Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This paper presents a unified and complete Kantorovich duality theory for MOT problem on general Polish product spaces with bounded continuous cost function. For marginal compact spaces, the duality identity is derived through a convex-analytic reformulation, that identifies the dual problem as a Fenchel-Rockafellar conjugate. We obtain dual attainment and show that optimal potentials may always be chosen in the class of $c$-conjugate families, thereby extending classical two-marginal conjugacy principle into a genuinely multimarginal setting. In non-compact setting, where direct compactness arguments are unavailable, we recover duality via a truncation-tightness procedure based on weak compactness of multimarginal transference plans and boundedness of the cost. We prove that the dual value is preserved under restriction to compact subsets and that admissible dual families can be regularized into uniformly bounded $c$-conjugate potentials. The argument relies on a refined use of $c$-splitting sets and their equivalence with multimarginal $c$-cyclical monotonicity. We then obtain dual attainment and exact primal-dual equality for MOT on arbitrary Polish spaces, together with a canonical representation of optimal dual potentials by $c$-conjugacy. These results provide a structural foundation for further developments in probabilistic and statistical analysis of MOT, including stability, differentiability, and asymptotic theory under marginal perturbations.

Bayesian Networks (BNs) are an important tool for assisting probabilistic reasoning, but despite being considered transparent models, people have trouble understanding them. Further, current User Interfaces (UIs) still do not clarify the reasoning of BNs. To address this problem, we have designed verbal and visual extensions to the standard BN UI, which can guide users through common inference patterns. We conducted a user study to compare our verbal, visual and combined UI extensions, and a baseline UI. Our main findings are: (1) users did better with all three types of extensions than with the baseline UI for questions about the impact of an observation, the paths that enable this impact, and the way in which an observation influences the impact of other observations; and (2) using verbal and visual modalities together is better than using either modality alone for some of these question types.

We propose new methods for learning Bayesian networks (BNs) that reliably support fast inference.

The rise of the machine learning (ML) model economy has intertwined markets for training datasets and pre-trained models. However, most pricing approaches still separate data and model transactions or rely on broker-centric pipelines that favor one side. Recent studies of data markets with externalities capture buyer interactions but do not yield a simultaneous and symmetric mechanism across data sellers, model producers, and model buyers. We propose a unified data-model coupled market that treats dataset and model trading as a single system. A supply-side mapping transforms dataset payments into buyer-visible model quotations, while a demand-side mapping propagates buyer prices back to datasets through Shapley-based allocation. Together, they form a closed loop that links four interactions: supply-demand propagation in both directions and mutual coupling among buyers and among sellers. We prove that the joint operator is a standard interference function (SIF), guaranteeing existence, uniqueness, and global convergence of equilibrium prices. Experiments demonstrate efficient convergence and improved fairness compared with broker-centric and one-sided baselines. The code is available on https://github.com/HongrunRen1109/Triple-Win-Pricing.

Multimodal sentiment analysis has received significant attention across diverse research domains. Despite advancements in algorithm design, existing approaches suffer from two critical limitations: insufficient learning of noise-contaminated unimodal data, leading to corrupted cross-modal interactions, and inadequate fusion of multimodal representations, resulting in discarding discriminative unimodal information while retaining multimodal redundant information. To address these challenges, this paper proposes a Double Information Bottleneck (DIB) strategy to obtain a powerful, unified compact multimodal representation. Implemented within the framework of low-rank Renyi's entropy functional, DIB offers enhanced robustness against diverse noise sources and computational tractability for high-dimensional data, as compared to the conventional Shannon entropy-based methods. The DIB comprises two key modules: 1) learning a sufficient and compressed representation of individual unimodal data by maximizing the task-relevant information and discarding the superfluous information, and 2) ensuring the discriminative ability of multimodal representation through a novel attention bottleneck fusion mechanism. Consequently, DIB yields a multimodal representation that effectively filters out noisy information from unimodal data while capturing inter-modal complementarity. Extensive experiments on CMU-MOSI, CMU-MOSEI, CH-SIMS, and MVSA-Single validate the effectiveness of our method. The model achieves 47.4% accuracy under the Acc-7 metric on CMU-MOSI and 81.63% F1-score on CH-SIMS, outperforming the second-best baseline by 1.19%. Under noise, it shows only 0.36% and 0.29% performance degradation on CMU-MOSI and CMU-MOSEI respectively.

This paper investigates automated skill decomposition using Large Language Models (LLMs) and proposes a rigorous, ontology-grounded evaluation framework. Our framework standardizes the pipeline from prompting and generation to normalization and alignment with ontology nodes. To evaluate outputs, we introduce two metrics: a semantic F1-score that uses optimal embedding-based matching to assess content accuracy, and a hierarchy-aware F1-score that credits structurally correct placements to assess granularity. We conduct experiments on ROME-ESCO-DecompSkill, a curated subset of parents, comparing two prompting strategies: zero-shot and leakage-safe few-shot with exemplars. Across diverse LLMs, zero-shot offers a strong baseline, while few-shot consistently stabilizes phrasing and granularity and improves hierarchy-aware alignment. A latency analysis further shows that exemplar-guided prompts are competitive - and sometimes faster - than unguided zero-shot due to more schema-compliant completions. Together, the framework, benchmark, and metrics provide a reproducible foundation for developing ontology-faithful skill decomposition systems.

Diffusion policies have recently emerged as a powerful class of visuomotor controllers for robot manipulation, offering stable training and expressive multi-modal action modeling. However, existing approaches typically treat action generation as an unconstrained denoising process, ignoring valuable a priori knowledge about geometry and control structure. In this work, we propose the Adaptive Diffusion Policy (ADP), a test-time adaptation method that introduces two key inductive biases into the diffusion. First, we embed a geometric manifold constraint that aligns denoising updates with task-relevant subspaces, leveraging the fact that the relative pose between the end-effector and target scene provides a natural gradient direction, and guiding denoising along the geodesic path of the manipulation manifold. Then, to reduce unnecessary exploration and accelerate convergence, we propose an analytically guided initialization: rather than sampling from an uninformative prior, we compute a rough registration between the gripper and target scenes to propose a structured initial noisy action. ADP is compatible with pre-trained diffusion policies and requires no retraining, enabling test-time adaptation that tailors the policy to specific tasks, thereby enhancing generalization across novel tasks and environments. Experiments on RLBench, CALVIN, and real-world datasets show that ADPro, an implementation of ADP, improves success rates, generalization, and sampling efficiency, achieving up to 25% faster execution and 9% points over strong diffusion baselines.

Precise and comprehensive situational awareness is a critical capability of modern autonomous systems. Deep neural networks that perceive task-critical details from rich sensory signals have become ubiquitous; however, their black-box behavior and sensitivity to environmental uncertainty and distribution shifts make them challenging to verify formally. Abstraction-based verification techniques for vision-based autonomy produce safety guarantees contingent on rigid assumptions, such as bounded errors or known unique distributions. Such overly restrictive and inflexible assumptions limit the validity of the guarantees, especially in diverse and uncertain test-time environments. We propose a methodology that unifies the verification models of perception with their offline validation. Our methodology leverages interval MDPs and provides a flexible end-to-end guarantee that adapts directly to the out-of-distribution test-time conditions. We evaluate our methodology on a synthetic perception Markov chain with well-defined state estimation distributions and a mountain car benchmark. Our findings reveal that we can guarantee tight yet rigorous bounds on overall system safety.