This paper proposes the DnD Filter, a differentiable filter that utilizes diffusion models for state estimation of dynamic systems. Unlike conventional differentiable filters, which often impose restrictive assumptions on process noise (e.g., Gaussianity), DnD Filter enables a nonlinear state update without such constraints by conditioning a diffusion model on both the predicted state and observational data, capitalizing on its ability to approximate complex distributions. We validate its effectiveness on both a simulated task and a real-world visual odometry task, where DnD Filter consistently outperforms existing baselines. Specifically, it achieves a 25\% improvement in estimation accuracy on the visual odometry task compared to state-of-the-art differentiable filters, and even surpasses differentiable smoothers that utilize future measurements. To the best of our knowledge, DnD Filter represents the first successful attempt to leverage diffusion models for state estimation, offering a flexible and powerful framework for nonlinear estimation under noisy measurements.

As a data-driven approach, multi-agent reinforcement learning (MARL) has made remarkable advances in solving cooperative residential load scheduling problems. However, centralized training, the most common paradigm for MARL, limits large-scale deployment in communication-constrained cloud-edge environments. As a remedy, distributed training shows unparalleled advantages in real-world applications but still faces challenge with system scalability, e.g., the high cost of communication overhead during coordinating individual agents, and needs to comply with data governance in terms of privacy. In this work, we propose a novel MARL solution to address these two practical issues. Our proposed approach is based on actor-critic methods, where the global critic is a learned function of individual critics computed solely based on local observations of households. This scheme preserves household privacy completely and significantly reduces communication cost. Simulation experiments demonstrate that the proposed framework achieves comparable performance to the state-of-the-art actor-critic framework without data governance and communication constraints.

Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09, Roc18]. However, designing provable algorithms for performing this sampling task is notoriously challenging. Existing posterior samplers for Bayesian sparse variable selection tasks either require strong assumptions about the signal-to-noise ratio (SNR) [YWJ16], only work when the measurement count grows at least linearly in the dimension [MW24], or rely on heuristic approximations to the posterior. We give the first provable algorithms for spike-and-slab posterior sampling that apply for any SNR, and use a measurement count sublinear in the problem dimension. Concretely, assume we are given a measurement matrix $\mathbf{X} \in \mathbb{R}^{n\times d}$ and noisy observations $\mathbf{y} = \mathbf{X}\mathbf{\theta}^\star + \mathbf{\xi}$ of a signal $\mathbf{\theta}^\star$ drawn from a spike-and-slab prior $\pi$ with a Gaussian diffuse density and expected sparsity k, where $\mathbf{\xi} \sim \mathcal{N}(\mathbb{0}_n, \sigma^2\mathbf{I}_n)$. We give a polynomial-time high-accuracy sampler for the posterior $\pi(\cdot \mid \mathbf{X}, \mathbf{y})$, for any SNR $\sigma^{-1}$ > 0, as long as $n \geq k^3 \cdot \text{polylog}(d)$ and $X$ is drawn from a matrix ensemble satisfying the restricted isometry property. We further give a sampler that runs in near-linear time $\approx nd$ in the same setting, as long as $n \geq k^5 \cdot \text{polylog}(d)$. To demonstrate the flexibility of our framework, we extend our result to spike-and-slab posterior sampling with Laplace diffuse densities, achieving similar guarantees when $\sigma = O(\frac{1}{k})$ is bounded.

Gaussian Process (GP) models are widely utilized as surrogate models in scientific and engineering fields. However, standard GP models are limited to continuous variables due to the difficulties in establishing correlation structures for categorical variables. To overcome this limitati on, we introduce WEighted Euclidean distance matrices Gaussian Process (WEGP). WEGP constructs the kernel function for each categorical input by estimating the Euclidean distance matrix (EDM) among all categorical choices of this input. The EDM is represented as a linear combination of several predefined base EDMs, each scaled by a positive weight. The weights, along with other kernel hyperparameters, are inferred using a fully Bayesian framework. We analyze the predictive performance of WEGP theoretically. Numerical experiments validate the accuracy of our GP model, and by WEGP, into Bayesian Optimization (BO), we achieve superior performance on both synthetic and real-world optimization problems.

In many practical applications of machine learning, a discrepancy often arises between a source distribution from which labeled training examples are drawn and a target distribution for which only unlabeled data is observed. Traditionally, two main scenarios have been considered to address this issue: covariate shift (CS), where only the marginal distribution of features changes, and label shift (LS), which involves a change in the class variable's prior distribution. However, these frameworks do not encompass all forms of distributional shift. This paper introduces a new setting, Conditional Probability Shift (CPS), which captures the case when the conditional distribution of the class variable given some specific features changes while the distribution of remaining features given the specific features and the class is preserved. For this scenario we present the Conditional Probability Shift Model (CPSM) based on modeling the class variable's conditional probabilities using multinomial regression. Since the class variable is not observed for the target data, the parameters of the multinomial model for its distribution are estimated using the Expectation-Maximization algorithm. The proposed method is generic and can be combined with any probabilistic classifier. The effectiveness of CPSM is demonstrated through experiments on synthetic datasets and a case study using the MIMIC medical database, revealing its superior balanced classification accuracy on the target data compared to existing methods, particularly in situations situations of conditional distribution shift and no apriori distribution shift, which are not detected by LS-based methods.

This paper addresses the challenge of allocating heterogeneous resources among multiple agents in a decentralized manner. Our proposed method, LGTC-IPPO, builds upon Independent Proximal Policy Optimization (IPPO) by integrating dynamic cluster consensus, a mechanism that allows agents to form and adapt local sub-teams based on resource demands. This decentralized coordination strategy reduces reliance on global information and enhances scalability. We evaluate LGTC-IPPO against standard multi-agent reinforcement learning baselines and a centralized expert solution across a range of team sizes and resource distributions. Experimental results demonstrate that LGTC-IPPO achieves more stable rewards, better coordination, and robust performance even as the number of agents or resource types increases. Additionally, we illustrate how dynamic clustering enables agents to reallocate resources efficiently also for scenarios with discharging resources.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

The controller enables the robot to perform smooth and natural skateboarding motions, with reliable mode identification and transitions under disturbances. Abstract --This paper introduces Discrete-time Hybrid Automata Learning (DHAL), a framework using on-policy Reinforcement Learning to identify and execute mode-switching without trajectory segmentation or event function learning. Hybrid dynamical systems, which include continuous flow and discrete mode switching, can model robotics tasks like legged robot locomotion. Model-based methods usually depend on predefined gaits, while model-free approaches lack explicit mode-switching knowledge. Current methods identify discrete modes via segmentation before regressing continuous flow, but learning high-dimensional complex rigid body dynamics without trajectory labels or segmentation is a challenging open problem. Our approach incorporates a beta policy distribution and a multi-critic architecture to model contact-guided motions, exemplified by a challenging quadrupedal robot skateboard task. I. INTRODUCTION Legged robots are often regarded as the ideal embodiment of robotic systems, designed to perform a wide range of tasks and navigate diverse destinations. Many of these tasks, such as skateboarding and boxing, are inherently contact-guided, involving complex sequences of contact events [1]. Designing and executing such contact-guided control is highly non-trivial due to two major challenges: (1) the hybrid dynamics system problem arising from the abrupt transitions introduced by contact events [2], and (2) the sparsity of contact events, which poses significant difficulties for both model-based and model-free control strategies. In model-based control, Hybrid Automata has been proposed as a powerful framework to model systems with both discrete and continuous dynamics [3, 4]. This framework has been widely applied to behavior planning [5] and legged locomotion. However, due to the combinatorial nature of hybrid dynamics, finding optimal policies for hybrid systems through model-based optimization is computationally challenging, especially for tasks with high-dimensional state and action spaces. Model-free RL requires minimal assumptions and can be applied to a diverse range of tasks across different dynamic systems [6, 7]. However, RL policies, often represented by deep neural networks, lack interpretability and fail to explicitly model hybrid dynamics [8].

Management of sensing resources is a non-trivial problem for future military air assets with future systems deploying heterogeneous sensors to generate information of the battlespace. Machine learning techniques including deep reinforcement learning (DRL) have been identified as promising approaches, but require high-fidelity training environments and feature extractors to generate information for the agent. This paper presents a deep reinforcement learning training approach, utilising the Stone Soup tracking framework as a feature extractor to train an agent for a sensor management task. A general framework for embedding Stone Soup tracker components within a Gymnasium environment is presented, enabling fast and configurable tracker deployments for RL training using Stable Baselines3. The approach is demonstrated in a sensor management task where an agent is trained to search and track a region of airspace utilising track lists generated from Stone Soup trackers. A sample implementation using three neural network architectures in a search-and-track scenario demonstrates the approach and shows that RL agents can outperform simple sensor search and track policies when trained within the Gymnasium and Stone Soup environment.

Generalized Bayesian Inference (GBI) provides a flexible framework for updating prior distributions using various loss functions instead of the traditional likelihoods, thereby enhancing the model robustness to model misspecification. However, GBI often suffers the problem associated with intractable likelihoods. Kernelized Stein Discrepancy (KSD), as utilized in a recent study, addresses this challenge by relying only on the gradient of the log-likelihood. Despite this innovation, KSD-Bayes suffers from critical pathologies, including insensitivity to well-separated modes in multimodal posteriors. To address this limitation, we propose a weighted KSD method that retains computational efficiency while effectively capturing multimodal structures. Our method improves the GBI framework for handling intractable multimodal posteriors while maintaining key theoretical properties such as posterior consistency and asymptotic normality. Experimental results demonstrate that our method substantially improves mode sensitivity compared to standard KSD-Bayes, while retaining robust performance in unimodal settings and in the presence of outliers.