Uncertainty Quantification

Also known as UQ

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44 papers in the last four weeks, up 110% on the four weeks before. 0.4% of all new papers.

Jul 13Week of Sep 28

Latest papers 431

Jul 3, 2026cs.LG

Joint distribution of upstream runoff governs downstream river-discharge prediction uncertainty in distributed ML models

Uncertainty quantification of hydrological predictions is necessary to inform operational decisions. Recent generative machine-learning methods have advanced probabilistic streamflow prediction, but have remained confined to lumped models that predict a basin outlet directly. At the same time, deterministic LSTM runoff models are increasingly applied at grid or catchment scale and routed through river networks to produce spatially continuous, physically consistent discharge fields. This technical note argues that moving probabilistic prediction from lumped to distributed models introduces a specific new requirement: the joint distribution of upstream runoff generation must be sampled jointly. In lumped inference, the model predicts the outlet distribution directly and can modulate spread from basin attributes. In distributed inference, downstream discharge is obtained by routing many upstream runoff predictions, so independent local sampling averages uncertainty away. Using Japan as a case study, we train two probabilistic basin-scale runoff LSTMs and route their runoff through a Hayami routing scheme. Randomly matching upstream ensemble members produces severely under-dispersed downstream ensembles, whereas a simple quantile matching strategy restores much of the spread of the direct basin-scale reference. The shift from lumped to distributed probabilistic hydrology therefore requires explicit attention to the spatial joint structure of runoff uncertainty.

Karan Ruparell, Tristan Hascoet, Takemasa Miyoshi +4

University of Reading, Department of Meteorology, Reading, UK · European Centre for Medium-Range Weather Forecasts (ECMWF), Reading, UK · RIKEN Center for Computational Sciences, Kobe, Japan +3

Uncertainty Quantification Time Series Forecasting Probabilistic Forecasting

Jul 3, 2026cs.LG

A Bayesian Framework for Evaluating Scenario Compatibility in Generative Population Synthesis

Scenario-based transportation analysis specifies future assumptions through aggregate population targets, whereas generative population synthesis models produce detailed individual-level realizations. When scenario targets are imposed on generative models, current practice relies on deterministic marginal calibration, implicitly assuming that the targets are compatible with the model's learned structural support. However, whether scenario-level constraints lie within the generative support--and how strongly they distort structural uncertainty--remains largely unexamined. We propose an ensemble-based Bayesian updating framework to quantify scenario compatibility in conditional population synthesis. A population-aware conditional variational autoencoder is developed to learn a distribution over plausible population structures while preserving aggregate fidelity. An ensemble of realizations sampled from the learned prior provides an empirical approximation of structural uncertainty. Scenario targets are treated as probabilistic evidence over aggregate statistics, and posterior weights are obtained through Bayesian updating across the ensemble. Scenario compatibility is quantified using effective sample size (ESS), which measures posterior concentration and the compression of structural uncertainty induced by conditioning. Experiments demonstrate that scenario impact depends not only on target magnitude but also on alignment with the learned joint structure, and reveal structural failure modes when targets fall outside prior ensemble support. The proposed framework provides a probabilistic diagnostic model for evaluating scenario feasibility and structural consistency before downstream projection and transportation planning.

Zhenlin Qin, Leizhen Wang, Yancheng Ling +1

Department of Civil and Architectural Engineering, KTH Royal Institute of Technology, Stockholm, Sweden. · Department of Data Science and Artificial Intelligence, Monash University, Melbourne, Australia. · Digital Futures, KTH Royal Institute of Technology, Stockholm, Sweden.

Uncertainty Quantification Bayesian Inference

Jul 3, 2026cs.LG

Robustness Meets Uncertainty: Evidential Adversarial Training for Robust Selective Classification

Safety-critical applications require classifiers that are both robust and reliable. Adversarial training is a widely adopted defense for improving robustness in deep neural networks; however, its effect on the reliability of predictive uncertainty remains underexplored. We investigate this gap through the lens of selective classification, which has rarely been systematically analyzed alongside adversarial robustness. We introduce a unified benchmark for the robustness-uncertainty trade-off. It standardizes architectures, augmentations, threat models, and evaluation metrics across clean, adversarial, and common-corruption settings. Across a wide range of state-of-the-art adversarial training methods, we uncover a recurring failure mode: several approaches improve robust accuracy while degrading uncertainty ranking, leading to poorer selective behavior. To address this, we propose Evidential Adversarial Training (EV-AT), which models uncertainty through a Dirichlet distribution and combines (i) an evidence-based loss promoting clean accuracy and reliable uncertainty with (ii) a robust evidence-alignment loss matching clean and adversarial predictions in log Dirichlet-parameter space. Extensive experiments show that EV-AT shifts the Pareto frontier of robustness-uncertainty trade-offs beyond prior state-of-the-art adversarial training methods. Our source code is publicly available at https://github.com/NicolasSournac/Robustness_Meets_Uncertainty.EV-AT.

Nicolas Sournac, Ahmed Baha Ben Jmaa, Bertrand Braeckeveldt

Multitel Research & Innovation Center, Artificial Intelligence Department, Belgium · TRAIL – Trusted AI Labs, Belgium

Adversarial Training Evidential Deep Learning Uncertainty Quantification Selective Prediction Neural Network Robustness Adversarial Robustness

Jul 3, 2026cs.LG

Trading Confidence: Comprehensive Uncertainty Estimation in Algorithmic Trading

Reinforcement Learning (RL) has emerged as a powerful approach in financial trading, enabling agents to learn optimal strategies through direct market interaction. However, financial markets are highly uncertain, with price fluctuations driven by stochastic volatility, model limitations, and regime shifts. Traditional RL models struggle in dynamic environments, often failing to adapt to sudden market disruptions, leading to suboptimal trading decisions. To address this challenge, we propose an uncertainty-aware RL framework that integrates distributional, epistemic, and aleatoric uncertainty estimations. Our approach enhances uncertainty estimation using SHAP-weighted reconstruction uncertainty, MC Dropout, and an LSTM-based technical indicator consensus mechanism. Experimental results on five major U.S. stock indices demonstrate that RL agents equipped with uncertainty estimation significantly outperform traditional models in return and risk management. This study advances uncertainty estimation in RL-based financial trading, with future research extending its application to other asset classes and alternative RL architectures for greater adaptability.

Lin Li, Li Rong Wang, Hsuan Fu +1

Nanyang Technological University 50 Nanyang Avenue, Singapore · Nanyang Technological University Centre for Frontier AI Research, A*STAR 50 Nanyang Avenue, Singapore · Laval University Quebec, Canada

Reinforcement Learning Uncertainty Quantification Aleatoric Uncertainty Algorithmic Trading Epistemic Uncertainty

Jul 2, 2026eess.IV

Self-Auditing Residual Drifting for Pathology-Preserving Accelerated Knee MRI

Accelerated magnetic resonance imaging reduces acquisition time, but reconstruction from undersampled k-space can blur diagnostically relevant structures or introduce failures that are not captured by global image metrics. We propose SA-RDM-DC, a Self-Auditing Residual generative Drifting Model with Data Consistency for accelerated knee MRI. The method adapts the newly proposed generative drifting paradigm to accelerated MRI by training a physics-conditioned drift field from the zero-filled reconstruction toward the fully sampled residual correction. It predicts image- and missing-k-space residual corrections, enforces data consistency with acquired k-space, uses frequency-aware and residual drifting supervision to recover fine detail, and produces dense error maps and slice-level risk scores in the same inference pass. We evaluate SA-RDM-DC on multi-coil fastMRI knee data at acceleration factors of 4, 8, and 12, with fastMRI+ pathology annotations for region-level and classifier-based task preservation, and on SKM-TEA for zero-shot and fine-tuned protocol-shift evaluation. Compared with zero-filled reconstruction, UNet-image-SENSE, DC-UNet, Score-Diffusion, ELF-Diff, SENSE-VarNet, and MoDL baselines, SA-RDM-DC achieves the highest SSIM across fastMRI acceleration factors while retaining subsecond per-slice inference and avoiding the long sampling time of iterative diffusion baselines. In pathology-aware analysis, SA-RDM-DC preserves lesion-region structural fidelity and reduces meniscus prediction instability. Its self-auditing scores strongly identify high-error reconstructions on fastMRI and partially transfer as a selective-review signal under SKM-TEA protocol shift. These results support reconstruction evaluation that jointly considers image fidelity, pathology preservation, runtime, and case-specific reliability.

Qing Lyu, Jianxu Wang, Mohammad Kawas +2

Department of Radiology & Biomedical Imaging, Yale School of Medicine, New Haven, CT 06510 USA · Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180 USA

Uncertainty Quantification Image Reconstruction Accelerated MRI Reconstruction

Jul 1, 2026cs.AI

Bayesian Uncertainty Propagation for Agentic RAG Pipelines: A Proof-of-Concept Study on Multi-Hop Question Answering

Trustworthy deployment of Agentic Retrieval-Augmented Generation (RAG) systems requires mechanisms for estimating when multi-stage reasoning pipelines may fail. This paper presents an uncertainty-aware Agentic Retrieval-Augmented Generation (RAG) framework in which planner, evaluator and generator stages produce uncertainty signals derived from semantic divergence and generator self-evaluation. These signals are propagated through a Bayesian Network (BN) to estimate system-level uncertainty and provide node-level indicators of potential failure points across the workflow. The approach is evaluated on StrategyQA and HotpotQA using GPT-3.5-Turbo and GPT-4.1-Nano, with Area Under the Receiver Operating Characteristic Curve (AUROC), Area Under the Accuracy-Rejection Curve (AUARC), Expected Calibration Error (ECE), and Brier Score used to assess discrimination, selective prediction and calibration. Results show that Bayesian propagation is more effective on HotpotQA, where uncertainty accumulates across multi-hop reasoning stages, while StrategyQA exposes limitations caused by miscalibration and unreliable upstream signals. The study positions Bayesian uncertainty propagation as a promising but preliminary mechanism for monitoring Agentic RAG systems, with future validation required in industrial domains such as Offshore Wind (OSW) maintenance decision support.

Louis Donaldson, Connor Walker, Koorosh Aslansefat +1

University of Hull, Hull HU6 7RX, UK

Uncertainty Quantification Agentic RAG LLM Uncertainty Estimation Uncertainty Propagation Uncertainty Calibration

Jul 1, 2026cs.CV

Uncertainty-aware tree height change regression

Monitoring canopy height change is essential for understanding carbon sinks and forest dynamics. Remote sensing enables consistent, large-scale observations of such changes, increasingly integrated with deep learning architectures such as Geospatial Foundation Models (GFMs). However, existing methods and datasets frame the problem as binary change detection, which overlooks both the continuous nature of change, especially for vegetation, and the inherent uncertainty in labels. We present the Canopy Height Change (CHC) dataset, providing 3

\mathrm{m}

resolution continuous canopy height differences and associated spatially resolved uncertainties across 10598

\mathrm{km}^2

of northern and western Spain. The dataset is paired with a co-located time series of PlanetScope satellite imagery. Based on the dataset, we introduce the task of uncertainty-aware change regression, associated metrics and strategies for fine-tuning GFMs. Furthermore, we evaluate state-of-the-art GFMs and highlight promising directions and remaining challenges for advancing continuous canopy height change estimation.

Max Gaber, Dimitri Gominski, Jaime C. Revenga +3

Department of Geosciences and Natural Resource Management, University of Copenhagen · Department of Mathematical Sciences, University of Copenhagen · Department of Computer Science and Electrical Engineering, University of Rostock +1

Uncertainty Quantification Geospatial Foundation Models Remote Sensing Change Detection

Jun 30, 2026cs.LG

CoMet: Context and Multiplicity Decomposition for Multimodal Uncertainty Estimation

Uncertainty estimation has been a long-standing challenge in AI models; it amounts to "knowing what you don't know," and metacognition is notoriously difficult even for humans (cf. the Dunning-Kruger effect). Although it is still far from solved even in simpler classification systems, tackling it in multimodal large language models (MLLMs) is becoming increasingly important. Within MLLMs, uncertainty can stem from any of the diverse sources as well as from their relationships, and further can stem from the unbounded answers in the open-ended setting. To tackle the issues, we propose CoMet, an MLLM uncertainty estimation method by decomposing uncertainty into a context-specific term and a multiplicity-specific term. The former captures ambiguity induced by the given context (e.g., task or prompt), while the latter captures how many plausible answers determined by the context remain compatible with the given input. We train a lightweight post-hoc uncertainty module to estimate these quantities, which enables efficient uncertainty estimation without autoregressive answer generation or repeated sampling. Experiments on various open-ended multimodal benchmarks, hallucination detection, and multiple-choice visual question answering benchmarks show that CoMet consistently improves uncertainty estimation over existing baselines while remaining efficient in practice. Code is available at https://github.com/princetonvisualai/comet_uncertainty

Sanghyuk Chun, William Yang, Amaya Dharmasiri +1

Princeton University

Uncertainty Quantification Multimodal Large Language Models LLM Uncertainty Estimation Uncertainty Decomposition

Jun 30, 2026eess.SP

Von Mises Based Uncertainty Quantification for Closely Spaced Automotive Radar Targets

This work investigates uncertainty-aware deep learning approaches for direction of arrival (DOA) estimation in automotive radar, focusing on probabilistic modeling and downstream integration. A circular-statistics-based von Mises (VM) ensemble (ENS) is compared with an evidential deep learning (EDL) framework based on a normal inverse gamma formulation, yielding a Student t predictive distribution in the Euclidean domain. The ENS framework produces angular predictions parameterized by (mu, kappa), enabling interpretable uncertainty aligned with directional geometry. Performance is evaluated under in distribution and multiple out-of-distribution conditions using risk coverage and ROC or AUROC analyses. Results indicate that ENS achieves lower uncertainty under nominal conditions and exhibits stronger sensitivity to severe perturbations, whereas EDL provides smoother uncertainty variation and slightly improved ranking consistency. Importantly, the ENS representation enables direct probabilistic integration into association modules via closed form VM likelihoods, facilitating a unified detection tracking pipeline. These findings highlight a trade-off between geometric consistency and statistical generality in uncertainty-aware DOA estimation.

Vinay Kulkarni, V. V. Reddy

International Institute of Information Technology, Bengaluru, India

Evidential Deep Learning Uncertainty Quantification Direction-of-Arrival Estimation Deep Ensembles

Jun 30, 2026cs.CV

Visual Semantic Entropy: Do Vision Language Models Recognize Visual Ambiguity?

Vision-language models can produce confident answers on visually ambiguous inputs, resulting in biased predictions. Common entropy-based methods, such as Semantic Entropy (SE), rely on output diversity. Yet our analysis shows that overconfident visual embeddings suppress output diversity under stochastic decoding, causing SE to underestimate uncertainty in such cases. Recent methods instead probe output diversity through input perturbations, including textual paraphrasing or joint text-image perturbations, and show improved performance. We study these approaches and reveals that the resulting variability is often dominated by textual changes rather than visual evidence, causing uncertainty estimates to reflect prompt sensitivity rather than visual ambiguity. We therefore propose Visual Semantic Entropy (VSE), which perturbs only the image to probe nearby visual variations while keeping the text query fixed. VSE measures uncertainty by clustering generated answers into semantic prototypes and computing the mass-weighted dispersion among them. Extensive evaluation across five modern vision-language models and five diverse VQA benchmarks demonstrates that VSE effectively captures visual ambiguity, establishing a new state-of-the-art for VLM uncertainty estimation.

Ta Duc Huy, Trang Nguyen, Townim Chowdhury +5

Australian Institute for Machine Learning, Adelaide University, Australia · Flinders University, Australia

VLM Evaluation Visual Question Answering Uncertainty Estimation for VLA Models Uncertainty Quantification

Jun 30, 2026cs.LG

Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification

Diffusion models enable probabilistic super-resolution and conditional generation, but pixel-space methods are computationally expensive and learned latent spaces often lack interpretable uncertainty quantification. We introduce Patch-PODiff-ViT, a structured latent diffusion framework in which the latent space is defined by patchwise Proper Orthogonal Decomposition (POD), a fixed linear orthonormal basis over local patches, rather than learned by a nonlinear autoencoder. This yields low-dimensional, variance-ordered tokens that preserve spatial structure and enable efficient diffusion in a structured low-dimensional latent space with a Vision Transformer. Because the decoder is fixed, linear, and orthonormal, latent coefficient uncertainty can be propagated directly to physical-space predictive variance, enabling analytic propagation of predictive variance through the linear decoder without Monte Carlo estimation in pixel space. Across sea surface temperature, medical imaging, and natural images, the method achieves strong reconstruction with fewer parameters and lower memory, while producing well-calibrated spatial uncertainty that closely matches empirical ensembles.

Onkar Jadhav, Tim French, Matthew Rayson +1

School of Earth and Oceans, UWA Oceans Institute University of Western Australia Crawley, WA, Australia · School of Physics, Mathematics and Computing, Computer Science and Software Engineering University of Western Australia Crawley, WA, Australia

Diffusion Models for Image Restoration Uncertainty Quantification Latent Diffusion Models Proper Orthogonal Decomposition Image Restoration

Jun 30, 2026cs.LG

Sequential sparse Gaussian process quantile regression

Quantile regression aims to estimate the conditional quantiles of a response variable from observed data. In a Bayesian setting, Gaussian process quantile regression provides uncertainty quantification but faces significant computational challenges due to the nonconjugacy of the asymmetric Laplace likelihood and the cost of posterior inference. We develop a sparse Gaussian process framework in which the quantile function is represented through a reduced set of inducing variables and posterior inference is performed using a Laplace approximation. A decomposition of the predictive uncertainty into conditional-prior and posterior-induced variance components is then exploited to drive two complementary adaptive mechanisms: inducing-input infilling and data acquisition. These mechanisms are combined within a sequential algorithm that allocates computational effort toward the dominant source of predictive uncertainty and adaptively controls model complexity. Numerical experiments on benchmark problems demonstrate the accuracy of the Laplace approximation, the benefits of variance-based inducing-input placement, and the effectiveness of the proposed sequential enrichment strategy compared with predefined data-acquisition strategies.

Hugo Nicolas, Olivier Le Maître

PLATON, CMAP · Inria, Center for Applied Mathematics, ´Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, France · CNRS, Center for Applied Mathematics, ´Ecole polytechnique, Institut Polytechnique de Paris, Palaiseau, France

Quantile Regression Uncertainty Quantification Gaussian Processes Bayesian Experimental Design Gaussian Process Regression

Jun 29, 2026cs.LG

A Transferable Learned Temporal Prior for Transmission Reconstruction and Decision-Relevant Uncertainty in Real Outbreak Labels

Reconstructing who infected whom often relies on case timing and published transmission links. However, two important questions remain: can a temporal pattern learned from other diseases transfer to a new outbreak, and how reliable are the transmission links used as ground truth? We learned a temporal prior from eleven disease groups using logistic regression. The model was locked before any target-outbreak data were accessed and was then tested without refitting on 29 Andes virus (ANDV) parent-ranking tasks. The locked prior achieved a mean reciprocal rank (MRR) of 0.571, compared with 0.274 for the strongest fair source-trained temporal baseline (permutation p<0.001). Its Top-1 accuracy was 37.9%, compared with 13.8%. The MRR advantage remained significant unless 7-8 favorable task outcomes were reversed. We separately examined the reliability of published transmission links. Among 75 epidemiologically linked inter-host pairs from the 2022 New York City mpox outbreak, 54.67% were genomically unresolved or unsupported as direct transmission links (exact 95% CI: 42.75-66.21%). We also tested whether retaining uncertain transmission edges changed source prioritization. In ANDV and Guangdong Delta outbreak graphs, the top-5 priority sets changed, with Jaccard similarity ranging from 0.429 to 0.667. These results show that temporal information learned across diseases can provide a useful ranking signal without target-specific refitting. They also show that uncertainty in published transmission links can affect which source cases are prioritized for investigation.

Md Ahsan Karim

Department of Computer Science and Engineering, National Institute of Textile Engineering and Research (NITER) Nayarhat, Savar, Dhaka-1350, Bangladesh

Uncertainty Quantification Temporal Link Prediction Transfer Learning

Jun 29, 2026cs.AI

Propagation ofInterval Belief Structures andImprecise Copulas for~Neural Network Verification

Quantitative verification of neural networks requires reasoning about probabilities under substantial uncertainty in both input distributions and their dependence structure. In realistic settings, this information is often only partially specified, and assuming precise probabilistic models can lead to unreliable results. We propose a sound framework for quantitative verification under imprecise probabilistic information, combining interval belief structures to represent marginal uncertainty with imprecise copulas to model uncertain dependence. We develop a propagation method for imprecisely coupled interval belief structures through feed-forward neural networks. Using mixed imprecise copula volumes, we derive sound push-forward constructions through affine transformations and activation functions. The resulting output can provide guaranteed lower and upper bounds on probabilistic safety properties, valid for all probability models compatible with the specified imprecise inputs.

Francesc Pifarre-Esquerda, Eric Goubault, Sylvie Putot

LIX · LIX, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France · X-DEP-INFO

Neural Network Verification Uncertainty Quantification

Jun 28, 2026stat.ML

Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamics

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this bidirectional flow can be used as a self-supervised consistency metric for uncertainty and error estimation, which enables the model to estimate test-time uncertainty and error without access to ground truth, by comparing how closely flowing forwards and backwards in time returns to the same predicted fields. We also demonstrate this methods's potential to serve as a non-invasive plasma diagnostic, and show how adaptive feedback can be used to make the model more robust based on sparse diagnostics or limited views/measurements.

Alexander Scheinker

Los Alamos National Laboratory, Los Alamos, NM, 87545.

Uncertainty Quantification Autoregressive Diffusion Latent Diffusion Models Diffusion Models Computational Fluid Dynamics

Jun 28, 2026cs.RO

Analyzing Uncertainty in the Spatial Representation of the Kinematic Bicycle Model

Locating a vehicle and determining its orientation in an uncertain environment is a critical challenge in autonomous vehicle navigation and path planning. To address these challenges, a vehicle estimates its pose while depending on sensor data that offer noisy measurements. These uncertainties in pose quantities are expressed mathematically as a covariance matrix. The real-time computation of the covariance matrix is critical because of the non-linearity involved in the kinematic model. The challenge is thus to evaluate the evolution of the covariance matrix of a vehicle's discretized stochastic kinematics. The purpose of this study is to obtain a near-accurate evolution of the covariance matrix of the rear-wheel bicycle kinematic model under uncertainties in wheel displacement and steering angle. We used Taylor's series to linearize the nonlinear trigonometric functions and provided closed-form expectations of random variables with the required accuracy. Our analytical findings are in good agreement with those obtained from Monte-Carlo simulations. Our contribution is probably the first detailed closed-form presentation of the covariance matrix constituents of the vehicle under evaluation, which were previously reported either incorrectly or incompletely. These findings aid in identifying the potential and constraints of the discretized kinematic model as well as its stochastic analysis. The techniques presented here are useful for the simultaneous localization and odometry self-calibration of certain mobile robots and autonomous vehicles.

Shafayat Abrar, M. Zaeem Baig, Shahir Ul Islam Anzal +1

Dhanani School of Science and Engineering Habib University, Karachi 75290

Uncertainty Quantification Covariance Estimation Robot State Estimation Robot Localization

Jun 28, 2026cs.LG

Randomized neural operator for parametric PDEs with fast training and conformal uncertainty quantification

Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training. We introduce PCA--RaNN, a randomized latent neural operator that combines PCA-based dimensionality reduction with fixed random features and a closed-form least-squares readout. It recasts latent operator learning as fixed-feature linear regression, reducing training time by one to three orders of magnitude across benchmarks while maintaining competitive accuracy. We introduce an energy-matched scaling rule and a lightweight two-parameter BFGS refinement to correct suboptimal feature scales. Ensemble averaging reduces predictive variance. On Burgers, Darcy, Navier--Stokes and backward heat equation benchmarks, PCA--RaNN provides a favorable speed--accuracy trade-off against operator-learning baselines. The ensemble supports split-conformal prediction intervals, and the linear readout enables rapid online adaptation via recursive least squares without retraining hidden features. This provides an efficient, uncertainty-aware surrogate for many-query scientific workflows.

Zirui Deng, Jingbo Sun, Deyu Meng +1

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Uncertainty Quantification PDE Surrogate Modeling PDE Operator Learning Neural Operators

Jun 27, 2026stat.ML

A Bayesian latent Gaussian process framework for aerodynamic uncertainty quantification

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places

94.2-95.8\%

of its predictive samples inside the released

95\%

truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

Geoffrey Davis, Ashwin Renganathan

Undergraduate research assistant, Aerospace Engineering, The Pennsylvania State University, University Park, PA 16802 · Assistant professor, Aerospace Engineering and the Institute of Computational and Data Science (ICDS), The Pennsylvania State University, University Park, PA 16802

Uncertainty Quantification Gaussian Processes Model Calibration Gaussian Process Regression

Jun 26, 2026cs.CL

From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models

Probe-based uncertainty estimation (UE) has emerged as a prominent approach to detect hallucinations in Large Language Models (LLMs) by learning uncertainty from internal model signals. Yet, recent methods vary simultaneously across feature design, training data construction, and evaluation setting, obscuring what actually drives performance. To address this issue, we propose a factorised study of probe-based UE under matched conditions. Our results show that raw hidden states and attention features are difficult to outperform in-domain. However, under distribution shift, structured and compressed features are more robust, suggesting that in-domain performance alone is insufficient to measure progress. Furthermore, prompting and label construction significantly affect probe behaviour. Building on these best-practice findings, we train benchmark-based pretrained probes that transfer reasonably well to open-ended factual generation, providing a stable off-the-shelf baseline. Our work encourages more deployment-oriented evaluation of probe-based uncertainty estimators. The code repository is available at https://github.com/ponhvoan/ProbeUE.

Ponhvoan Srey, Xiaobao Wu, Cong-Duy Nguyen +3

Nanyang Technological University · Shanghai Jiao Tong University · VinUniversity +1

Uncertainty Quantification Hallucination in Language Models LLM Uncertainty Estimation Language Model Robustness Language Model Probing

Jun 25, 2026stat.ML

Ribbon: Scalable Approximation and Robust Uncertainty Quantification

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for modern machine-learning models because they require posterior sampling or repeated model refitting. We introduce Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty. Ribbon replaces repeated refitting with an influence-function linearization around a single fitted model, preserving the first-order data-reweighting structure of the Bayesian bootstrap while requiring only post-hoc linear algebra. Ribbon approximates the Bayesian-bootstrap or weighted-likelihood-bootstrap refitting target. With a general concentration parameter, Ribbon gives a calibrated Dirichlet-reweighting family whose uncertainty scale can be tuned on validation data. We show that Ribbon is asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification and recovers the robust sandwich covariance under misspecification. Across synthetic regression, MNIST classification, and California Housing benchmarks, Ribbon provides competitive predictive performance and improved calibration in several settings while avoiding repeated model retraining.

Graham Gibson, John Tipton, Kellin Rumsey +1

Uncertainty Quantification Uncertainty Calibration

Jun 25, 2026cs.LG

Uncertainty quantification via conformal prediction in data assimilation

Quantifying the evolution of uncertainty is critical to both probabilistic forecasting and data assimilation in numerical weather prediction. In this study, we investigate the applicability of conformal prediction (CP), a recent machine learning (ML) method, to quantify uncertainty in a controlled, idealized setting. We use the one dimensional modified shallow water model, designed to mimic the convective process. CP provides a set of possible outcomes with a chosen confidence level. Here, we compare and evaluate the average empirical coverage, the average interval length, miss low, miss high and average interval score loss (AISL) for three variants of CP, namely a) Standard CP, b) Normalized CP and c) Conformalized Quantile Regression. We further compare these CP-based uncertainty estimates with traditional ensemble-based measures such as standard deviation intervals and ensemble spread. In addition, we investigate the integration of CP-derived uncertainty within the data assimilation cycle through CP perturbations. Our results highlight the strengths and limitations of each approach, providing insight into the effectiveness of CP to complement common ensemble-based uncertainty quantification in simplified atmospheric models.

Catherine George, Alireza Javanmardi, Tijana Janjić +1

Mathematisches Institut für Maschinelles Lernen und Data Science, Katholische Universität Eichstätt-Ingolstadt · Institute of Informatics, LMU Munich, Munich Center for Machine Learning (MCML)

Uncertainty Quantification Data Assimilation Conformal Prediction

Jun 25, 2026cs.LG

Decision-Aligned Evaluation of Uncertainty Quantification

Uncertainty estimates in machine learning are typically evaluated using generic metrics such as the negative log-likelihood and expected calibration error, yet good performance on such metrics does not necessarily imply high utility in downstream decisions. We introduce decision-alignment, a criterion that reveals which evaluation metrics meaningfully align with downstream utilities. Applying this framework, we show that many widely used uncertainty metrics are either misaligned with common decision problems or encode pathological prior beliefs about the downstream task. We then propose prior-weighted utility metrics, a special class of proper scoring rules that provides decision-aligned uncertainty evaluation. Across benchmark experiments and real-world case studies, our metrics consistently align with realized decision utility, while conventional metrics do not. Our results surface flaws in the current UQ evaluation protocol and offer a principled extension of existing metrics toward decision-relevant UQ evaluation.

Annika Schneider, Tommy Rochussen, Joshua Stiller +1

1Technical University of Munich · 2Helmholtz AI · 3MCML +3

Uncertainty Quantification Proper Scoring Rules Decision-Making under Uncertainty

Jun 24, 2026cs.AI

Estimating Uncertainty in Classifier Performance with Applications to Large Language Models and Nested Data

Researchers increasingly use text classification--supervised models or large language models--to measure constructs from natural language, providing metrics such as recall and precision as evidence of their validity. Yet, though these metrics are point estimates subject to sampling variation, measures of uncertainty are inconsistently reported alongside them. Further, when they are reported, they are often estimated with methods that are not appropriate when relevant labelled datasets are small or performance is high. To increase and improve confidence interval reporting in the field, this paper evaluates confidence interval methods for performance metrics under conditions typical of social science text classification: small to moderate sample sizes, infrequent constructs, and texts nested within individuals. Across simulations, default methods such as the Wald interval and the basic percentile bootstrap are the least accurate, with coverage sometimes far below the nominal 95% level. Accuracy is improved with the use of Agresti-Coull, Wilson, Clopper-Pearson, and a novel pseudo-count regularized bootstrap (which is particularly relevant to the calculation of F1). When texts are nested within individuals, we demonstrate that adjustment for both effective N and the appropriate degrees of freedom is necessary for producing accurate analytic intervals. Among bootstrap intervals, the hierarchical bootstrap is more accurate than the cluster bootstrap when individuals produce a moderate number of texts but overly conservative when individuals produce only a few. By providing guidance to the field on appropriate interval estimation, we aim to improve the transparency of machine learning applications, and to encourage greater attention to the validation sample size at the design stage.

Kylie Anglin

Department of Educational Psychology, Neag School of Education, University of Connecticut

LLM Evaluation Confidence Region Estimation Uncertainty Quantification Automated Evaluation

Jun 24, 2026cs.AI

Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes

Markov decision processes (MDPs) are a classic model of decision making under uncertainty, exhibiting both non-deterministic choice as well as probabilistic uncertainty. Traditionally, exact knowledge of the underlying probabilities is assumed. However, this often is unrealistic, e.g.\ when modelling cyber-physical systems or biological processes. Here, statistical methods provide a way towards obtaining meaningful guarantees. The classical approach is to gather samples in the MDP, use these to draw statistical conclusions about the transition probabilities, and from there obtain bounds on the true value; then, if these bounds are too broad, repeat. However, existing implementations of this approach are either subtly incorrect or sub-optimal, and quite often both. We present several \emph{confidence sequences}, which are specifically designed for such \enquote{online} settings, implement all of them in an efficient tool, and show their practical applicability. In particular, we show that they outperform classical \enquote{union-bound} style approaches, and overall our implementation requires 50x less samples on average than previous state of the art.

Konstantin Kueffner, Tobias Meggendorfer, Maximilian Weininger +1

Institute of Science and Technology Austria, Klosterneuburg, Austria · Lancaster University Leipzig, Leipzig, Germany · Ruhr-University Bochum, Bochum, Germany +1

Markov Decision Processes Uncertainty Quantification Markov Models Formal Verification

Jun 24, 2026cs.LG

Uncertainty Quantification for Computer-Use Agents: A Benchmark across Vision-Language Models and GUI Grounding Datasets

Computer-use agents turn vision-language model (VLM) predictions into executable GUI clicks, so reliable uncertainty estimates are essential for rejection, calibration, miss-severity ranking, and spatial safety regions. Yet evidence on post-hoc uncertainty quantification (UQ) for these agents is fragmented across isolated model and dataset pairs, leaving it unclear whether UQ rankings stay stable when the agent, benchmark, or observable interface changes. We present Argus, a cross-regime benchmark for post-hoc UQ in single-step executable GUI grounding: a 27-method open-weight matrix over 4 VLM agents and 4 datasets, plus an 8-method closed-source matrix across 3 frontier vendors where logits, hidden states, and attention maps are unavailable. Evaluated methods span logit-based scores, sampling and consistency measures, hidden-state and density estimators (Mahalanobis, SAPLMA), attention-based scores, P(True) and verbalised-confidence prompting, and split-conformal prediction. The main finding is selective transfer: UQ rankings are stable across datasets for a fixed model, but degrade across model classes and observable interfaces. Hidden-state and density methods are the most stable open-weight family, while CoCoA-1MCA, Focus, sampling-based scores, and verbalised self-assessment win in specific regimes. Within-model ranking transfer is strong (Spearman rho up to 0.969), but cross-tier transfer to closed-source vendors averages only +0.08, so closed-source UQ should be reranked on the target rather than extrapolated. Conformal click regions show score-level discrimination is not enough for deployment: locally weighted disks shrink radii by 40-60% when the plug-in UQ is calibrated, but coverage degrades under calibration-test or interface mismatch. We release per-item records, calibration/test splits, UQ scores, and analysis scripts for regime-aware UQ selection in GUI agents.

Divake Kumar, Sina Tayebati, Devashri Naik +5

University of Illinois Chicago · Intel Labs · Capital One AI Labs

Computer-Use Agent Benchmarks Uncertainty Quantification Computer-Use Agents GUI Grounding Conformal Prediction AI Agent Benchmarks+1

Jun 23, 2026cs.LG

Efficient Analytic Uncertainty Quantification for Multi-Modal Regression

Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning. Existing UQ methods for regression tasks mainly operate under the assumption that the conditional label marginal satisfies single-peak parametric models, e.g., Gaussians, where the negative log-likelihood function simplifies to the mean square error. However, such single-peak assumptions fail in regression tasks featuring multi-modal distributions. On the other hand, semi-parametric methods which achieve strong regression performance for multi-modal distributions often lack efficient quantification on their prediction variances. In this work, we extend UQ techniques based on Variational Bayesian Inference (VBI) to two widely used semi-parametric regression models that yield histogram-like reconstructions of the conditional label densities: Quantile Regression (QR) and Classification Restoration (CR). Our approach introduces a unified, distribution-agnostic framework that simultaneously achieves accurate estimation of complex conditional distributions and highly efficient UQ. Theoretically, our method is grounded in novel formulations of QR and CR within the VBI framework, yielding analytic Evidence Lower Bounds (ELBO) to streamline training and a closed-form or analytically approximated predictive density for efficient inference. Empirically, we evaluate our methods on three large-scale regression benchmarks with multi-modal label distributions. Our framework outperforms state-of-the-art multi-modal regression baselines, and even matches predictive performance of computationally expensive ensemble models. Furthermore, by leveraging epistemic uncertainty estimation, our approach enables highly data-efficient active learning strategies.

Kun Jin, James Harrison, Jiawei Li +8

1Google · 2Google DeepMind

Quantile Regression Uncertainty Quantification Variational Inference

Jun 22, 2026cs.CV

UECP: Uncertainty-Enhanced Collaborative Perception

Collaborative perception serves as a pivotal solution to enhance the perception capability of individual agents in autonomous driving, where a core challenge lies in seeking reliable evidence to quantify and weight the contribution of each participating agent. Existing methods typically rely on a confidence map, which is co-trained with the detection head, but it is inherently correlated with the detection results and thus fails to provide unbiased physical evidence. Furthermore, how to deeply integrate evidence into the cooperative fusion process remains an open question. To address these issues, this paper first proposes an uncertainty map, a physically grounded and unambiguous metric for evaluating perception quality. This map is directly supervised by real-time sensor signals, i.e., LiDAR point density, ensuring decoupling from detection noise and thereby providing physical scenario-aware evidence for weighting agent contribution. Based on this map, we develop the Uncertainty-Enhanced Collaborative Perception (UECP) framework, centered on the Uncertainty-Aware Pyramid Fusion (UAPF) module. UAPF uses a coarse-to-fine strategy, with two key components: Uncertainty-Weighted Downsampling (UWD) for high-fidelity feature preservation, and Uncertainty-Guided Residual Fusion (UGRF) to reinforce ego features, suppressing noise and ensuring robust fusion. Extensive experiments on real-world datasets show UECP outperforms state-of-the-art methods in effectiveness and robustness by embedding the uncertainty map into fusion. Code will be publicly available.

Kang Yang, Tianci Bu, Peng Wang +3

Renmin University of China, Beijing, China · College of Systems Engineering, National University of Defense Technology, Changsha, China · Intelligent Shipping Center, China Waterborne Transport Research Institute, Beijing, China

Uncertainty Quantification Autonomous Driving Perception Multi-Scale Feature Fusion Cooperative Perception

Jun 22, 2026cs.AI

The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models

Recent advancements in Large Language Models (LLMs) have enabled sophisticated reasoning and content generation, yet their inherent stochasticity poses significant challenges for ensuring predictive credibility. While traditional uncertainty taxonomy paradigms, such as the dichotomy of aleatoric and epistemic uncertainties, provide conceptual foundations, they often fail to capture the multi-component and multi-stage nature of LLM generation and struggle to evaluate the effectiveness of various Uncertainty Quantification (UQ) methods. In this paper, we propose a granular uncertainty taxonomy that systematically attributes LLM uncertainty into input-level, parameter-level, token-level, and decoding-process sources. Correspondingly, we categorize existing UQ methods into Bayesian, ensemble, consensus-based, and single-pass approaches. Furthermore, we introduce a comprehensive evaluation framework covering diverse generation settings and metrics. We empirically evaluate 21 typical UQ methods across three prominent LLM families, including Qwen3, Llama 3.2, and DeepSeek-V3, on benchmarks such as TriviaQA, GSM8K, and HumanEval. Our experimental results demonstrate that (i) the effectiveness of UQ methods is sensitive to task types and generation settings; (ii) consensus-based methods, typed Deg and EigV, consistently outperform other UQ approaches; and (iii) larger model scales correlate with lower uncertainty estimates, suggesting an empirical scaling law for LLM uncertainty. This work bridges the gap between theoretical origins and practical deployment, providing a versatile diagnostic tool for systematically quantifying uncertainty in LLM applications.

Xiang-Jun Ou, Shuang Liang, Xin-Yu Hu +3

National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210063, China. · School of Intelligent Science and Technology, Nanjing University, Suzhou 215163, China.

LLM Evaluation Uncertainty Quantification LLM Uncertainty Estimation

Jun 21, 2026cs.CV

Interpretable Uncertainty Routing Separating Emotion Ambiguity from Distribution Shift in Facial Expression Recognition

Facial expression recognition (FER) is inherently ambiguous: human annotators frequently disagree, and models deployed in real environments face distribution shift. Crucially, these two conditions demand different downstream actions, as ambiguous in-distribution faces should be reported with their ambiguity whereas out-of-distribution inputs should be rejected. However, a single uncertainty score conflates the two. In this study, uncertainty decomposition into aleatoric and epistemic components for FER is investigated, and Uncertainty-Aware Routing (UAR), an inference-time routing mechanism that exploits the separation, is introduced. Specifically, aleatoric and epistemic uncertainties are obtained from a Deep Ensemble of fully fine-tuned DINOv2 models and are each validated against an independent external signal: aleatoric against human annotator disagreement, and epistemic against distribution shift induced by image corruptions. The proposed dual-validation protocol reveals that aleatoric recovers annotator disagreement with Spearman correlation 0.66 (95% CI: 0.64-0.68), and epistemic detects corruption-induced shifts, achieving average AUROC of 0.699 at the highest corruption severity. UAR retains approximately 1.8 times more ambiguous in-distribution faces than single-uncertainty routing at a matched out-of-distribution rejection rate. A strong label-distribution-learning baseline achieves comparable disagreement recovery but cannot separate ambiguity from shift and therefore cannot route, establishing that the value of decomposition lies in the separation enabling interpretable and differentiated action selection.

Keito Inoshita, Takato Ueno

Faculty of Business and Commerce, Kansai University, Suita, Japan · Data Science and AI Innovation Research Promotion Center, Shiga University, Hikone, Japan · Graduate School of Data Science, Shiga University, Hikone, Japan

Uncertainty Quantification Selective Prediction Facial Expression Recognition Aleatoric Uncertainty OOD Detection Uncertainty Decomposition+1

Jun 21, 2026cs.CV

Modular Diffusion Models for Structured Visual Recognition

Traditional supervised methods for structured visual recognition tasks -- such as object detection, segmentation, and scene graph generation -- often produce deterministic, fixed outputs, limiting their ability to capture the inherent uncertainty in complex visual scenes. As a consequence, such point estimates are unable to capture the prediction uncertainty (or multi modality) intrinsic to these problems, often arising from natural ambiguities (e.g., ambiguity in size of partially occluded objects, local ambiguity of exact segmentation boundary, etc.) as well as noise and sparsity of training data. To address this limitation, we present Modular Diffusion Models (MDMs), a simple and novel framework that learns a distribution over structured outputs for a given input image. MDMs decompose the diffusion process into distinct, task-specific modules, each focused on capturing a different aspect of the structured information space, such as object categories, spatial locations, and inter-object relationships. This modular design allows each component to be learned independently, with seamless integration at inference without additional training. Furthermore, the modularity of MDMs enables the diffusion process to easily operate over the heterogeneous output space common in many structured learning tasks (e.g., a continuous bounding boxes and discrete class labels). Experimental results over three distinct structured tasks -- object detection, instance segmentation, and scene graph generation -- highlight the benefits of our proposed framework.

Siddhesh Khandelwal, Björn Ommer, Leonid Sigal

Department of Compute Science, University of British Columbia · Vector Institute for AI · CompVis, Ludwig Maximilian University of Munich +2

Scene Graph Generation Uncertainty Quantification Instance Segmentation Object Detection Structured Prediction Diffusion Models