The theoretical study of Bayesian neural networks was initiated by Neal [29] who proved that if a shallow Bayesian neural network is initialized with independent Gaussian parameters (i.e., biases and weights), then the output of the network converges in distribution to a Gaussian process, as the number of neurons grows large ( i.e., in the wide width limit). This result was extended to Bayesian deep neural networks two decades later (see [16, 22, 26]) and only recently it has been made quantitative by the use of the optimal transport theory (see [6] and [33]), by the Stein method for Gaussian approximation (see [3, 4, 8, 13]), and by alternative techniques ([7, 11]). Another promising approach to analyze Bayesian neural networks is through the lens of large deviations. First results in this direction are given in [23]. These findings have been successively generalized in [2, 34]. A different perspective is provided by the so-called mean field analysis of networks (see [27, 15]). The advantage of the Bayesian framework is that it allows to include in the model both prior knowledge and observed data through a prior distribution on network's parameters and a likelihood function, respectively. The emergence of Gaussian processes helped to understand how large neural networks work, how to make them more efficient, and motivated the use of Bayesian regression inference methods, see [22]. However, as noticed by [28] and [21], the connection with Gaussian processes also highlighted the limitations of wide width neural networks with independent and Gaussian distributed weights.

Transductive learning is a supervised machine learning task in which, unlike in traditional inductive learning, the unlabelled data that require labelling are a finite set and are available at training time. Similarly to inductive learning contexts, transductive learning contexts may be affected by dataset shift, i.e., may be such that the IID assumption does not hold. We here propose a method, tailored to transductive classification contexts, for performing model selection (i.e., hyperparameter optimisation) when the data exhibit prior probability shift, an important type of dataset shift typical of anti-causal learning problems. In our proposed method the hyperparameters can be optimised directly on the unlabelled data to which the trained classifier must be applied; this is unlike traditional model selection methods, that are based on performing cross-validation on the labelled training data. We provide experimental results that show the benefits brought about by our method.

Traffic congestion due to uncertainties, such as accidents, is a significant issue in urban areas, as the ripple effect of accidents causes longer delays, increased emissions, and safety concerns. To address this issue, we propose a robust framework for predicting the impact of accidents on congestion. We implement Automated Machine Learning (AutoML)-enhanced Deep Embedding Clustering (DEC) to assign congestion labels to accident data and predict congestion probability using a Bayesian Network (BN). The Simulation of Urban Mobility (SUMO) simulation is utilized to evaluate the correctness of BN predictions using evidence-based scenarios. Results demonstrate that the AutoML-enhanced DEC has outperformed traditional clustering approaches. The performance of the proposed BN model achieved an overall accuracy of 95.6%, indicating its ability to understand the complex relationship of accidents causing congestion. Validation in SUMO with evidence-based scenarios demonstrated that the BN model's prediction of congestion states closely matches those of SUMO, indicating the high reliability of the proposed BN model in ensuring smooth urban mobility.

--In vertical federated learning (VFL), multiple enterprises address aligned sample scarcity by leveraging massive locally unaligned samples to facilitate collaborative learning. However, unaligned samples across different parties in VFL can be extremely class-imbalanced, leading to insufficient feature representation and limited model prediction space. Specifically, class-imbalanced problems consist of intra-party class imbalance and inter-party class imbalance, which can further cause local model bias and feature contribution inconsistency issues, respectively. T o address the above challenges, we propose Proto-EVFL, an enhanced VFL framework via dual prototypes. We first introduce class prototypes for each party to learn relationships between classes in the latent space, allowing the active party to predict unseen classes. We further design a probabilistic dual prototype learning scheme to dynamically select unaligned samples by conditional optimal transport cost with class prior probability. Moreover, a mixed prior guided module guides this selection process by combining local and global class prior probabilities. Finally, we adopt an adaptive gated feature aggregation strategy to mitigate feature contribution inconsistency by dynamically weighting and aggregating local features across different parties. We proved that Proto-EVFL, as the first bi-level optimization framework in VFL, has a convergence rate of 1 / T . Even in a zero-shot scenario with one unseen class, it outperforms baselines by at least 6.97%. NTRODUCTION indicates equal contribution, * represents the corresponding authors Wei Guo, Yiyang Duan and Fuzhen Zhuang are with the School of Artificial Intelligence, Beihang University, Beijing 100083, China (e-mail: { guowei, duanyiyang, zhuangfuzhen }@buaa.edu.cn). Xiao Zhang is with the School of Computer Science and Technology, Shan-dong University, Shandong 266237, China (e-mail: xiaozhang@sdu.edu.cn). Zhaojun Hu is with the Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing 100872, China (e-mail: huzhao-jun@ruc.edu.cn).

State-space models are pivotal for dynamic system analysis but often struggle with outlier data that deviates from Gaussian distributions, frequently exhibiting skewness and heavy tails. This paper introduces a robust extension utilizing the asymmetric Laplace distribution, specifically tailored to capture these complex characteristics. We propose an efficient variational Bayes algorithm and a novel single-loop parameter estimation strategy, significantly enhancing the efficiency of the filtering, smoothing, and parameter estimation processes. Our comprehensive experiments demonstrate that our methods provide consistently robust performance across various noise settings without the need for manual hyperparameter adjustments. In stark contrast, existing models generally rely on specific noise conditions and necessitate extensive manual tuning. Moreover, our approach uses far fewer computational resources, thereby validating the model's effectiveness and underscoring its potential for practical applications in fields such as robust control and financial modeling.

Fusing information from human observations can help robots overcome sensing limitations in collaborative tasks. However, an uncertainty-aware fusion framework requires a grounded likelihood representing the uncertainty of human inputs. This paper presents a Feature Pyramid Likelihood Grounding Network (FP-LGN) that grounds spatial language by learning relevant map image features and their relationships with spatial relation semantics. The model is trained as a probability estimator to capture aleatoric uncertainty in human language using three-stage curriculum learning. Results showed that FP-LGN matched expert-designed rules in mean Negative Log-Likelihood (NLL) and demonstrated greater robustness with lower standard deviation. Collaborative sensing results demonstrated that the grounded likelihood successfully enabled uncertainty-aware fusion of heterogeneous human language observations and robot sensor measurements, achieving significant improvements in human-robot collaborative task performance.

Planning in modern LLM agents relies on the utilization of LLM as an internal world model, acquired during pretraining. However, existing agent designs fail to effectively assimilate new observations into dynamic updates of the world model. This reliance on the LLM's static internal world model is progressively prone to misalignment with the underlying true state of the world, leading to the generation of divergent and erroneous plans. We introduce a hierarchical agent architecture, CoEx, in which hierarchical state abstraction allows LLM planning to co-evolve with a dynamically updated model of the world. CoEx plans and interacts with the world by using LLM reasoning to orchestrate dynamic plans consisting of subgoals, and its learning mechanism continuously incorporates these subgoal experiences into a persistent world model in the form of a neurosymbolic belief state, comprising textual inferences and code-based symbolic memory. We evaluate our agent across a diverse set of agent scenarios involving rich environments and complex tasks including ALFWorld, PDDL, and Jericho. Our experiments show that CoEx outperforms existing agent paradigms in planning and exploration.

Gradient-based Markov Chain Monte Carlo methods have recently received much attention for sampling discrete distributions, with notable examples such as Norm Constrained Gradient (NCG), Auxiliary Variable Gradient (AVG), and Discrete Hamiltonian Assisted Metropolis Sampling (DHAMS). In this work, we propose the Preconditioned Discrete-HAMS (PDHAMS) algorithm, which extends DHAMS by incorporating a second-order, quadratic approximation of the potential function, and uses Gaussian integral trick to avoid directly sampling a pairwise Markov random field. The PDHAMS sampler not only satisfies generalized detailed balance, hence enabling irreversible sampling, but also is a rejection-free property for a target distribution with a quadratic potential function. In various numerical experiments, PDHAMS algorithms consistently yield superior performance compared with other methods.

InsurTech refers to the use of state-of-the-art technology, including both emerging hardware and software, to address inefficiencies across the insurance value chain and further explore new opportunities to reshape traditional business operations. InsurTech encompasses a broad spectrum of technology-driven innovations, including, but not limited to, telematics, usage-based insurance, and the integration of Internet of Things (IoT) sensors. In this study, we focus on a specific class of InsurTech, an Insurtech data vendor, that provides insurance companies with next-generation data solutions. We leverage new and diverse external data sources, such as social media data and online content, to enrich the internal database, thereby empowering actuarial analytics and gaining more accurate insights into risk profiles and policyholder behavior. Specifically, by integrating alternative data sources beyond traditional information, insurance companies can uncover previously unrecognized risk factors, reduce bias in existing features, and identify more accurate risk exposures based on the operational characteristics of the insured entities.

We develop a unified Data Processing Inequality PAC-Bayesian framework -- abbreviated DPI-PAC-Bayesian -- for deriving generalization error bounds in the supervised learning setting. By embedding the Data Processing Inequality (DPI) into the change-of-measure technique, we obtain explicit bounds on the binary Kullback-Leibler generalization gap for both Rényi divergence and any $f$-divergence measured between a data-independent prior distribution and an algorithm-dependent posterior distribution. We present three bounds derived under our framework using Rényi, Hellinger \(p\) and Chi-Squared divergences. Additionally, our framework also demonstrates a close connection with other well-known bounds. When the prior distribution is chosen to be uniform, our bounds recover the classical Occam's Razor bound and, crucially, eliminate the extraneous \(\log(2\sqrt{n})/n\) slack present in the PAC-Bayes bound, thereby achieving tighter results. The framework thus bridges data-processing and PAC-Bayesian perspectives, providing a flexible, information-theoretic tool to construct generalization guarantees.