Uncertainty Calibration

Accurate delineation of the Clinical Target Volume (CTV) is essential for radiotherapy planning, yet remains time-consuming and difficult to assess, especially for complex treatments such as Total Marrow and Lymph Node Irradiation (TMLI). While deep learning-based auto-segmentation can reduce workload, safe clinical deployment requires reliable cues indicating where models may be wrong. In this work, we propose a budget-aware uncertainty-driven quality assurance (QA) framework built on nnU-Net, combining uncertainty quantification and post-hoc calibration to produce voxel-wise uncertainty maps (based on predictive entropy) that can guide targeted manual review. We compare temperature scaling (TS), deep ensembles (DE), checkpoint ensembles (CE), and test-time augmentation (TTA), evaluated both individually and in combination on TMLI as a representative use case. Reliability is assessed through ROI-masked calibration metrics and uncertainty--error alignment under realistic revision constraints, summarized as AUC over the top 0-5% most uncertain voxels. Across configurations, segmentation accuracy remains stable, whereas TS substantially improves calibration. Uncertainty-error alignment improves most with calibrated checkpoint-based inference, leading to uncertainty maps that highlight more consistently regions requiring manual edits. Overall, integrating calibration with efficient ensembling seems a promising strategy to implement a budget-aware QA workflow for radiotherapy segmentation.

To ensure safe clinical integration, deep learning models must provide more than just high accuracy; they require dependable uncertainty quantification. While current Medical Vision Transformers perform well, they frequently struggle with overconfident predictions and a lack of transparency, issues that are magnified by the noisy and imbalanced nature of clinical data. To address this, we enhanced the modified Medical Transformer (MedFormer) that incorporates prototype-based learning and uncertainty-guided routing, by utilizing a Dirichlet distribution for per-token evidential uncertainty, our framework can quantify and localize ambiguity in real-time. This uncertainty is not just an output but an active participant in the training process, filtering out unreliable feature updates. Furthermore, the use of class-specific prototypes ensures the embedding space remains structured, allowing for decisions based on visual similarity. Testing across four modalities (mammography, ultrasound, MRI, and histopathology) confirms that our approach significantly enhances model calibration, reducing expected calibration error (ECE) by up to 35%, and improves selective prediction, even when accuracy gains are modest.

Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by sampling input parameter distributions or by augmenting deterministic outputs with uncertainty representations, including distribution-free and distributional methods. However, sampling-based methods are often computationally prohibitive for real-time applications, and many existing uncertainty representations either ignore input dependence or rely on restrictive Gaussian assumptions that fail to capture asymmetry and heavy-tailed behavior. Therefore, we extend the ACCurate and Reliable Uncertainty Estimate (ACCRUE) framework to learn input-dependent, non-Gaussian uncertainty distributions, specifically two-piece Gaussian and asymmetric Laplace forms, using a neural network trained with a loss function that balances predictive accuracy and reliability. Through synthetic and real-world experiments, we show that the proposed approach captures an input-dependent uncertainty structure and improves probabilistic forecasts relative to existing methods, while maintaining flexibility to model skewed and non-Gaussian errors.

Uncertainty quantification (UQ) is essential for deploying deep learning models in safety critical applications, yet no consensus exists on which UQ method performs best across different data modalities and distribution shifts. This paper presents a comprehensive benchmark of ten widely used UQ baselines including MC Dropout, SWAG, ensemble methods, temperature scaling, energy based OOD, Mahalanobis, hyperbolic classifiers, ENN, Taylor Sensus, and split conformal prediction against a simplified yet highly effective variant of VOLTA that retains only a deep encoder, learnable prototypes, cross entropy loss, and post hoc temperature scaling. We evaluate all methods on CIFAR 10 (in distribution), CIFAR 100, SVHN, uniform noise (out of distribution), CIFAR 10 C (corruptions), and Tiny ImageNet features (tabular). VOLTA achieves competitive or superior accuracy (up to 0.864 on CIFAR 10), significantly lower expected calibration error (0.010 vs. 0.044 to 0.102 for baselines), and strong OOD detection (AUROC 0.802). Statistical testing over three random seeds shows that VOLTA matches or outperforms most baselines, with ablation studies confirming the importance of adaptive temperature and deep encoders. Our results establish VOLTA as a lightweight, deterministic, and well calibrated alternative to more complex UQ approaches.

Accurate tree height estimation is vital for ecological monitoring and biomass assessment. We apply quantile regression to existing tree height estimation models based on satellite data to incorporate uncertainty quantification. Most current approaches for tree height estimation rely on point predictions, which limits their applicability in risk-sensitive scenarios. In this work, we show that, with minor modifications of a given prediction head, existing models can be adapted to provide statistically calibrated uncertainty estimates via quantile regression. Furthermore, we demonstrate how our results correlate with known challenges in remote sensing (e.g., terrain complexity, vegetation heterogeneity), indicating that the model is less confident in more challenging conditions.

Accurate reconstruction of environmental scalar fields from sparse onboard observations is essential for autonomous vehicles engaged in aquatic monitoring. Beyond point estimates, principled uncertainty quantification is critical for active sensing strategies such as Informative Path Planning, where epistemic uncertainty drives data collection decisions. This paper compares Gaussian Processes, Monte Carlo Dropout, Deep Ensembles, and Evidential Deep Learning for simultaneous scalar field reconstruction and uncertainty decomposition under three perceptual models representative of real sensor modalities. Results show that Evidential Deep Learning achieves the best reconstruction accuracy and uncertainty calibration across all sensor configurations at the lowest inference cost, while Gaussian Processes are fundamentally limited by their stationary kernel assumption and become intractable as observation density grows. These findings support Evidential Deep Learning as the preferred method for uncertainty-aware field reconstruction in real-time autonomous vehicle deployments.

Healthcare foundation models have largely followed paradigms from natural language processing and computer vision, emphasizing large scale pretraining and deterministic representations over heterogeneous clinical data. However, clinical observations are inherently incomplete, reflecting sparse, irregular, and modality dependent measurements of an underlying physiologic state. In this work, we propose a framework for uncertainty aware foundation modeling that represents each patient not as a point embedding, but as a distribution over plausible latent states. By learning set valued representations and enforcing consistency across partial views of the same patient, the model captures what is invariantly inferable while explicitly encoding epistemic uncertainty. We integrate this formulation with multimodal encoders and scalable self supervised objectives, combining reconstruction, contrastive alignment, and distributional regularization. Across diverse clinical tasks, our approach improves predictive performance, robustness under missing data, and uncertainty calibration relative to strong baselines. These results suggest that modeling what is not observed rather than only what is constitutes a critical inductive bias for healthcare foundation models.

Monitoring deforestation-driven carbon emissions requires both spatially explicit and temporally continuous estimates of aboveground biomass density (AGBD) with calibrated uncertainty. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides reliable LIDAR-derived AGBD, but its orbital sampling causes irregular spatiotemporal coverage, and occasional operational interruptions, including a 13-month hibernation from March 2023 to April 2024, leave extended gaps in the observational record. Prior work has used machine learning approaches to fill GEDI's spatial gaps using satellite-derived features, but temporal interpolation of biomass through unobserved periods, particularly across active disturbance events, remains largely unaddressed. Moreover, standard ensemble methods for biomass mapping have been shown to produce systematically miscalibrated prediction intervals. To address these gaps, we extend the Attentive Neural Process (ANP) framework, previously applied to spatial biomass interpolation, to jointly sparse spatiotemporal settings using geospatial foundation model embeddings. We treat space and time symmetrically, empirically validating a form of space-for-time substitution in which observations from nearby locations at other times inform predictions at held-out periods. Our results demonstrate that the ANP produces well-calibrated uncertainty estimates across disturbance regimes, supporting its use in Measurement, Reporting, and Verification (MRV) applications that require reliable uncertainty quantification for forest carbon accounting.

In modern process industries, data-driven models are important tools for real-time monitoring when key performance indicators are difficult to measure directly. While accurate predictions are essential, reliable uncertainty quantification (UQ) is equally critical for safety, reliability, and decision-making, but remains a major challenge in current data-driven approaches. In this work, we introduce a diffusion-based posterior sampling framework that inherently produces well-calibrated predictive uncertainty via faithful posterior sampling, eliminating the need for post-hoc calibration. In extensive evaluations on synthetic distributions, the Raman-based phenylacetic acid soft sensor benchmark, and a real ammonia synthesis case study, our method achieves practical improvements over existing UQ techniques in both uncertainty calibration and predictive accuracy. These results highlight diffusion samplers as a principled and scalable paradigm for advancing uncertainty-aware modeling in industrial applications.

Reconstructing high-dimensional spatiotemporal fields from sparse sensor measurements is critical in a wide range of scientific applications. The SHallow REcurrent Decoder (SHRED) architecture is a recent state-of-the-art architecture that reconstructs high-quality spatial domain from hyper-sparse sensor measurement streams. An important limitation of SHRED is that in complex, data-scarce, high-frequency, or stochastic systems, portions of the spatiotemporal field must be modeled with valid uncertainty estimation. We introduce UQ-SHRED, a distributional learning framework for sparse sensing problems that provides uncertainty quantification through a neural network-based distributional regression called engression. UQ-SHRED models the uncertainty by learning the predictive distribution of the spatial state conditioned on the sensor history. By injecting stochastic noise into sensor inputs and training with an energy score loss, UQ-SHRED produces predictive distributions with minimal computational overhead, requiring only noise injection at the input and resampling through a single architecture without retraining or additional network structures. On complicated synthetic and real-life datasets including turbulent flow, atmospheric dynamics, neuroscience and astrophysics, UQ-SHRED provides a distributional approximation with well-calibrated confidence intervals. We further conduct ablation studies to understand how each model setting affects the quality of the UQ-SHRED performance, and its validity on uncertainty quantification over a set of different experimental setups.

Uncertainty estimation (UE) aims to quantify uncertainty in large language model (LLM) outputs to flag potential hallucinations and support reliable deployment. However, UE metrics often exhibit unstable performance across models and datasets, limiting their practical utility. We formalise this phenomenon as proxy failure, arising because UE metrics are derived from model behaviour rather than being explicitly grounded in factual correctness. We show that when mutual information between a UE score and correctness is low, the score's discriminability must be close to chance. To address this, we propose Truth AnChoring (TAC), a lightweight post-hoc calibration method that maps raw UE scores to truth-aligned correctness probabilities. Even with noisy and few-shot supervision, TAC continues to improve calibration, providing a practical calibration protocol. Our findings highlight the limitations of treating heuristic UE metrics as direct indicators of uncertainty about factual correctness, and position our TAC as a principled step toward more reliable uncertainty estimation for LLMs. The code repository is available at https://github.com/ponhvoan/TruthAnchor/.

A robust decision-making process must take into account uncertainty, especially when the choice involves inherent risks. Because artificial intelligence (AI) systems are increasingly integrated into decision-making workflows, managing uncertainty relies more and more on the metacognitive capabilities of these systems; i.e, their ability to assess the reliability of and regulate their own decisions. Hence, it is crucial to employ robust methods to measure the metacognitive abilities of AI. This paper is primarily a methodological contribution that highlights a key limitation of commonly used measures of AI metacognitive sensitivity--the ability to generate confidence ratings that distinguish correct from incorrect responses. We then draw attention to the meta-d' framework, a well-established approach from psychology and neuroscience designed to address this limitation. Moreover, we propose to leverage signal detection theory (SDT) to measure the ability of AIs to spontaneously regulate their decisions based on uncertainty and risk. To demonstrate the practical utility of these psychophysical frameworks, we conduct two series of experiments on three large language models (LLMs)--GPT-5, DeepSeek-V3.2-Exp, and Mistral-Medium-2508.

Quantifying predictive uncertainty is essential for real world machine learning applications, especially in scenarios requiring reliable and interpretable predictions. Many common parametric approaches rely on neural networks to estimate distribution parameters by optimizing the negative log likelihood. However, these methods often encounter challenges like training instability and mode collapse, leading to poor estimates of the mean and variance of the target output distribution. In this work, we propose the Neural Energy Gaussian Mixture Model (NE-GMM), a novel framework that integrates Gaussian Mixture Model (GMM) with Energy Score (ES) to enhance predictive uncertainty quantification. NE-GMM leverages the flexibility of GMM to capture complex multimodal distributions and leverages the robustness of ES to ensure well calibrated predictions in diverse scenarios. We theoretically prove that the hybrid loss function satisfies the properties of a strictly proper scoring rule, ensuring alignment with the true data distribution, and establish generalization error bounds, demonstrating that the model's empirical performance closely aligns with its expected performance on unseen data. Extensive experiments on both synthetic and real world datasets demonstrate the superiority of NE-GMM in terms of both predictive accuracy and uncertainty quantification.

Miscalibrated confidence scores are a practical obstacle to deploying AI in clinical settings. A model that is always overconfident offers no useful signal for deferral. We present a multi-agent framework that combines domain-specific specialist agents with Two-Phase Verification (Wu et al., 2024) and S-Score Weighted Fusion to improve both calibration and discrimination in medical multiple-choice question answering. Four specialist agents (respiratory, cardiology, neurology, gastroenterology) generate independent diagnoses using Qwen2.5-7B-Instruct. Each diagnosis undergoes a two-phase self-verification process that measures internal consistency and produces a Specialist Confidence Score (S-score). The S-scores drive a weighted fusion strategy that selects the final answer and calibrates the reported confidence. We evaluate on high-disagreement subsets of MedQA-USMLE and MedMCQA (100 and 250 questions). All results are specific to this filtered regime. On MedQA-250, the full system achieves ECE = 0.091 (74.4% reduction over the single-specialist baseline) and AUROC = 0.630 (+0.056) at 59.2% accuracy. Calibration gains of 49-74% hold across all four settings. Ablation analysis reveals that Two-Phase Verification drives ECE reduction while multi-agent reasoning drives AUROC improvement, suggesting that consistency checking and ensemble aggregation address different failure modes of LLM uncertainty. Whether the resulting confidence signal is sufficient to support clinical deferral decisions in practice remains a direction for future investigation.

Real-world time series exhibit temporally structured uncertainty: volatility clusters in turbulent regimes, dissipates in stable periods, and shifts abruptly around structural breaks. Yet many probabilistic forecasting methods estimate predictive uncertainty as an independent per-step quantity, leaving the evolution and persistence of volatility regimes under-modeled. We formalize this missing dimension as temporal uncertainty dynamics and instantiate it in the Volatility Dynamics Variational Autoencoder (VolDy-VAE), a non-autoregressive generative forecaster with a location-scale decoder. VolDy-VAE combines a location path for mean prediction with a recurrent scale path that transfers and evolves a volatility hidden state from the look-back window to the forecasting horizon, enabling temporally coherent predictive variances. This design yields an adaptive attenuation mechanism: high-variance observations receive lower influence on the location estimate while their uncertainty is preserved through explicit scale predictions. We further provide a simplified regime-switching analysis showing that, when variances are known or consistently estimated, the volatility-aware objective reduces to inverse-variance weighting, whereas MSE-based estimators remain unbiased but statistically inefficient. Experiments on nine benchmarks show that VolDy-VAE improves forecasting accuracy and uncertainty calibration over competitive probabilistic and point-forecasting baselines while maintaining low inference latency; plug-in studies further indicate that the VolDy principle can benefit GAN, Koopman VAE, and Transformer backbones. The source code is publicly available at https://github.com/wangyijunlyy/VolDy-VAE.

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.

Vision-Language-Action (VLA) models enable general-purpose robotic policies by mapping visual observations and language instructions to low-level actions, but they often lack reliable introspection. A common practice is to compute a token-level uncertainty signal and take its mean over a rollout. However, mean aggregation can dilute short-lived but safety-critical uncertainty spikes in continuous control. In particular, successful rollouts may contain localized high-entropy segments due to benign noise or non-critical micro-adjustments, while failure rollouts can appear low-entropy for most timesteps and only exhibit brief spikes near the onset of failure. We propose a unified uncertainty quantification approach for predicting rollout success versus failure that (1) uses max-based sliding window pooling to preserve transient risk signals, (2) applies motion-aware stability weighting to emphasize high-frequency action oscillations associated with unstable behaviors, and (3) performs DoF-adaptive calibration via Bayesian Optimization to prioritize kinematically critical axes. Experiments on the LIBERO benchmark show that our method substantially improves failure prediction accuracy and yields more reliable signals for failure detection, which can support downstream human-in-the-loop interventions.

Missing values are common in photovoltaic (PV) power data, yet the uncertainty they induce is not propagated into predictive distributions. We develop a framework that incorporates missing-data uncertainty into short-term PV forecasting by combining stochastic multiple imputation with Rubin's rule. The approach is model-agnostic and can be integrated with standard machine-learning predictors. Empirical results show that ignoring missing-data uncertainty leads to overly narrow prediction intervals. Accounting for this uncertainty improves interval calibration while maintaining comparable point prediction accuracy. These results demonstrate the importance of propagating imputation uncertainty in data-driven PV forecasting.

Super-resolution (SR) of satellite imagery is challenging due to the lack of paired low-/high-resolution data. Recent self-supervised SR methods overcome this limitation by exploiting the temporal redundancy in burst observations, but they lack a mechanism to quantify uncertainty in the reconstruction. In this work, we introduce a novel self-supervised loss that allows to estimate uncertainty in image super-resolution without ever accessing the ground-truth high-resolution data. We adopt a decision-theoretic perspective and show that minimizing the corresponding Bayesian risk yields the posterior mean and variance as optimal estimators. We validate our approach on a synthetic SkySat L1B dataset and demonstrate that it produces calibrated uncertainty estimates comparable to supervised methods. Our work bridges self-supervised restoration with uncertainty quantification, making a practical framework for uncertainty-aware image reconstruction.

Real-world decision-making, from tax compliance assessment to medical diagnosis, requires aggregating multiple noisy and potentially contradictory evidence sources. Existing approaches either lack explicit uncertainty quantification (neural aggregation methods) or rely on manually engineered discrete predicates (probabilistic logic frameworks), limiting scalability to unstructured data. We introduce Latent Posterior Factors (LPF), a framework that transforms Variational Autoencoder (VAE) latent posteriors into soft likelihood factors for Sum-Product Network (SPN) inference, enabling tractable probabilistic reasoning over unstructured evidence while preserving calibrated uncertainty estimates. We instantiate LPF as LPF-SPN (structured factor-based inference) and LPF-Learned (end-to-end learned aggregation), enabling a principled comparison between explicit probabilistic reasoning and learned aggregation under a shared uncertainty representation. Across eight domains (seven synthetic and the FEVER benchmark), LPF-SPN achieves high accuracy (up to 97.8%), low calibration error (ECE 1.4%), and strong probabilistic fit, substantially outperforming evidential deep learning, LLMs and graph-based baselines over 15 random seeds. Contributions: (1) A framework bridging latent uncertainty representations with structured probabilistic reasoning. (2) Dual architectures enabling controlled comparison of reasoning paradigms. (3) Reproducible training methodology with seed selection. (4) Evaluation against EDL, BERT, R-GCN, and large language model baselines. (5) Cross-domain validation. (6) Formal guarantees in a companion paper.

Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x. However, these distributions are often locally miscalibrated, especially for high-stakes tail events where accurate uncertainty quantification is most needed to establish trust in models. Local miscalibration occurs because training data often lack examples of low-frequency events. The goal of this paper is to describe a simple, yet flexible framework that, at deployment, produces interpretable diagnostics and a robust correction mechanism of predictive distributions when train examples are limited. With this goal in mind, we introduce a semiparametric version of the Local Amortized Diagnostic and Reshaping (LADaR) framework that posits a covariate-dependent parametric model for a diagnostic transport map regressed nonparametrically on inputs to describe how to correct tail probabilities across the feature space to match calibration data. These maps provide the user with local, real-time diagnostics and a reshaped predictive distribution that can be related back to physical processes in the input space. We apply these semiparametric diagnostic transport maps to short-term tropical cyclone intensity forecasting to detect evolutionary modes linked to local miscalibration in the National Hurricane Center's forecasts and improve predictions for severe weather hazards.

Deep neural networks (DNNs) have become integral to a wide range of scientific and practical applications due to their flexibility and strong predictive performance. Despite their accuracy, however, DNNs frequently exhibit poor calibration, often assigning overly confident probabilities to incorrect predictions. This limitation underscores the growing need for integrated mechanisms that provide reliable uncertainty estimation. In this article, we compare two prominent approaches for uncertainty quantification: a Bayesian approximation via Monte Carlo Dropout and the nonparametric Conformal Prediction framework. Both methods are assessed using two convolutional neural network architectures; H-CNN VGG16 and GoogLeNet, trained on the Fashion-MNIST dataset. The empirical results show that although H-CNN VGG16 attains higher predictive accuracy, it tends to exhibit pronounced overconfidence, whereas GoogLeNet yields better-calibrated uncertainty estimates. Conformal Prediction additionally demonstrates consistent validity by producing statistically guaranteed prediction sets, highlighting its practical value in high-stakes decision-making contexts. Overall, the findings emphasize the importance of evaluating model performance beyond accuracy alone and contribute to the development of more reliable and trustworthy deep learning systems.

Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions to represent the multi-modal distribution over future pedestrian positions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e. calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Control on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.

Foundation models are increasingly being deployed in contexts where understanding the uncertainty of their outputs is critical to ensuring responsible deployment. While Bayesian methods offer a principled approach to uncertainty quantification, their computational overhead renders their use impractical for training or inference at foundation model scale. State-of-the-art models achieve parameter counts in the trillions through carefully engineered sparsity including Mixture-of-Experts (MoE) layers. In this work, we demonstrate calibrated uncertainty at scale by introducing Variational Mixture-of-Experts Routing (VMoER), a structured Bayesian approach for modelling uncertainty in MoE layers. VMoER confines Bayesian inference to the expert-selection stage which is typically done by a deterministic routing network. We instantiate VMoER using two inference strategies: amortised variational inference over routing logits and inferring a temperature parameter for stochastic expert selection. Across fine-tuning tested foundation models, VMoER improves routing stability under noise by 38%, reduces calibration error by 94%, and increases out-of-distribution AUROC by 12%, while incurring less than 1% additional FLOPs. These results suggest VMoER offers a scalable path toward robust and uncertainty-aware foundation models.

The reliable operation of modern power grids requires probabilistic load forecasts with well-calibrated uncertainty estimates. However, existing deep learning models produce overconfident point predictions that fail catastrophically under extreme weather distributional shifts. This study proposes a Bayesian Transformer (BT) framework that integrates three complementary uncertainty mechanisms into a PatchTST backbone: Monte Carlo Dropout for epistemic parameter uncertainty, variational feed-forward layers with log-uniform weight priors, and stochastic attention with learnable Gaussian noise perturbations on pre-softmax logits, representing, to the best of our knowledge, the first application of Bayesian attention to probabilistic load forecasting. A seven-level multi-quantile pinball-loss prediction head and post-training isotonic regression calibration produce sharp, near-nominally covered prediction intervals. Evaluation of five grid datasets (PJM, ERCOT, ENTSO-E Germany, France, and Great Britain) augmented with NOAA covariates across 24, 48, and 168-hour horizons demonstrates state-of-the-art performance. On the primary benchmark (PJM, H=24h), BT achieves a CRPS of 0.0289, improving 7.4% over Deep Ensembles and 29.9% over the deterministic LSTM, with 90.4% PICP at the 90% nominal level and the narrowest prediction intervals (4,960 MW) among all probabilistic baselines. During heat-wave and cold snap events, BT maintained 89.6% and 90.1% PICP respectively, versus 64.7% and 67.2% for the deterministic LSTM, confirming that Bayesian epistemic uncertainty naturally widens intervals for out-of-distribution inputs. Calibration remained stable across all horizons (89.8-90.4% PICP), while ablation confirmed that each component contributed a distinct value. The calibrated outputs directly support risk-based reserve sizing, stochastic unit commitment, and demand response activation.

Financial time-series forecasting is a high-stakes problem where regime shifts and shocks make point-accurate yet overconfident models dangerous. We propose Uncertainty-Gated Generative Modeling (UGGM), which treats uncertainty as an internal control signal that gates (i) representation via gated reparameterization, (ii) propagation via similarity and confidence routing, and (iii) generation via uncertainty-controlled predictive distributions, together with uncertainty-driven regularization and calibration to curb miscalibration. Instantiated on Weak Innovation AutoEncoder (WIAE-GPF), our UG-WIAE-GPF significantly improves risk-sensitive forecasting, delivering a 63.5% MSE reduction on NYISO (0.3508 $\rightarrow$ 0.1281), with improved robustness under shock intervals (mSE: 0.2739 $\rightarrow$ 0.1748).

This study examines the role of uncertainty estimation (UE) methods in multilingual text classification under noisy and non-topical conditions. Using a complex-vs-simple sentence classification task across several languages, we evaluate a range of UE techniques against a range of metrics to assess their contribution to making more robust predictions. Results indicate that while methods relying on softmax outputs remain competitive in high-resource in-domain settings, their reliability declines in low-resource or domain-shift scenarios. In contrast, Monte Carlo dropout approaches demonstrate consistently strong performance across all languages, offering more robust calibration, stable decision thresholds, and greater discriminative power even under adverse conditions. We further demonstrate the positive impact of UE on non-topical classification: abstaining from predicting the 10% most uncertain instances increases the macro F1 score from 0.81 to 0.85 in the Readme task. By integrating UE with trustworthiness metrics, this study provides actionable insights for developing more reliable NLP systems in real-world multilingual environments. See https://github.com/Nouran-Khallaf/To-Predict-or-Not-to-Predict

Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.

In this work, we investigate uncertainty-aware neural network models for blood glucose prediction and adverse glycemic event identification in Type 1 diabetes. We consider three families of sequence models based on LSTM, GRU, and Transformer architectures, with uncertainty quantification enabled by either Monte Carlo dropout or through evidential output layers compatible with Deep Evidential Regression. Using the HUPA-UCM diabetes dataset for validation, we find that Transformer-based models equipped with evidential output heads provide the most effective uncertainty-aware framework, achieving consistently higher predictive accuracies and better-calibrated uncertainty estimates whose magnitudes significantly correlate with prediction errors. We further evaluate the clinical risk of each model using the recently proposed Diabetes Technology Society error grid, with risk categories defined by international expert consensus. Our results demonstrate the value of integrating principled uncertainty quantification into real-time machine-learning-based blood glucose prediction systems.

Robust waypoint prediction is crucial for mobile robots operating in open-world, safety-critical settings. While Imitation Learning (IL) methods have demonstrated great success in practice, they are susceptible to distribution shifts: the policy can become dangerously overconfident in unfamiliar states. In this paper, we present ELLIPSE, a method building on multivariate deep evidential regression to output waypoints and multivariate Student-t predictive distributions in a single forward pass. To reduce covariate-shift-induced overconfidence under viewpoint and pose perturbations near expert trajectories, we introduce a lightweight domain augmentation procedure that synthesizes plausible viewpoint/pose variations without collecting additional demonstrations. To improve uncertainty reliability under environment/domain shift (e.g., unseen staircases), we apply a post-hoc isotonic recalibration on probability integral transform (PIT) values so that prediction sets remain plausible during deployment. We ground the discussion and experiments in staircase waypoint prediction, where obtaining robust waypoint and uncertainty is pivotal. Extensive real world evaluations show that ELLIPSE improves both task success rate and uncertainty coverage compared to baselines.