Unified Bayesian framework for uncertainty quantification in mechanics.
problem Propagation of input uncertainties and inference of unknown parameters.
method Bayesian probability theory for forward and inverse problems.
result Unified theoretical framework for both forward and inverse UQ.
The semantic map calibrates uncertainty from language model probabilities.
problem Uncertainty in language model probabilities for professional decisions.
method Prespecified semantic map linking probabilities of verbal responses to probabilities of declared states.
result Language-derived probabilities outperform printed numerical probabilities and recover valid uncertainty coverage.
A new method decomposes subjective risk into epistemic and aleatoric uncertainties.
problem Uncertainty quantification in modeling decisions.
method Subjective risk decomposition using strictly proper loss.
result Recovery of classic uncertainty measures and new learning-theoretic connections.
Extends GP regression to complex Helmholtz problems, improving wavefield inference in brain elastography.
problem Infer complex Helmholtz wavefields from sparse, noisy data.
method Operator-informed Gaussian processes, realifying complex operator into real blocks, using PDE residuals and boundary traces.
result Competitive with finite-difference and neural-network methods, reconstructs brain shear curl field with high correlation.
TSCoNet forecasts correlated geophysical fields with uncertainty estimates.
problem Accurate and reliable forecasts of correlated geophysical fields across many locations.
method Two-stage CNN-LSTM coupled with Gaussian copula.
result Calibrated prediction intervals without sacrificing point accuracy.
New method predicts spatial events like hurricanes and earthquakes with uncertainty.
problem Quantifying uncertainty in natural hazard predictions.
method Representing spatial point clouds as empirical measures, constraining prediction sets to spatial data manifold, using Wasserstein distance.
result Achieves near-nominal coverage and lower energy/manifold distances compared to baselines.
Integrates neural encoders into GLMMs for multimodal data analysis.
problem Scalable Bayesian inference for GLMMs assumes low-dimensional tabular predictors and does not handle high-dimensional modalities.
method Jointly learns modality-specific neural encoders with GLMM objective, performs variance-corrected stochastic-gradient MCMC.
result Preserves interpretable fixed and random effects while scaling to large longitudinal datasets.
Paper accelerates conformal prediction by using approximate leave-one-out estimators.
problem Limited computational cost for conformal prediction.
method Incorporates approximate leave-one-out estimators to accelerate conformal prediction.
result ALO-based methods achieve comparable coverage and efficiency to exact methods but with significantly reduced runtime.
STOIC improves energy demand forecasting with reliable uncertainty estimates.
problem Accurate point forecasts alone are insufficient for energy systems; reliable uncertainty estimates are needed.
method Integrates graph-based forecasting with tabular foundation models for zero-shot calibration of spatial-temporal residuals.
result STOIC delivers more reliable and robust uncertainty estimates for complex graph-structured energy time series.
Optimizes data splitting for shorter conformal prediction intervals.
problem Minimizing prediction interval length while maintaining coverage.
method Theoretical framework for optimal data splitting in split conformal prediction.
result Analytical characterizations of length-optimal split ratios in various settings.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
Bayesian framework predicts aerodynamic uncertainty from sparse measurements.
problem Calibrating aerodynamic models with sparse and uncertain measurements.
method Bayesian latent Gaussian process for surrogate model calibration.
result Calibrated surrogate model accurately predicts aerodynamic uncertainty.
Ribbon: Scalable Approximation and Robust Uncertainty Quantification
problem Reliably quantifying predictive uncertainty for complex models
method Ribbon, a scalable approximation to Dirichlet-reweighted bootstrap uncertainty
result Asymptotically equivalent to a flat-prior Laplace approximation under correct likelihood specification, recovers robust sandwich covariance under misspecification
Decision-alignment evaluates uncertainty quantification for decision-relevant UQ
problem Evaluation of uncertainty quantification metrics
method Introduce decision-alignment
result Proper scoring rules align with decision utility
Rigorous uncertainty quantification of probabilistic AI weather forecasts with conformal prediction
problem Calibrated uncertainty quantification in probabilistic weather forecasts
method Conformal prediction
result Calibrated uncertainty at no expense to other probabilistic metrics
Score-based martingale posteriors improve uncertainty quantification in deep neural networks.
problem Uncertainty quantification in deep neural networks
method Score-based martingale posteriors
result SMPs provide a fast, deterministic way to simulate the limiting random variable.
A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems
problem Forecasting complex dynamical systems
method Kernel autonomous ODE approach based on Gaussian Processes and Quadratic Order Model Reduction
result Full model outperforms ROM methods in terms of accuracy or computational costs
Bayesian Neural ODEs improve vessel trajectory prediction with better uncertainty estimates.
problem Challenges in predicting vessel trajectories from irregular AIS data.
method Adopted a Gaussian process (GP) kernel-based prior on the vector field evaluated at measurement points, combined with probabilistic multiple shooting for long trajectories.
result Improved accuracy and uncertainty quantification in vessel trajectory predictions.
Bayesian framework for SSP problem learns optimal strategy through interactions.
problem Sequential decision-making in stochastic shortest path problems.
method Develops a Bayesian framework to learn optimal action-value function Q∗ through interactions, avoiding unrealistic assumptions. result Demonstrates data efficiency and uncertainty quantification compared to other methods.
Proposes integrating global and local entropy for more reliable LLMs.
problem Uncertainty in large language models (LLMs) leads to unreliable predictions.
method Measures global uncertainty from hidden-state matrices and local uncertainty from tokens, combining them via a multiplicative gate.
result Global-Local Uncertainty (GLU) outperforms unsupervised baselines across multiple models and benchmarks.
ProbRes calibrates probabilistic forecasts by learning volatility dynamics.
problem Quantifying risk and uncertainty in time series forecasting.
method ProbRes learns conditional mean and volatility separately, generating well-calibrated prediction intervals.
result ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.
Tabular FMs struggle with reliable uncertainty quantification.
problem Uncertainty quantification in tabular foundation models.
method Compared TabPFN and Gaussian processes (GPs) across various regression tasks.
result GP outperforms TabPFN in data-scarce settings and when kernels are good priors.
Proposes a weighted conformal approach for cluster label uncertainty.
problem Cluster label uncertainty in unlabeled data.
method Develops a conformal inference algorithm to correct label mismatch.
result Improves confidence set size in nonlinear and high-dimensional clustering.
New algorithm provides robust uncertainty quantification without parameter tuning.
problem Real-world machine learning predictors need reliable uncertainty quantification.
method Parameter-free, group-conditional online prediction algorithm.
result Achieves best group-conditional coverage guarantees.
New method improves uncertainty quantification in latent variable models.
problem Uncertainty quantification in latent variable models with SGLD-Gibbs.
method Statistical scaling limit theory for SGLD-Gibbs, proposing hyperparameter tuning.
result Explicit guidance on hyperparameter tuning for SGLD-Gibbs ensures meaningful uncertainty quantification.
New method improves uncertainty quantification for large batch sizes and misspecified models.
problem Challenges in tuning algorithms for accurate uncertainty quantification in large batch sizes and misspecified models.
method Proposes new discrete-time approximations to SGD and SGLD, proving error bounds for practical tuning.
result Quantitative, non-asymptotic error bounds for accurate predictions of covariance and autocorrelation time.
Last-layer approximation improves UQ performance without sacrificing computational efficiency.
problem Epistemic uncertainty quantification for deep neural networks.
method Comparison of full-network and last-layer linearization using theoretical and empirical approaches.
result Last-layer approximation yields comparable UQ performance with improved computational efficiency.
CROP verifies clean prefixes in reasoning traces, improving downstream repair accuracy.
problem Uncertainty in reasoning traces prevents full certification of entire responses.
method CROP selects a calibrated threshold to certify the longest prefix with low risk proxies.
result CROP improves downstream repair accuracy by preserving valid reasoning and discarding misleading suffixes.
Low-rank framework for task-specific LLM ranking from sparse comparisons.
problem Challenges in reliable task-specific ranking of LLMs under sparse, imbalanced comparisons.
method Low-rank modeling of task-by-model ability matrix, max-norm accurate estimator, task-wise top-K recovery guarantees, uncertainty quantification framework.
result Improves sample efficiency and produces tighter, better-calibrated ranking certificates.
Conf-Gen applies uncertainty quantification to generative models.
problem Uncertainty quantification for unsupervised generative models.
method Adapts CRC to generative tasks, relaxing theoretical assumptions.
result Demonstrates flexibility and correctness of AI agent outputs.
New framework models uncertainty in classification debates.
problem Weak interpretability of existing uncertainty quantification methods.
method Courtroom analogy and Mixture of Dirichlet Experts (MoDEX) model.
result MoDEX achieves state-of-the-art uncertainty quantification performance.
Enhances uncertainty estimation in neural networks using Dirichlet-based MC Dropout.
problem Deterministic predictions without uncertainty estimates in neural networks.
method Integrates Dirichlet-based framework within Monte Carlo Dropout.
result Improves quality of uncertainty estimates in deep learning models.
CASCADE improves uncertainty communication in Parkinson's disease medication management.
problem Uncertainty in clinical decision-making for Parkinson's disease patients.
method CASCADE uses a novel conformal prediction framework to adaptively scale prediction intervals based on classification uncertainty.
result CASCADE produces more efficient and robust prediction intervals for Parkinson's disease patients.
Study evaluates uncertainty in BP estimation from PPG signals under domain shift.
problem Uncertainty quantification in healthcare, especially for cuffless BP estimation.
method Compared deep ensembles, Monte Carlo dropout, and various recalibration techniques.
result Deep ensembles provide stronger robustness under domain shift.
SON learns SPDE solutions and uncertainty from noisy data.
problem Uncertainty quantification in SPDEs with unknown model uncertainties.
method Combining DeepONet and SNNs, SON models stochasticity and predicts uncertainty.
result SON accurately captures solution structure and quantifies predictive uncertainty.
A cubing strategy identifies stable hyperparameter regions for uncertainty quantification in spatial deep learning.
problem Uncertainty quantification in spatial deep learning models.
method Cubing-based diagnostic framework to recursively partition hyperparameter space and evaluate regions using scoring rules.
result Our approach produces competitive or superior predictive intervals compared to a statistical baseline model.
Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.
problem Uncertainty quantification in safety-critical settings requires conservative bounds, but existing methods often fail to compose and are overly conservative.
method Proposes a learning framework that trains neural networks to produce context-aware Gaussian overbounds with provable conservatism.
result The method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments.
New framework models epistemic uncertainty in GNNs using random sets.
problem Uncertainty in graph neural network predictions.
method Introduces a belief function (random set) approach to model epistemic uncertainty in GNNs.
result Demonstrates superior uncertainty quantification on various graph datasets.
Spatial Adapter adds structured spatial representation to frozen predictors.
problem Efficiently adding spatial structure to pre-trained models.
method Structured spatial decomposition and closed-form covariance for residual fields.
result Adapter improves spatial prediction and uncertainty quantification.
Unified taxonomy for ML uncertainty in physics, validated.
problem Uncertainty quantification in machine learning for physics.
method Unified taxonomy, principled validation tools.
result Illustrated validation tools with examples.
New bounds for kernel regression under non-Gaussian noise.
problem Uncertainty quantification for function estimates from noisy observations.
method Novel non-asymptotic probabilistic uniform error bounds for kernel-based regression.
result Proposed bounds apply to a broad class of non-Gaussian noise distributions.
New methods improve Laplace approximations for deep neural networks by selecting key parameters.
problem Improving uncertainty quantification in deep neural networks using computationally feasible approximations.
method Gradient-Laplace and Greedy-Laplace methods for selecting parameters in sub-network Laplace approximations.
result Gradient-Laplace method outperforms existing heuristic approaches and provides formal optimality guarantees.
Estimates proxy-based inference adjustments for distribution shifts.
problem Imperfect proxy data leads to biased inference.
method Empirical calibration of proxy-primary metric discrepancy as a random effect.
result Empowers inference without individual-level response data.
MissBGM uses AI and Bayesian modeling for better missing data imputation.
problem Missing data imputation in data science, especially with uncertainty quantification.
method AI-powered Bayesian generative modeling with explicit modeling of missingness mechanisms.
result MissBGM provides principled posterior uncertainty over imputations and superior performance.
PBI inference may not be calibrated if predictive model is inaccurate.
problem Uncertainty quantification in PBI may be unreliable if the predictive model is not accurate.
method Predictive Bayesian inference with a forward predictive model.
result Posterior concentration depends on the predictive model, leading to potential calibration issues.
Bayesian online learning algorithm for one-pass data, achieving frequentist validity and uncertainty quantification.
problem Theoretical limitations in Bayesian online learning, especially in the one-pass setting.
method Proposed a new Bayesian online learning algorithm with a warm-start phase for the one-pass regime, establishing convergence rates and valid uncertainty quantification.
result The sequentially updated posterior attains optimal convergence rates and valid uncertainty quantification without diverging mini-batch sample sizes.
VLM judges rank well but score poorly; task difficulty and annotation quality affect interval width.
problem VLMs as judges lack reliability indicators in multimodal evaluations.
method Conformal prediction using score-token log-probabilities.
result Evaluation uncertainty is task-dependent, affecting interval width and reliability.
Study on estimating conditional risk in machine learning.
problem Estimating expected loss of prediction models given input features.
method Analyzed in classification and regression settings, showing equivalence to standard regression. Developed theoretical insights and empirical validation.
result Conditional risk calibration is distinct from existing uncertainty quantification problems.
This paper simplifies conditional Sobol' indices calculation using PCE bases.
problem Computational inefficiency and lack of consistency in evaluating conditional Sobol' indices.
method Analytical extraction of conditional Sobol' indices via basis decomposition of PCE expansions.
result Derives closed-form expressions for conditional Sobol' indices.
CDM models counterfactual outcomes in longitudinal data with improved accuracy.
problem Predicting counterfactual outcomes in longitudinal data with complex time-dependent confounding.
method Causal Diffusion Model (CDM) using denoising diffusion architecture with relational self-attention.
result CDM outperforms state-of-the-art methods in generating full probabilistic distributions of counterfactual outcomes.
Bayesian method identifies dynamical models with uncertainty quantification.
problem Uncertainty in selecting governing equations for dynamical systems.
method Bayesian sparse identification with model averaging.
result Accurately recovers sparse interaction structures with uncertainty quantification.
Generative models help make decisions under changing data distributions.
problem Making decisions based on historical data when the actual data distribution changes.
method Flow- and score-based generative models to represent and transform distributions.
result Generative models can learn nominal uncertainty, create stressed distributions, and produce conditional distributions.
New method calibrates LLMs for safety-critical tasks with scalable Bayesian inference.
problem Overconfidence in LLMs after fine-tuning for specific tasks.
method Orthogonalized Low-Rank Adapters (PoLAR) with variational Bayesian inference.
result Scalable and well-calibrated uncertainty estimation for LLMs.
NE-GMM uses ES and GMM to improve uncertainty quantification.
problem Challenges in estimating mean and variance of complex distributions.
method Integrates Gaussian Mixture Model with Energy Score.
result NE-GMM outperforms in predictive accuracy and uncertainty quantification.
Paper proposes a new method to quantify uncertainty in machine learning models.
problem Quantifying uncertainty in multiclass classification models.
method Distance-based approach using Integral Probability Metrics (IPMs).
result Effective uncertainty measures for multiclass classification.
Generative Score Inference improves uncertainty quantification for multimodal data.
problem Accurate uncertainty quantification in multimodal learning tasks.
method Generative Score Inference (GSI) uses synthetic samples to approximate conditional score distributions.
result GSI achieves state-of-the-art performance in hallucination detection and image captioning uncertainty estimation.
Bayesian Scattering offers a simple baseline for image data uncertainty.
problem Lack of interpretable, mathematically grounded uncertainty quantification methods for image data.
method Coupling wavelet scattering transform with a simple probabilistic head.
result Bayesian Scattering provides sensible uncertainty estimates under distribution shifts.
The paper proposes a new framework for accurate uncertainty representation and propagation.
problem Inaccurate representation and propagation of uncertainty in measurement systems.
method The paper introduces a comprehensive framework using Gaussian Mixture Models (GMMs) for representing and propagating quantitative attributes in measurement systems.
result GMMs offer improved accuracy in representing and propagating measurement uncertainty compared to traditional Gaussian methods, while maintaining computational tractability.
We quantify predictive uncertainty using the posterior predictive variance.
problem Quantifying uncertainty in predictive models.
method Using the law of total variance, we generate expansions for the posterior predictive variance.
result Identify the main contributors to prediction intervals and quantify term-wise uncertainty.
Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.
problem Incomplete knowledge of physical laws from experimental data.
method Bayesian symbolic regression using Reversible Jump Markov Chain Monte Carlo.
result Uncertainty quantification in recovered model structures.