Aleatoric Uncertainty

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Aleatoric uncertainty describes variability that remains even when a model has learned the available patterns, such as measurement noise, ambiguous labels, or inherently stochastic outcomes. Researchers estimate it with predictive distributions, heteroscedastic models, and probabilistic or Bayesian methods, often separating it from epistemic uncertainty caused by limited knowledge. Evaluation commonly examines calibration, predictive intervals, proper scoring rules, and whether uncertainty tracks independent signals such as annotator disagreement or changing noise levels. A central challenge is that estimates depend on how uncertainty is defined and modeled, and separating irreducible variability from model error is not always identifiable or reliable.

Latest papers

44 papers4 papers in the last four weeks, down 20% on the four weeks before. 0.0% of all new papers.

Apr 18, 2026

Complementing Self-Consistency with Cross-Model Disagreement for Uncertainty Quantification

Large language models (LLMs) often produce confident yet incorrect responses, and uncertainty quantification is one potential solution to more robust usage. Recent works routinely rely on self-consistency to estimate aleatoric uncertainty (AU), yet this proxy collapses when models are overconfident and produce the same incorrect answer across samples. We analyze this regime and show that cross-model semantic disagreement is higher on incorrect answers precisely when AU is low. Motivated by this, we introduce an epistemic uncertainty (EU) term that operates in the black-box access setting: EU uses only generated text from a small, scale-matched ensemble and is computed as the gap between inter-model and intra-model sequence-semantic similarity. We then define total uncertainty (TU) as the sum of AU and EU. In a comprehensive study across five 7-9B instruction-tuned models and ten long-form tasks, TU improves ranking calibration and selective abstention relative to AU, and EU reliably flags confident failures where AU is low. We further characterize when EU is most useful via agreement and complementarity diagnostics.

Kimia Hamidieh, Veronika Thost, Walter Gerych +2

1MIT · MIT-IBM Watson AI Lab · 3WPI +1

Selective Prediction Confidence Estimation in Language Models LLM Reliability LLM Uncertainty Estimation Aleatoric Uncertainty Uncertainty Calibration+2

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Apr 13, 2026

Retrieval-Augmented Generation Must Move Beyond Factual Grounding to Represent Diverse Opinions

Retrieval-Augmented Generation (RAG) systems are built on an unexamined assumption - that queries have correct answers and retrieval should converge toward them. This position paper argues that this creates a factual bias where RAG systems optimize for reducing epistemic uncertainty while ignoring the aleatoric uncertainty, inherent in opinion-rich content. The consequences go beyond technical limitations- due to risk of minority voice erasure and risk of opinion manipulation. To address this, we formalize opinion-aware retrieval through uncertainty quantification and derive a unified objective using the Wasserstein distance. As an existence proof, we present Opinion-Aware RAG (O-RAG), which enriches documents with LLM-extracted, entity-linked opinion metadata before indexing. Across e-commerce seller forums and public hotel reviews, O-RAG reduces Wasserstein distance to corpus-level sentiment distributions by 18-48%, and human evaluators preferred its responses 79.2% of the time. We close with a research agenda for opinion-aware RAG.

Aditya Agrawal, Alwarappan Nakkiran, Aman Singh Thakur +2

Retrieval-Augmented Generation Aleatoric Uncertainty

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Apr 2, 2026

Enhancing the Reliability of Medical AI through Expert-guided Uncertainty Modeling

Artificial intelligence (AI) systems accelerate medical workflows and improve diagnostic accuracy in healthcare, serving as second-opinion systems. However, the unpredictability of AI errors poses a significant challenge, particularly in healthcare contexts, where mistakes can have severe consequences. A widely adopted safeguard is to pair predictions with uncertainty estimation, enabling human experts to focus on high-risk cases while streamlining routine verification. Current uncertainty estimation methods, however, remain limited, particularly in quantifying aleatoric uncertainty, which arises from data ambiguity and noise. To address this, we propose a novel approach that leverages disagreement in expert responses to generate targets for training machine learning models. These targets are used in conjunction with standard data labels to estimate two components of uncertainty separately, as given by the law of total variance, via a two-ensemble approach, as well as its lightweight variant. We validate our method on binary image classification, binary and multi-class image segmentation, and multiple-choice question answering. Our experiments demonstrate that incorporating expert knowledge can enhance uncertainty estimation quality by

9\%

50\%

depending on the task, making this source of information invaluable for the construction of risk-aware AI systems in healthcare applications.

Aleksei Khalin, Ekaterina Zaychenkova, Aleksandr Yugay +4

Kharkevich Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow, Russia · Moscow Insitute of Physics and Technology, Dolgoprudny, Russia · Skolkovo Institute of Science and Technology, Moscow, Russia +2

Aleatoric Uncertainty Uncertainty Quantification Segmentation Uncertainty Estimation Uncertainty Decomposition

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Apr 2, 2026

Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty

Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric uncertainty, must be considered. This poses a significant challenge due to heavy computational demands. Machine learning techniques are thus introduced as metamodels to alleviate this burden. However, the "black box" nature of Machine learning models underscores the necessity of avoiding overly confident predictions, particularly when data and training efforts are insufficient. This creates a need, in addition to considering the aleatoric uncertainty, of estimating the uncertainty related to the prediction confidence, i.e., epistemic uncertainty, for machine learning-based metamodels. We developed a probabilistic metamodeling technique based on a variational long short-term memory (LSTM) with augmented inputs to simultaneously capture aleatoric and epistemic uncertainties. Key random system parameters are treated as augmented inputs alongside excitation series carrying record-to-record variability to capture the full range of aleatoric uncertainty. Meanwhile, epistemic uncertainty is effectively approximated via the Monte Carlo dropout scheme. Unlike computationally expensive full Bayesian approaches, this method incurs negligible additional training costs while enabling nearly cost-free uncertainty simulation. The proposed technique is demonstrated through multiple case studies involving stochastic seismic or wind excitations. Results show that the calibrated metamodels accurately reproduce nonlinear response time histories and provide confidence bounds indicating the associated epistemic uncertainty.

Manisha Sapkota, Min Li, Bowei Li

Department of Civil, Environmental, and Construction Engineering, Texas Tech University, 2500 Broadway St, Lubbock 79409, TX, USA · Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy 12180, NY, USA · National Wind Institute, Texas Tech University, 1009 Canton Ave, Lubbock 79409, TX, USA

Surrogate Modeling Uncertainty Propagation Long Short-Term Memory Networks Epistemic Uncertainty Structural Mechanics Aleatoric Uncertainty

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Mar 28, 2026

Quantification of Credal Uncertainty: A Distance-Based Approach

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

Xabier Gonzalez-Garcia, Siu Lun Chau, Julian Rodemann +6

Dept. of Statistics, CS & Mathematics, Public Univ. of Navarre · EPIC Lab, Nanyang Technological Univ. Singapore · Rational Intelligence Lab, CISPA Helmholtz Center for Information Security +7

Uncertainty Quantification Aleatoric Uncertainty Integral Probability Metrics Uncertainty Decomposition Epistemic Uncertainty

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Mar 20, 2026

Beyond the Mean: Distribution-Aware Loss Functions for Bimodal Regression

Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue arises in scenarios where the likelihood of error inferred from learned representations follows a bimodal distribution, resulting from the coexistence of confident and ambiguous predictions. Standard regression approaches often struggle to adequately express this predictive uncertainty, as they implicitly assume unimodal Gaussian noise, leading to mean-collapse behavior in such settings. Although Mixture Density Networks (MDNs) can represent different distributions, they suffer from severe optimization instability. We propose a family of distribution-aware loss functions integrating normalized RMSE with Wasserstein and Cramér distances. When applied to standard deep regression models, our approach recovers bimodal distributions without the volatility of mixture models. Validated across four experimental stages, our results show that the proposed Wasserstein loss establishes a new Pareto efficiency frontier: matching the stability of standard regression losses like MSE in unimodal tasks while reducing Jensen-Shannon Divergence by 45% on complex bimodal datasets. Our framework strictly dominates MDNs in both fidelity and robustness, offering a reliable tool for aleatoric uncertainty estimation in trustworthy AI systems.

Abolfazl Mohammadi-Seif, Carlos Soares, Rita P. Ribeiro +1

Department of Engineering, Universitat Pompeu Fabra, Roc Boronat St., Barcelona, 08018, Barcelona, Spain. · Department of Engineering, University of Porto, Praça de Gomes Teixeira, Porto, 4099-002, Portugal. · Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal. +1

Aleatoric Uncertainty Uncertainty Quantification Robust Loss Functions

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Mar 19, 2026

Rethinking Uncertainty Quantification and Entanglement in Image Segmentation

Uncertainty quantification (UQ) is crucial in safety-critical applications such as medical image segmentation. Total uncertainty is typically decomposed into data-related aleatoric uncertainty (AU) and model-related epistemic uncertainty (EU). Many methods exist for modeling AU (such as Probabilistic UNet, Diffusion) and EU (such as ensembles, MC Dropout), but it is unclear how they interact when combined. Additionally, recent work has revealed substantial entanglement between AU and EU, undermining the interpretability and practical usefulness of the decomposition. We present a comprehensive empirical study covering a broad range of AU-EU model combinations, propose an entanglement proxy based on the relative performance of uncertainty measures, and evaluate model combinations across downstream uncertainty quantification tasks. Ensembles consistently show more favorable proxy values and superior performance. Softmax models usually beat other AU methods, except in calibration where the results are dataset-dependent. A softmax ensemble performs remarkably well on all tasks. Finally, we analyze potential sources of uncertainty entanglement and outline directions for mitigating this effect.

Jakob Lønborg Christensen, Vedrana Andersen Dahl, Morten Rieger Hannemose +2

Technical University of Denmark, DTU Compute · University of Lucerne, Faculty of Health Sciences and Medicine, Switzerland

Uncertainty Quantification Deep Ensembles Aleatoric Uncertainty Segmentation Uncertainty Estimation Uncertainty Calibration Uncertainty Decomposition+1

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Mar 11, 2026

CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice, understanding the reason behind a model's uncertainty and the type of uncertainty it represents can support risk-aware decisions, enhance user trust, and guide additional data collection. However, many existing methods only address a single type of uncertainty or require modifications and retraining of the base model, making them difficult to adopt in real-world systems. We introduce CUPID (Comprehensive Uncertainty Plug-in estImation moDel), a general-purpose module that jointly estimates aleatoric and epistemic uncertainty without modifying or retraining the base model. CUPID can be flexibly inserted into any layer of a pretrained network. It models aleatoric uncertainty through a learned Bayesian identity mapping and captures epistemic uncertainty by analyzing the model's internal responses to structured perturbations. We evaluate CUPID across a range of tasks, including classification, regression, and out-of-distribution detection. The results show that it consistently delivers competitive performance while offering layer-wise insights into the origins of uncertainty. By making uncertainty estimation modular, interpretable, and model-agnostic, CUPID supports more transparent and trustworthy AI. Related code and data are available at https://github.com/a-Fomalhaut-a/CUPID.

Xinran Xu, Xiuyi Fan

Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore · College of Computing and Data Science, Nanyang Technological University, Singapore · Centre for Medical Technologies & Innovations, National Health Group, Singapore

Uncertainty Quantification Epistemic Uncertainty Uncertainty Decomposition Aleatoric Uncertainty

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Mar 9, 2026

TRIAGE: Type-Routed Interventions via Aleatoric-Epistemic Gated Estimation in Robotic Manipulation and Adaptive Perception -- Don't Treat All Uncertainty the Same

Most uncertainty-aware robotic systems collapse prediction uncertainty into a single scalar score and use it to trigger uniform corrective responses. This aggregation obscures whether uncertainty arises from corrupted observations or from mismatch between the learned model and the true system dynamics. As a result, corrective actions may be applied to the wrong component of the closed loop, degrading performance relative to leaving the policy unchanged. We introduce a lightweight post hoc framework that decomposes uncertainty into aleatoric and epistemic components and uses these signals to regulate system responses at inference time. Aleatoric uncertainty is estimated from deviations in the observation distribution using a Mahalanobis density model, while epistemic uncertainty is detected using a noise robust forward dynamics ensemble that isolates model mismatch from measurement corruption. The two signals remain empirically near orthogonal during closed loop execution and enable type specific responses. High aleatoric uncertainty triggers observation recovery, while high epistemic uncertainty moderates control actions. The same signals also regulate adaptive perception by guiding model capacity selection during tracking inference. Experiments demonstrate consistent improvements across both control and perception tasks. In robotic manipulation, the decomposed controller improves task success from 59.4% to 80.4% under compound perturbations and outperforms a combined uncertainty baseline by up to 21.0%. In adaptive tracking inference on MOT17, uncertainty-guided model selection reduces average compute by 58.2% relative to a fixed high capacity detector while preserving detection quality within 0.4%. Code and demo videos are available at https://divake.github.io/uncertainty-decomposition/.

Divake Kumar, Sina Tayebati, Devashri Naik +4

University of Illinois at Chicago · Intel Labs

Robotic Control Uncertainty Decomposition Robotic Manipulation Epistemic Uncertainty Aleatoric Uncertainty

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Mar 1, 2026

Epistemic Gain, Aleatoric Cost: Uncertainty Decomposition in Multi-Agent Debate for Math Reasoning

Multi-Agent Debate (MAD) has shown promise in improving reasoning and reducing hallucinations, yet it remains unclear how information exchange shapes individual reasoning behavior. Empirically, MAD exhibits paradoxical phenomena, including rising accuracy with increasing token entropy and marked differences between homogeneous and heterogeneous agent combinations. In this paper, we introduce a Bayesian uncertainty analysis framework for MAD, which decomposes answer-level predictive uncertainty into epistemic uncertainty and aleatoric uncertainty, corresponding to the potential gain and cost of debate. Across multiple agent configurations, we find that effective debate depends on achieving high epistemic gain under controlled aleatoric cost. Building on this insight, we design an uncertainty-guided multi-agent reinforcement learning algorithm that encourages lower aleatoric cost and more effective epistemic information utilization. Experiments show that our approach simultaneously enhances each agent's accuracy and promotes a more productive debate process, providing an operational Bayesian perspective for understanding and improving MAD.

Dan Qiao, Binbin Chen, Fengyu Cai +7

School of Data Science, The Chinese University of Hong Kong, Shenzhen, China · ByteDance, Beijing, China · Technical University of Darmstadt, Darmstadt, Germany +2

Multi-Agent Debate Epistemic Uncertainty Aleatoric Uncertainty Multi-Agent Reinforcement Learning

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Jan 7, 2026

Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization, and the influence of measurement noise on aleatoric uncertainty. Overall, the findings highlight the capability of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management by tracking aleatoric and epistemic sources of uncertainty.

Ibai Ramirez, Jokin Alcibar, Joel Pino +2

Department of Electronics and Computer Science Mondragon University Arrasate-Mondragon, 20500, Spain · CARTIF Technology Centre Valladolid, 47151, Spain · Department of Physical Chemistry University of the Basque Country (EHU)[cs.LG] Basque Centre for Applied Mathematics (BCAM) Leioa, 20018, Spain +1

Bayesian Neural Networks Uncertainty Quantification Predictive Maintenance Physics-Informed ML Aleatoric Uncertainty Uncertainty Calibration

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Oct 29, 2025

Uncertainty Quantification for Regression: A Unified Framework based on kernel scores

Regression tasks, notably in safety-critical domains, require reliable uncertainty quantification, yet the literature remains largely classification-focused. To address this, we introduce a family of measures for total, aleatoric, and epistemic uncertainty in multivariate regression based on strictly proper kernel scores. The framework provides a principled recipe for designing new uncertainty measures whose behavior, such as tail sensitivity or out-of-distribution responsiveness, is governed by the choice of the underlying kernel, while also encompassing existing measures under a joint analysis. We prove explicit correspondences between properties of the kernel and behavior of resulting uncertainty measures, yielding concrete design guidelines for practitioners. Extensive experiments across structured regression tasks, including spatial and functional domains, demonstrate effectiveness on downstream tasks such as out-of-distribution detection and active learning, and reveal that different kernel choices lead to distinct trade-offs, offering practitioners guidance for task-specific selection.

Christopher Bülte, Yusuf Sale, Gitta Kutyniok +1

LMU Munich · 2Munich Center for Machine Learning (MCML) · 3DLR-German Aerospace Center +2

Uncertainty Quantification Aleatoric Uncertainty Uncertainty Decomposition Epistemic Uncertainty

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Jul 10, 2025

CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in a balanced manner. We propose CLEAR, a calibration method with two distinct parameters,

γ_1

and

γ_2

, to combine the two uncertainty components and improve the conditional coverage of predictive intervals for regression tasks. CLEAR is compatible with any pair of aleatoric and epistemic estimators; we show how it can be used with (i) quantile regression for aleatoric uncertainty and (ii) ensembles drawn from the Predictability-Computability-Stability (PCS) framework for epistemic uncertainty. Across 17 diverse real-world datasets, CLEAR achieves an average improvement of 28.3% and 17.5% in the interval width compared to the two individually calibrated baselines while maintaining nominal coverage. Similar improvements are observed when applying CLEAR to Deep Ensembles (epistemic) and Simultaneous Quantile Regression (aleatoric). The benefits are especially evident in scenarios dominated by high aleatoric or epistemic uncertainty. Project page: https://unco3892.github.io/clear/

Ilia Azizi, Juraj Bodik, Jakob Heiss +1

Department of Operations, HEC, University of Lausanne, Switzerland · BegooAI, Switzerland · Department of Statistics, University of California, Berkeley, USA +1

Uncertainty Quantification Aleatoric Uncertainty Uncertainty Calibration Regression Prediction Intervals Epistemic Uncertainty

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Apr 25, 2025

An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression

Uncertainty quantification is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.

Christopher Bülte, Yusuf Sale, Timo Löhr +3

1LMU Munich · 2Munich Center for Machine Learning (MCML) · 3DLR-German Aerospace Center +2

Uncertainty Quantification Aleatoric Uncertainty Epistemic Uncertainty

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