Uncertainty Quantification

Trust and ethical concerns due to the widespread deployment of opaque machine learning (ML) models motivating the need for reliable model explanations. Post-hoc model-agnostic explanation methods addresses this challenge by learning a surrogate model that approximates the behavior of the deployed black-box ML model in the locality of a sample of interest. In post-hoc scenarios, neither the underlying model parameters nor the training are available, and hence, this local neighborhood must be constructed by generating perturbed inputs in the neighborhood of the sample of interest, and its corresponding model predictions. We propose Expected Active Gain for Local Explanations (EAGLE), a post-hoc model-agnostic explanation framework that formulates perturbation selection as an information-theoretic active learning problem. By adaptively sampling perturbations that maximize the expected information gain, EAGLE efficiently learns a linear surrogate explainable model while producing feature importance scores along with the uncertainty/confidence estimates. Theoretically, we establish that cumulative information gain scales as $\mathcal{O}(d \log t)$, where $d$ is the feature dimension and $t$ represents the number of samples, and that the sample complexity grows linearly with $d$ and logarithmically with the confidence parameter $1/δ$. Empirical results on tabular and image datasets corroborate our theoretical findings and demonstrate that EAGLE improves explanation reproducibility across runs, achieves higher neighborhood stability, and improves perturbation sample quality as compared to state-of-the-art baselines such as Tilia, US-LIME, GLIME and BayesLIME.

Complex engineered systems require coordinated design choices across heterogeneous components under conflicting objectives and uncertain specifications. Monotone co-design provides a compositional framework for such problems. Performance of each subsystem is modeled with a design problem: a relation specifying what resources suffice to provide each functionality. Existing uncertain co-design models rely on interval bounds, which support worst-case reasoning but cannot represent probabilistic risk or multi-stage adaptive decisions. We develop a distributional extension of co-design that models uncertain design outcomes as distributions over design problems and supports adaptive decision processes through Markov-kernel re-parameterizations. Using quasi-measurable and quasi-universal spaces, we show that the standard co-design compositions remain compositional under this richer uncertainty, and introduce queries and observations extracting probabilistic trade-offs, including feasibility probabilities, confidence bounds, and distributions of minimal required resources. A task-driven unmanned aerial vehicle case study shows how the framework captures risk-sensitive and information-dependent design choices that interval models cannot express.

This paper develops a measure-theoretic framework establishing when and how a possibilistic representation of incomplete knowledge contracts into a probabilistic representation of intrinsic stochastic variability. Epistemic uncertainty is encoded by a possibility distribution and its dual necessity measure, defining a credal set bounding all probability measures consistent with current evidence. As evidence accumulates, the credal set contracts. The epistemic collapse condition marks the transition: the Choquet integral converges to the Lebesgue integral over the unique limiting density. We prove this rigorously (Theorem 4.5), with all assumptions explicit and a full treatment of the non-consonant case. We introduce the aggregate epistemic width W, establish its axiomatic properties, provide a canonical normalization, and give a feasible online proxy resolving a circularity in prior formulations. Section 7 develops the dynamics of epistemic contraction: evidence induces compatibility, compatibility performs falsification, posterior possibility is the min-intersection of prior possibility and compatibility, and a credibility-directed flow governs support geometry contraction. This is not belief updating. It is knowledge contraction. Probability theory is the limiting geometry of that process. The UKF and ESPF solve different problems by different mechanisms. The UKF minimizes MSE, asserts truth, and requires a valid generative model. The ESPF minimizes maximum entropy and surfaces what evidence has not ruled out. When the world is Gaussian and the model valid, both reach the same estimate by entirely different routes -- convergent optimality, not hierarchical containment. We prove this (Theorem 9.1) and compare both on a 2-day, 877-step orbital tracking scenario. Both achieve 1-meter accuracy. The UKF is accurate but epistemically silent. The ESPF is accurate and epistemically honest.

We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior distributions are assigned to the unknown model parameters. Specifically, we assume the target image is sparse in its spatial gradient and impose a total variation prior model. A Markov chain Monte Carlo (MCMC) method, based on a split-and-augmented Gibbs sampler, is then used to sample from the resulting joint posterior distribution of the unknown parameters. Experiments conducted using single- and multi-coil datasets demonstrate the superior performance of the proposed framework over optimisation-based compressed sensing algorithms. Additionally, our framework effectively quantifies uncertainty, showing strong correlation with error maps computed from reconstructed and ground-truth images.

Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters. Studies have successfully incorporated uncertainties related to external loads from natural hazards, but few have simultaneously addressed loading and parameter uncertainties within structural systems while accounting for prediction uncertainty of neural networks. To address these gaps, three metamodeling frameworks were formulated, each coupling a feature-extraction module implemented through a multi-layer perceptron (MLP), a message-passing neural network (MPNN), or an autoencoder (AE) with a long short-term memory (LSTM) network using Monte Carlo dropout and a negative log-likelihood loss. The resulting architectures (MLP-LSTM, MPNN-LSTM, and AE-LSTM) were validated on two case studies: a multi-degree-of-freedom Bouc-Wen system and a 37-story fiber-discretized nonlinear steel moment-resisting frame, both subjected to stochastic seismic excitation and structural parameter uncertainty. All three approaches achieved low prediction errors: the MLP-LSTM yielded the most accurate results for the lower-dimensional Bouc-Wen system, whereas the MPNN-LSTM and AE-LSTM provided superior performance on the more complex steel-frame model. Moreover, a consistent correlation between predictive variance and actual error confirms the suitability of these frameworks for active-learning strategies and for assessing model confidence in structural response predictions.

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situation, where direct screening or random sampling of model parameters leads to exhaustive training times and evaluations at unphysical parameter values. Our solution is to decouple uncertainty quantification from network architecture. Instead of sampling network weights, we introduce the model-parameter distribution as an input to network training via Markov chain Monte Carlo (MCMC). In this way, the surrogate achieves the same uncertainty quantification as the underlying physical model, but with substantially reduced computation time. The approach is fully agnostic with respect to the neural network choice. In our examples, we present a quantile emulator for prediction and a novel autoencoder-based ODE network emulator that can flexibly estimate different trajectory paths corresponding to different ODE model parameters. Moreover, we present a mathematical analysis that provides a transparent way to relate potential performance loss to measurable distribution mismatch.

Machine learning methods for identifying molecular structures from tandem mass spectra (MS/MS) have advanced rapidly, yet current approaches still exhibit significant error rates. In high-stakes applications such as clinical metabolomics and environmental screening, incorrect annotations can have serious consequences, making it essential to determine when a prediction can be trusted. In this work, we introduce a selective prediction framework for molecular structure retrieval from MS/MS spectra, separating low-risk predictions automatically from lower-confidence predictions. We formulate the problem within the risk-coverage tradeoff framework and systematically evaluate uncertainty quantification strategies at three levels: input-level distance in the learned representation, fingerprint-level uncertainty over predicted molecular fingerprint bits, and retrieval-level uncertainty over candidate rankings. We compare scoring functions including first-order confidence measures, aleatoric and epistemic uncertainty estimates from second-order distributions, as well as distance-based measures in the latent space. All experiments are conducted on the MassSpecGym benchmark. Our analysis reveals that while fingerprint-level uncertainty scores are poor proxies for retrieval success, retrieval-level total uncertainty provides the overall strongest rejection criterion, and first-order confidence measures are computationally inexpensive, strong baselines. We demonstrate that by applying distribution-free risk control via generalisation bounds, practitioners can specify a tolerable error rate and obtain a subset of annotations satisfying that constraint with high probability.

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.

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.

Ranked decision systems -- recommenders, ad auctions, clinical triage queues -- must decide when to intervene in ranked outputs and when to abstain. We study when confidence-based abstention monotonically improves decision quality, and when it fails. The formal conditions are simple: rank-alignment and no inversion zones. The substantive contribution is identifying why these conditions hold or fail: the distinction between structural uncertainty (missing data, e.g., cold-start) and contextual uncertainty (missing context, e.g., temporal drift). Empirically, we validate this distinction across three domains: collaborative filtering (MovieLens, 3 distribution shifts), e-commerce intent detection (RetailRocket, Criteo, Yoochoose), and clinical pathway triage (MIMIC-IV). Structural uncertainty produces near-monotonic abstention gains in all domains; structurally grounded confidence signals (observation counts) fail under contextual drift, producing as many monotonicity violations as random abstention on our MovieLens temporal split. Context-aware alternatives -- ensemble disagreement and recency features -- substantially narrow the gap (reducing violations from 3 to 1--2) but do not fully restore monotonicity, suggesting that contextual uncertainty poses qualitatively different challenges. Exception labels defined from residuals degrade substantially under distribution shift (AUC drops from 0.71 to 0.61--0.62 across three splits), providing a clean negative result against the common practice of exception-based intervention. The results provide a practical deployment diagnostic: check C1 and C2 on held-out data before deploying a confidence gate, and match the confidence signal to the dominant uncertainty type.

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.

Physics-informed neural networks (PINNs) have shown promise in addressing the ill-posed deconvolution problem in computed tomography perfusion (CTP) imaging for acute ischemic stroke assessment. However, existing PINN-based approaches remain deterministic and do not quantify uncertainty associated with violations of physics constraints, limiting reliability assessment. We propose Evidential Perfusion Physics-Informed Neural Networks (EPPINN), a framework that integrates evidential deep learning with physics-informed modeling to enable uncertainty-aware perfusion parameter estimation. EPPINN models arterial input, tissue concentration, and perfusion parameters using coordinate-based networks, and places a Normal--Inverse--Gamma distribution over the physics residual to characterize voxel-wise aleatoric and epistemic uncertainty in physics consistency without requiring Bayesian sampling or ensemble inference. The framework further incorporates physiologically constrained parameterization and stabilization strategies to promote robust per-case optimization. We evaluate EPPINN on digital phantom data, the ISLES 2018 benchmark, and a clinical cohort. On the evaluated datasets, EPPINN achieves lower normalized mean absolute error than classical deconvolution and PINN baselines, particularly under sparse temporal sampling and low signal-to-noise conditions, while providing conservative uncertainty estimates with high empirical coverage. On clinical data, EPPINN attains the highest voxel-level and case-level infarct-core detection sensitivity. These results suggest that evidential physics-informed learning can improve both accuracy and reliability of CTP analysis for time-critical stroke assessment. Source code is available at https://github.com/jhlee0619/EPPINN.

AI-powered answer engines are inherently non-deterministic: identical queries submitted at different times can produce different responses and cite different sources. Despite this stochastic behavior, current approaches to measuring domain visibility in generative search typically rely on single-run point estimates of citation share and prevalence, implicitly treating them as fixed values. This paper argues that citation visibility metrics should be treated as sample estimators of an underlying response distribution rather than fixed values. We conduct an empirical study of citation variability across three generative search platforms--Perplexity Search, OpenAI SearchGPT, and Google Gemini--using repeated sampling across three consumer product topics. Two sampling regimes are employed: daily collections over nine days and high-frequency sampling at ten-minute intervals. We show that citation distributions follow a power-law form and exhibit substantial variability across repeated samples. Bootstrap confidence intervals reveal that many apparent differences between domains fall within the noise floor of the measurement process. Distribution-wide rank stability analysis further demonstrates that citation rankings are unstable across samples, not only among top-ranked domains but throughout the frequently cited domain set. These findings demonstrate that single-run visibility metrics provide a misleadingly precise picture of domain performance in generative search. We argue that citation visibility must be reported with uncertainty estimates and provide practical guidance for sample sizes required to achieve interpretable confidence intervals.

Safe predictions are a crucial requirement for integrating predictive models into clinical decision support systems. One approach to improving trustworthiness is to enable models to express uncertainty about individual predictions. However, current machine learning models frequently lack reliable uncertainty estimation, hindering real-world deployment. This limitation is particularly evident in multimodal settings, where models must effectively integrate heterogeneous information. In this work, we propose MedCertAIn, a predictive uncertainty framework that leverages multimodal clinical data to improve model performance and reliability for in-hospital mortality risk prediction as an indicator of patient deterioration. We design data-driven priors over neural network parameters using a hybrid strategy that considers cross-modal similarity in self-supervised latent representations and modality-specific data corruptions. We train and evaluate the models with such priors using clinical time-series and chest X-ray images from the publicly available datasets MIMIC-IV and MIMIC-CXR. Our results show that MedCertAIn achieves competitive predictive performance and substantial gains in selective prediction compared with the evaluated deterministic and stochastic baselines. These findings highlight the promise of data-driven priors in advancing robust, uncertainty-aware AI tools for high-stakes clinical applications. Our implementation is publicly available at: https://github.com/jlaitue/medcertain.

End-to-end (E2E) driving has become a cornerstone of both industry deployment and academic research, offering a single learnable pipeline that maps multi-sensor inputs to actions while avoiding hand-engineered modules. However, the reliability of such pipelines strongly depends on how well they handle uncertainty: sensors are noisy, semantics can be ambiguous, and interaction with other road users is inherently stochastic. Uncertainty also appears in multiple forms: classification vs. localization, and, crucially, in both static map elements and dynamic agents. Existing E2E approaches model only static-map uncertainty, leaving planning vulnerable to overconfident and unreliable inputs. We present UniUncer, the first lightweight, unified uncertainty framework that jointly estimates and uses uncertainty for both static and dynamic scene elements inside an E2E planner. Concretely: (1) we convert deterministic heads to probabilistic Laplace regressors that output per-vertex location and scale for vectorized static and dynamic entities; (2) we introduce an uncertainty-fusion module that encodes these parameters and injects them into object/map queries to form uncertainty-aware queries; and (3) we design an uncertainty-aware gate that adaptively modulates reliance on historical inputs (ego status or temporal perception queries) based on current uncertainty levels. The design adds minimal overhead and drops throughput by only $\sim$0.5 FPS while remaining plug-and-play for common E2E backbones. On nuScenes (open-loop), UniUncer reduces average L2 trajectory error by 7%. On NavsimV2 (pseudo closed-loop), it improves overall EPDMS by 10.8% and notable stage two gains in challenging, interaction-heavy scenes. Ablations confirm that dynamic-agent uncertainty and the uncertainty-aware gate are both necessary.

Robots that share space with people need human motion predictions with reliable uncertainty, not just accurate means. This paper presents a structured multitask variational Gaussian process (GP) for probabilistic full-body human motion prediction. The model integrates one-shot prediction of the full horizon, multitask outputs that couple future time steps, a factorization into one sparse variational GP per joint-dimension pair of the rotation representation, and a continuous 6D rotation representation with forward kinematics that preserves bone lengths. Its predictive distribution is available in closed form: a Gaussian with full temporal covariance for each rotation coordinate, which downstream planners operating in rotation coordinates can use without sampling, density estimation, or forward kinematics. On Human3.6M, the model achieves lower kernel-density-estimated negative log-likelihood (KDE NLL) than Motron and DLow at every prediction step, 22-52 nats below Motron. Empirical coverage is conservative at the 50% and 80% levels and close to nominal at 95% over a 2 s horizon. The probabilistic model uses 0.24 M parameters, about seven times fewer than Motron, and a separately trained 0.35 M-parameter deterministic variant has a mean angle error 3-22% higher than Motron's. Ablations confirm the benefit of the 6D representation and show that, at a fixed training budget, factorized joint outputs outperform coupled right-arm alternatives in NLL and CRPS while using less memory. These results show that compact, structured GPs provide analytic, temporally structured uncertainty with conservative empirical coverage for robotic systems.

Deep learning (DL) has enabled impressive advances in robotic perception, yet its limited robustness and lack of interpretability hinder reliable deployment in safety critical applications. We propose a concept termed perceptive shared autonomy, in which uncertainty estimates from DL based perception are used to regulate the level of autonomy. Specifically, when the robot's perception is confident, semi-autonomous manipulation is enabled to improve performance; when uncertainty increases, control transitions to haptic teleoperation for maintaining robustness. In this way, high-performing but uninterpretable DL methods can be integrated safely into robotic systems. A key technical enabler is an uncertainty aware DL based point cloud registration approach based on the so called Neural Tangent Kernels (NTK). We evaluate perceptive shared autonomy on challenging aerial manipulation tasks through a user study of 15 participants and realization of mock-up industrial scenarios, demonstrating reliable robotic manipulation despite failures in DL based perception. The resulting system, named SPIRIT, improves both manipulation performance and system reliability. SPIRIT was selected as a finalist of a major industrial innovation award.

Data assimilation (DA) combines model forecasts and observations to estimate the optimal state of the atmosphere with its uncertainty, providing initial conditions for weather prediction and reanalyses for climate research. Yet, existing traditional and machine-learning DA methods struggle to achieve accuracy, efficiency and uncertainty quantification simultaneously. Here, we propose HLOBA (Hybrid-Ensemble Latent Observation-Background Assimilation), a three-dimensional hybrid-ensemble DA method that operates in an atmospheric latent space learned via an autoencoder (AE). HLOBA maps both model forecasts and observations into a shared latent space via the AE encoder and an end-to-end Observation-to-Latent-space mapping network (O2Lnet), respectively, and fuses them through a Bayesian update with weights inferred from time-lagged ensemble forecasts. Both idealized and real-observation experiments demonstrate that HLOBA matches dynamically constrained four-dimensional DA methods in both analysis and forecast skill, while achieving end-to-end inference-level efficiency and theoretical flexibility applies to any forecasting model. Moreover, by exploiting the error decorrelation property of latent variables, HLOBA enables element-wise uncertainty estimates for its latent analysis and propagates them to model space via the decoder. Idealized experiments show that this uncertainty highlights large-error regions and captures their seasonal variability.

Reliable navigation in cluttered environments requires perception outputs that are not only accurate but also equipped with uncertainty sets suitable for safe control. An inverse perception contract (IPC) provides such a connection by mapping perceptual estimates to sets that contain the ground truth with high confidence. Existing IPC formulations, however, instantiate uncertainty as a single ellipsoidal set and rely on deterministic trust scores to guide robot motion. Such a representation cannot capture the multi-modal and irregular structure of fine-grained perception errors, often resulting in over-conservative sets and degraded navigation performance. In this work, we introduce Gaussian Mixture-based Inverse Perception Contract (GM-IPC), which extends IPC to represent uncertainty with unions of ellipsoidal confidence sets derived from Gaussian mixture models. This design moves beyond deterministic single-set abstractions, enabling fine-grained, multi-modal, and non-convex error structures to be captured with formal guarantees. A learning framework is presented that trains GM-IPC to account for probabilistic inclusion, distribution matching, and empty-space penalties, ensuring both validity and compactness of the predicted sets. We further show that the resulting uncertainty characterizations can be leveraged in downstream planning frameworks for real-time safe navigation, enabling less conservative and more adaptive robot motion while preserving safety in a probabilistic manner.

Building reliable classifiers is a fundamental challenge for deploying machine learning in real-world applications. A reliable system should not only detect out-of-distribution (OOD) inputs but also anticipate in-distribution (ID) errors by assigning low confidence to potentially misclassified samples. Yet, most prior work treats OOD detection and failure prediction as separated problems, overlooking their closed connection. We argue that reliability requires evaluating them jointly. To this end, we propose a unified evaluation framework that integrates OOD detection and failure prediction, quantified by our new metrics DS-F1 and DS-AURC, where DS denotes double scoring functions. Experiments on the OpenOOD benchmark show that double scoring functions yield classifiers that are substantially more reliable than traditional single scoring approaches. Our analysis further reveals that OOD-based approaches provide notable gains under simple or far-OOD shifts, but only marginal benefits under more challenging near-OOD conditions. Beyond evaluation, we extend the reliable classifier SURE and introduce SURE+, a new approach that significantly improves reliability across diverse scenarios. Together, our framework, metrics, and method establish a new benchmark for trustworthy classification and offer practical guidance for deploying robust models in real-world settings. The source code is publicly available at https://github.com/Intellindust-AI-Lab/SUREPlus.

Vision-Language Models (VLMs) with their multimodal capabilities have demonstrated remarkable success in almost all domains, including education, transportation, healthcare, energy, finance, law, and retail. Nevertheless, the utilization of VLMs in healthcare applications raises crucial concerns due to the sensitivity of large-scale medical data and the trustworthiness of these models (reliability, transparency, and security). This study proposes a logit-level uncertainty quantification (UQ) framework for histopathology image analysis using VLMs to deal with these concerns. UQ is evaluated for three VLMs using metrics derived from temperature-controlled output logits. The proposed framework demonstrates a critical separation in uncertainty behavior. While VLMs show high stochastic sensitivity (cosine similarity (CS) $<0.71$ and $<0.84$, Jensen-Shannon divergence (JS) $<0.57$ and $<0.38$, and Kullback-Leibler divergence (KL) $<0.55$ and $<0.35$, respectively for mean values of VILA-M3-8B and LLaVA-Med v1.5), near-maximal temperature impacts ($Δ_T \approx 1.00$), and displaying abrupt uncertainty transitions, particularly for complex diagnostic prompts. In contrast, the pathology-specific PRISM model maintains near-deterministic behavior (mean CS $>0.90$, JS $<0.10$, KL $<0.09$) and significantly minimal temperature effects across all prompt complexities. These findings emphasize the importance of logit-level uncertainty quantification to evaluate trustworthiness in histopathology applications utilizing VLMs.

Although high-resolution mapping of pan-Arctic sea ice with reliable corresponding uncertainty is essential for operational sea ice concentration (SIC) charting, it is a difficult task due to key challenges, such as the subtle nature of ice signature features, inexact SIC labels, model uncertainty, and data heterogeneity. This study presents a novel Bayesian High-Resolution Transformer approach for 200 meter resolution pan-Arctic SIC mapping and uncertainty quantification using Sentinel-1, RADARSAT Constellation Mission (RCM), and Advanced Microwave Scanning Radiometer 2 (AMSR2) data. First, to improve small and subtle sea ice feature (e.g., cracks/leads, ponds, and ice floes) extraction, we design a novel high-resolution Transformer model with both global and local modules that can better discern the subtle differences in sea ice patterns. Second, to address low-resolution and inexact SIC labels, we design a geographically-weighted weakly supervised loss function to supervise the model at region level instead of pixel level, and to prioritize pure open water and ice pack signatures while mitigating the impact of ambiguity in the marginal ice zone (MIZ). Third, to improve uncertainty quantification, we design a Bayesian extension of the proposed Transformer model, treating its parameters as random variables to more effectively capture uncertainties. Fourth, to address data heterogeneity, we fuse three different data types (Sentinel-1, RCM, and AMSR2) at decision-level to improve both SIC mapping and uncertainty quantification. The proposed approach is evaluated under pan-Arctic minimum-extent conditions in 2021 and 2025. Results demonstrate that the proposed model achieves 0.70 overall feature detection accuracy using Sentinel-1 data, while also preserving pan-Arctic SIC patterns (Sentinel-1 R\textsuperscript{2} = 0.90 relative to the ARTIST Sea Ice product).

Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while standard neural surrogates often fail to provide accurate and efficient sensitivities for optimization. We introduce Shape-DINO, a derivative-informed neural operator framework for learning PDE solution operators on families of varying geometries, with a particular focus on accelerating PDE-constrained shape OUU. Shape-DINOs encode geometric variability through diffeomorphic mappings to a fixed reference domain and employ a derivative-informed operator learning objective that jointly learns the PDE solution and its Fréchet derivatives with respect to design variables and uncertain parameters, enabling accurate state predictions and reliable gradients for large-scale OUU. We establish a priori error bounds linking surrogate accuracy to optimization error and prove universal approximation results for multi-input reduced basis neural operators in suitable $C^1$ norms. We demonstrate efficiency and scalability on three representative shape OUU problems, including boundary design for a Poisson equation and shape design governed by steady-state Navier-Stokes exterior flows in two and three dimensions. Across these examples, Shape-DINOs produce more reliable optimization results than operator surrogates trained without derivative information. In our examples, Shape-DINOs achieve 3-8 orders-of-magnitude speedups in state and gradient evaluations. Counting training data generation, Shape-DINOs reduce necessary PDE solves by 1-2 orders-of-magnitude compared to a strictly PDE-based approach for a single OUU problem. Moreover, Shape-DINO construction costs can be amortized across many objectives and risk measures, enabling large-scale shape OUU for complex systems.

Density-based clustering is a well-established framework that defines clusters through topological or geometric features of the data-generating density, yielding flexible procedures that have proven effective on large and complex datasets. We address the problem of obtaining scalable Bayesian-style uncertainty quantification by combining density-based clustering with martingale posterior distributions. Density uncertainty is first quantified through a fully parallelized predictive resampling scheme driven by model score functions, naturally accommodating modern differentiable density estimators such as normalizing flows. Posterior samples of the clustering are then obtained by applying density-based clustering to each random density sampled from the martingale posterior, enabling inference on any clustering-related quantity. Casting the estimand as a density functional also enables a rigorous frequentist convergence analysis. We illustrate the method through applications to image and single-cell RNA sequencing data, where it recovers meaningful clustering structures, including the assignment of previously unseen data and biologically interpretable cell grouping, while running in minutes on a single GPU.

Multimodal Variational Autoencoders have emerged as a popular tool to extract effective representations from rich multimodal data. However, such models rely on fusion strategies in latent space that destroy the joint statistical structure of the multimodal data, with profound implications for generation and uncertainty quantification. In this work, we introduce Correlated Variational Autoencoders (CoVAE), a new generative architecture that captures the correlations between modalities. We test CoVAE on a number of real and synthetic data sets demonstrating both accurate cross-modal reconstruction and effective quantification of the associated uncertainties.

Detection Transformer (DETR) and its variants show strong performance on object detection, a key task for autonomous systems. However, a critical limitation of these models is that their confidence scores only reflect semantic uncertainty, failing to capture the equally important spatial uncertainty. This results in an incomplete assessment of the detection reliability. On the other hand, Deep Ensembles can tackle this by providing high-quality spatial uncertainty estimates. However, their immense memory consumption makes them impractical for real-world applications. A cheaper alternative, Monte Carlo (MC) Dropout, suffers from high latency due to the need of multiple forward passes during inference to estimate uncertainty. To address these limitations, we introduce GroupEnsemble, an efficient and effective uncertainty estimation method for DETR-like models. GroupEnsemble simultaneously predicts multiple individual detection sets by feeding additional diverse groups of object queries to the transformer decoder during inference. Each query group is transformed by the shared decoder in isolation and predicts a complete detection set for the same input. An attention mask is applied to the decoder to prevent inter-group query interactions, ensuring each group detects independently to achieve reliable ensemble-based uncertainty estimation. By leveraging the decoder's inherent parallelism, GroupEnsemble efficiently estimates uncertainty in a single forward pass without sequential repetition. We validated our method under autonomous driving scenes and common daily scenes using the Cityscapes and COCO datasets, respectively. The results show that a hybrid approach combining MC-Dropout and GroupEnsemble outperforms Deep Ensembles on several metrics at a fraction of the cost. The code is available at https://github.com/yutongy98/GroupEnsemble.

Modern e-commerce platforms employ various auction mechanisms to allocate paid slots for a given item. To scale this approach to the millions of auctions, the platforms suggest promotion tools based on the autobidding algorithms. These algorithms typically depend on the Click-Through-Rate (CTR) and Conversion-Rate (CVR) estimates provided by a pre-trained machine learning model. However, the predictions of such models are uncertain and can significantly affect the performance of the autobidding algorithm. To address this issue, we propose the DenoiseBid method, which corrects the generated CTRs and CVRs to make the resulting bids more efficient in auctions. The underlying idea of our method is to employ a Bayesian approach and replace noisy CTR or CVR estimates with those from recovered distributions. To demonstrate the performance of the proposed approach, we perform extensive experiments on the synthetic, iPinYou, and BAT datasets. To evaluate the robustness of our approach to the noise scale, we use synthetic noise and noise estimated from the predictions of the pre-trained machine learning model.

Uncertainty quantification (UQ) in deep learning regression is of wide interest, as it supports critical applications including sequential decision making and risk-sensitive tasks. In heteroskedastic regression, where the uncertainty of the target depends on the input, a common approach is to train a neural network that parameterizes the mean and the variance of the predictive distribution. Still, training deep heteroskedastic regression models poses practical challenges in the trade-off between uncertainty quantification and mean prediction, such as optimization difficulties, representation collapse, and variance overfitting. In this work we identify previously undiscussed fallacies and propose a simple and efficient procedure that addresses these challenges jointly by post-hoc fitting a variance model across the intermediate layers of a pretrained network on a hold-out dataset. We demonstrate that our method achieves on-par or state-of-the-art uncertainty quantification on several molecular graph datasets, without compromising mean prediction accuracy and remaining cheap to use at prediction time.

Millimeter-wave radar offers unique advantages in adverse weather but suffers from low spatial fidelity, severe azimuth ambiguity, and clutter-induced spurious returns. Existing methods mainly focus on improving spatial perception effectiveness via coarse-to-fine cross-modal supervision, yet often overlook the ambiguous feature-to-label mapping, which may lead to ill-posed geometric inference and pose fundamental challenges to downstream perception tasks. In this work, we propose RaUF, a spatial uncertainty field learning framework that models radar measurements through their physically grounded anisotropic properties. To resolve conflicting feature-to-label mapping, we design an anisotropic probabilistic model that learns fine-grained uncertainty. To further enhance reliability, we propose a Bidirectional Domain Attention mechanism that exploits the mutual complementarity between spatial structure and Doppler consistency, effectively suppressing spurious or multipath-induced reflections. Extensive experiments on public benchmarks and real-world datasets demonstrate that RaUF delivers highly reliable spatial detections with well-calibrated uncertainty. Moreover, downstream case studies further validate the enhanced reliability and scalability of RaUF under challenging real-world driving scenarios.

Every mechanistic circuit carries an invisible asterisk: it reflects not just the model's computation, but the analyst's choice of pruning threshold. Change that choice and the circuit changes, yet current practice treats a single pruned subgraph as ground truth with no way to distinguish robust structure from threshold artifacts. We introduce CIRCUS, which reframes circuit discovery as a problem of uncertainty over explanations. CIRCUS prunes one attribution graph under B configurations, assigns each edge an empirical inclusion frequency s(e) in [0,1] measuring how robustly it survives across the configuration family, and extracts a consensus circuit of edges present in every view. This yields a principled core/contingent/noise decomposition (analogous to posterior model-inclusion indicators in Bayesian variable selection) that separates robust structure from threshold-sensitive artifacts, with negligible overhead. On Gemma-2-2B and Llama-3.2-1B, consensus circuits are 40x smaller than the union of all configurations while retaining comparable influence-flow explanatory power, consistently outperform influence-ranked and random baselines, and are confirmed causally relevant by activation patching.