Uncertainty Quantification (UQ) is crucial for reliable image segmentation.

Uncertainty Quantification (UQ) is vital for decision makers as it offers insights into the potential reliability of data and model, enabling more informed and risk-aware decision-making. Graphical models, capable of representing data with complex dependencies, are widely used across domains.Existing sampling-based UQ methods are unbiased but cannot guarantee convergence and are time-consuming on large-scale graphs. There are fast UQ methods for graphical models with closed-form solutions and convergence guarantee but with uncertainty underestimation.We propose, a UQ method that utilizes a novel linear propagation of uncertainty to model uncertainty among related nodes additively instead of multiplicatively, to offer linear scalability, guaranteed convergence, and closed-form solutions without underestimating uncertainty.Theoretically, we decompose the expected prediction error of the graphical model and prove that the uncertainty computed by is the of the decomposition.Experimentally, we demonstrate that is consistent with the sampling-based method but with linear scalability and fast convergence.Moreover, outperforms competitors in uncertainty-based active learning on four real-world graph datasets, achieving higher accuracy with a lower labeling budget.

Uncertainty quantification (UQ) is essential for creating trustworthy machine learning models. Recent years have seen a steep rise in UQ methods that can flag suspicious examples, however, it is often unclear what exactly these methods identify. In this work, we propose a framework for categorizing uncertain examples flagged by UQ methods. We introduce the confusion density matrix---a kernel-based approximation of the misclassification density---and use this to categorize suspicious examples identified by a given uncertainty method into three classes: out-of-distribution (OOD) examples, boundary (Bnd) examples, and examples in regions of high in-distribution misclassification (IDM). Through extensive experiments, we show that our framework provides a new and distinct perspective for assessing differences between uncertainty quantification methods, thereby forming a valuable assessment benchmark.

Large language models(LLMs) are increasingly expanding their real-world applications across domains, e.g., question answering, autonomous driving, and automatic software development. Despite this achievement, LLMs, as data-driven systems, often make incorrect predictions, which can lead to potential losses in safety-critical scenarios. To address this issue and measure the confidence of model outputs, multiple uncertainty quantification(UQ) criteria have been proposed. However, even though important, there are limited tools to integrate these methods, hindering the practical usage of UQ methods and future research in this domain. To bridge this gap, in this paper, we introduce UncertaintyZoo, a unified toolkit that integrates 29 uncertainty quantification methods, covering five major categories under a standardized interface. Using UncertaintyZoo, we evaluate the usefulness of existing uncertainty quantification methods under the code vulnerability detection task on CodeBERT and ChatGLM3 models. The results demonstrate that UncertaintyZoo effectively reveals prediction uncertainty. The tool with a demonstration video is available on the project site https://github.com/Paddingbuta/UncertaintyZoo.

Quantifying uncertainty in deep regression models is important both for understanding the confidence of the model and for safe decision-making in high-risk domains. Existing approaches that yield prediction intervals overlook distributional information, neglecting the effect of multimodal or asymmetric distributions on decision-making. Similarly, full or approximated Bayesian methods, while yielding the predictive posterior density, demand major modifications to the model architecture and retraining. We introduce MCNF, a novel post hoc uncertainty quantification method that produces both prediction intervals and the full conditioned predictive distribution. MCNF operates on top of the underlying trained predictive model; thus, no predictive model retraining is needed. We provide experimental evidence that the MCNF-based uncertainty estimate is well calibrated, is competitive with state-of-the-art uncertainty quantification methods, and provides richer information for downstream decision-making tasks.

Claim-level Uncertainty Quantification (UQ) is a promising approach to mitigate the lack of reliability in Large Language Models (LLMs). We introduce MUCH, the first claim-level UQ benchmark designed for fair and reproducible evaluation of future methods under realistic conditions. It includes 4,873 samples across four European languages (English, French, Spanish, and German) and four instruction-tuned open-weight LLMs. Unlike prior claim-level benchmarks, we release 24 generation logits per token, facilitating the development of future white-box methods without re-generating data. Moreover, in contrast to previous benchmarks that rely on manual or LLM-based segmentation, we propose a new deterministic algorithm capable of segmenting claims using as little as 0.2% of the LLM generation time. This makes our segmentation approach suitable for real-time monitoring of LLM outputs, ensuring that MUCH evaluates UQ methods under realistic deployment constraints. Finally, our evaluations show that current methods still have substantial room for improvement in both performance and efficiency.

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there is considerable risk of poor performance when deployed in practical measurement scenarios leading to negative patient outcomes. Reliable uncertainties accompanying predictions can provide guidance to clinicians in their interpretation of the trustworthiness of model outputs. It is therefore of interest to compare the effectiveness of different approaches. Here we implement an unprecedented set of eight uncertainty quantification (UQ) techniques to models trained on two clinically relevant prediction tasks: Atrial Fibrillation (AF) detection (classification), and two variants of blood pressure regression. We formulate a comprehensive evaluation procedure to enable a rigorous comparison of these approaches. We observe a complex picture of uncertainty reliability across the different techniques, where the most optimal for a given task depends on the chosen expression of uncertainty, evaluation metric, and scale of reliability assessed. We find that assessing local calibration and adaptivity provides practically relevant insights about model behaviour that otherwise cannot be acquired using more commonly implemented global reliability metrics. We emphasise that criteria for evaluating UQ techniques should cater to the model's practical use case, where the use of a small number of measurements per patient places a premium on achieving small-scale reliability for the chosen expression of uncertainty, while preserving as much predictive performance as possible.

Uncertainty Quantification (UQ) research has primarily focused on closed-book factual question answering (QA), while contextual QA remains unexplored, despite its importance in real-world applications. In this work, we focus on UQ for the contextual QA task and propose a theoretically grounded approach to quantify epistemic uncertainty. We begin by introducing a task-agnostic, token-level uncertainty measure defined as the cross-entropy between the predictive distribution of the given model and the unknown true distribution. By decomposing this measure, we isolate the epistemic component and approximate the true distribution by a perfectly prompted, idealized model. We then derive an upper bound for epistemic uncertainty and show that it can be interpreted as semantic feature gaps in the given model's hidden representations relative to the ideal model. We further apply this generic framework to the contextual QA task and hypothesize that three features approximate this gap: context-reliance (using the provided context rather than parametric knowledge), context comprehension (extracting relevant information from context), and honesty (avoiding intentional lies). Using a top-down interpretability approach, we extract these features by using only a small number of labeled samples and ensemble them to form a robust uncertainty score. Experiments on multiple QA benchmarks in both in-distribution and out-of-distribution settings show that our method substantially outperforms state-of-the-art unsupervised (sampling-free and sampling-based) and supervised UQ methods, achieving up to a 13-point PRR improvement while incurring a negligible inference overhead.

The rapid advancement of large language models (LLMs) has transformed the landscape of natural language processing, enabling breakthroughs across a wide range of areas including question answering, machine translation, and text summarization. Yet, their deployment in real-world applications has raised concerns over reliability and trustworthiness, as LLMs remain prone to hallucinations that produce plausible but factually incorrect outputs. Uncertainty quantification (UQ) has emerged as a central research direction to address this issue, offering principled measures for assessing the trustworthiness of model generations. We begin by introducing the foundations of UQ, from its formal definition to the traditional distinction between epistemic and aleatoric uncertainty, and then highlight how these concepts have been adapted to the context of LLMs. Building on this, we examine the role of UQ in hallucination detection, where quantifying uncertainty provides a mechanism for identifying unreliable generations and improving reliability. We systematically categorize a wide spectrum of existing methods along multiple dimensions and present empirical results for several representative approaches. Finally, we discuss current limitations and outline promising future research directions, providing a clearer picture of the current landscape of LLM UQ for hallucination detection.