We consider a covariate-assisted ranking model grounded in the Plackett--Luce framework. Unlike existing works focusing on pure covariates or individual effects with fixed covariates, our approach integrates individual effects with dynamic covariates. This added flexibility enhances realistic ranking yet poses significant challenges for analyzing the associated estimation procedures. This paper makes an initial attempt to address these challenges. We begin by discussing the sufficient and necessary condition for the model's identifiability. We then introduce an efficient alternating maximization algorithm to compute the maximum likelihood estimator (MLE). Under suitable assumptions on the topology of comparison graphs and dynamic covariates, we establish a quantitative uniform consistency result for the MLE with convergence rates characterized by the asymptotic graph connectivity. The proposed graph topology assumption holds for several popular random graph models under optimal leading-order sparsity conditions. A comprehensive numerical study is conducted to corroborate our theoretical findings and demonstrate the application of the proposed model to real-world datasets, including horse racing and tennis competitions.

This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process that evolves jointly in the space of parameters and latent variables and exploit the fact that the stationary distribution of this diffusion concentrates around the maximum marginal likelihood estimate of the parameters. We then provide two explicit discretisations of this diffusion as practical algorithms to estimate parameters of statistical models. For each algorithm, we obtain nonasymptotic rates of convergence for the case where the joint log-likelihood is strongly concave with respect to latent variables and parameters. In particular, we provide convergence analysis for the diffusion together with the discretisation error, providing convergence rate estimates for the algorithms in Wasserstein-2 distance. To demonstrate the utility of the introduced methodology, we provide numerical experiments that demonstrate the effectiveness of the proposed diffusion for statistical inference and the stability of the numerical integrators utilised for discretisation. Our setting covers a broad number of applications, including unsupervised learning, statistical inference, and inverse problems.

Causal structure learning (CSL) refers to the task of learning causal relationships from data. Advances in CSL now allow learning of causal graphs in diverse application domains, which has the potential to facilitate data-driven causal decision-making. Real-world CSL performance depends on a number of $\textit{context-specific}$ factors, including context-specific data distributions and non-linear dependencies, that are important in practical use-cases. However, our understanding of how to assess and select CSL methods in specific contexts remains limited. To address this gap, we present $\textit{CausalRegNet}$, a multiplicative effect structural causal model that allows for generating observational and interventional data incorporating context-specific properties, with a focus on the setting of gene perturbation experiments. Using real-world gene perturbation data, we show that CausalRegNet generates accurate distributions and scales far better than current simulation frameworks. We illustrate the use of CausalRegNet in assessing CSL methods in the context of interventional experiments in biology.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate a new posterior sampling scheme for unconditional diffusion models.

Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms pose significant challenges that require advanced estimation techniques. Gaussian variational inference (GVI) offers an optimization perspective on the estimation problem, providing analytically tractable solutions and efficiencies derived from the geometry of Gaussian space. We propose a Sequential Gaussian Variational Inference (S-GVI) method to address nonlinearity and provide efficient sequential inference processes. Our approach integrates sequential Bayesian principles into the GVI framework, which are addressed using statistical approximations and gradient updates on the information geometry. Validations through simulations and real-world experiments demonstrate significant improvements in state estimation over the Maximum A Posteriori (MAP) estimation method.

As LLMs become increasingly prevalent across various applications, it is critical to establish safety guardrails to moderate input/output content of LLMs. Existing guardrail models treat various safety categories independently and fail to explicitly capture the intercorrelations among them. This has led to limitations such as ineffectiveness due to inadequate training on long-tail data from correlated safety categories, susceptibility to jailbreaking attacks, and inflexibility regarding new safety categories. To address these limitations, we propose $R^2$-Guard, a robust reasoning enabled LLM guardrail via knowledge-enhanced logical reasoning. Specifically, $R^2$-Guard comprises two parts: data-driven category-specific learning and reasoning components. The data-driven guardrail models provide unsafety probabilities of moderated content on different safety categories. We then encode safety knowledge among different categories as first-order logical rules and embed them into a probabilistic graphic model (PGM) based reasoning component. The unsafety probabilities of different categories from data-driven guardrail models are sent to the reasoning component for final inference. We employ two types of PGMs: Markov logic networks (MLNs) and probabilistic circuits (PCs), and optimize PCs to achieve precision-efficiency balance via improved graph structure. To further perform stress tests for guardrail models, we employ a pairwise construction method to construct a new safety benchmark TwinSafety, which features principled categories. We demonstrate the effectiveness of $R^2$-Guard by comparisons with eight strong guardrail models on six safety benchmarks, and demonstrate the robustness of $R^2$-Guard against four SOTA jailbreaking attacks. $R^2$-Guard significantly surpasses SOTA method LlamaGuard by 30.2% on ToxicChat and by 59.5% against jailbreaking attacks.

Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions.

Cognitive diagnosis has been developed for decades as an effective measurement tool to evaluate human cognitive status such as ability level and knowledge mastery. It has been applied to a wide range of fields including education, sport, psychological diagnosis, etc. By providing better awareness of cognitive status, it can serve as the basis for personalized services such as well-designed medical treatment, teaching strategy and vocational training. This paper aims to provide a survey of current models for cognitive diagnosis, with more attention on new developments using machine learning-based methods. By comparing the model structures, parameter estimation algorithms, model evaluation methods and applications, we provide a relatively comprehensive review of the recent trends in cognitive diagnosis models. Further, we discuss future directions that are worthy of exploration. In addition, we release two Python libraries: EduData for easy access to some relevant public datasets we have collected, and EduCDM that implements popular CDMs to facilitate both applications and research purposes.

We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.

This article investigates a control system within the context of six-generation wireless networks. The control performance optimization confronts the technical challenges that arise from the intricate interactions between communication and control sub-systems, asking for a co-design. Accounting for the system dynamics, we formulate the sequential co-design decision-makings of communication and control over the discrete time horizon as a Markov decision process, for which a practical offline learning framework is proposed. Our proposed framework integrates large language models into the elements of reinforcement learning. We present a case study on the age of semantics-aware communication and control co-design to showcase the potentials from our proposed learning framework. Furthermore, we discuss the open issues remaining to make our proposed offline learning framework feasible for realworld implementations, and highlight the research directions for future explorations. Index Terms 6G, control performance optimization, communication and control co-design, Markov decision process, reinforcement learning, large language models. Wireless networked control systems (NCSs) have been focal in contemporary engineering and industrial applications, owing to the flexibility, scalability and cost-savings [1].