We contribute PAC-Bayes generalisation bounds for heavy-tailed losses under the sole assumption of bounded variance of the loss function. Under that assumption, we extend previous results from \citet{kuzborskij2019efron}. Our key technical contribution is exploiting an extention of Markov's inequality for supermartingales. Our proof technique unifies and extends different PAC-Bayesian frameworks by providing bounds for unbounded martingales as well as bounds for batch and online learning with heavy-tailed losses.

Cell transmission models enable the quantification of the motion of traffic participants on a high level of aggregation. This provides computational advantages in comparison to microscopic traffic models that capture the motion of traffic participants in great detail. This gain in computational efficiency is sometimes disadvantageously associated with lower granularity, which complicates the representation of complex traffic modules and interactions of traffic participants. In this paper, we propose a rigorous framework for cell transmission models that incorporates three important features: a) The cells are identified with the nodes of a graph. We introduce a precise notation for the directions of the traffic participants within each cell. This allows the construction of cell transmission models for general traffic networks.

Standard Bayesian learning is known to have suboptimal generalization capabilities under misspecification and in the presence of outliers. PAC-Bayes theory demonstrates that the free energy criterion minimized by Bayesian learning is a bound on the generalization error for Gibbs predictors (i.e., for single models drawn at random from the posterior) under the assumption of sampling distributions uncontaminated by outliers. This viewpoint provides a justification for the limitations of Bayesian learning when the model is misspecified, requiring ensembling, and when data is affected by outliers. In recent work, PAC-Bayes bounds -- referred to as PAC$^m$ -- were derived to introduce free energy metrics that account for the performance of ensemble predictors, obtaining enhanced performance under misspecification. This work presents a novel robust free energy criterion that combines the generalized logarithm score function with PAC$^m$ ensemble bounds. The proposed free energy training criterion produces predictive distributions that are able to concurrently counteract the detrimental effects of misspecification -- with respect to both likelihood and prior distribution -- and outliers.

We introduce GEDI, a Bayesian framework that combines existing self-supervised learning objectives with likelihood-based generative models. This framework leverages the benefits of both GEnerative and DIscriminative approaches, resulting in improved symbolic representations over standalone solutions. Additionally, GEDI can be easily integrated and trained jointly with existing neuro-symbolic frameworks without the need for additional supervision or costly pre-training steps. We demonstrate through experiments on real-world data, including SVHN, CIFAR10, and CIFAR100, that GEDI outperforms existing self-supervised learning strategies in terms of clustering performance by a significant margin. The symbolic component further allows it to leverage knowledge in the form of logical constraints to improve performance in the small data regime.

Traffic congestion caused by non-recurring incidents such as vehicle crashes and debris is a key issue for Traffic Management Centers (TMCs). Clearing incidents in a timely manner is essential for improving safety and reducing delays and emissions for the traveling public. However, TMCs and other responders face a challenge in predicting the duration of incidents (until the roadway is clear), making decisions of what resources to deploy difficult. To address this problem, this research developed an analytical framework and end-to-end machine-learning solution for predicting incident duration based on information available as soon as an incident report is received. Quality predictions of incident duration can help TMCs and other responders take a proactive approach in deploying responder services such as tow trucks, maintenance crews or activating alternative routes. The predictions use a combination of classification and regression machine learning modules. The performance of the developed solution has been evaluated based on the Mean Absolute Error (MAE), or deviation from the actual incident duration as well as Area Under the Curve (AUC) and Mean Absolute Percentage Error (MAPE). The results showed that the framework significantly improved incident duration prediction compared to methods from previous research.

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a simple but effective approximation $\hat \pi$ to $\pi$ for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which $\hat \pi$ is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when $\pi$ is log-concave.

This paper introduces a stochastic plug-and-play (PnP) sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm based on split Gibbs sampling (SGS) draws inspiration from the alternating direction method of multipliers (ADMM). It divides the challenging task of posterior sampling into two simpler sampling problems. The first problem depends on the likelihood function, while the second is interpreted as a Bayesian denoising problem that can be readily carried out by a deep generative model. Specifically, for an illustrative purpose, the proposed method is implemented in this paper using state-of-the-art diffusion-based generative models. Akin to its deterministic PnP-based counterparts, the proposed method exhibits the great advantage of not requiring an explicit choice of the prior distribution, which is rather encoded into a pre-trained generative model. However, unlike optimization methods (e.g., PnP-ADMM) which generally provide only point estimates, the proposed approach allows conventional Bayesian estimators to be accompanied by confidence intervals at a reasonable additional computational cost. Experiments on commonly studied image processing problems illustrate the efficiency of the proposed sampling strategy. Its performance is compared to recent state-of-the-art optimization and sampling methods.

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty through the posterior distribution. Practical posterior computation is commonly performed via MCMC, which can be computationally infeasible for high dimensional models with many observations. In this article we discuss the potential to improve posterior computation using ideas from machine learning. Concrete future directions are explored in vignettes on normalizing flows, Bayesian coresets, distributed Bayesian inference, and variational inference.