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.

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a fully probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations.

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 in classification tasks. 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.

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 crucial for reliable image segmentation.

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.