Introduces hierarchical uncertainty using U-sequences.
problem Tackles Ellsberg's paradox in multi-layer uncertainty.
method Uses category theory to construct U-sequences and endofunctors.
result Constructs a universal uncertainty space for multi-layer uncertainty.
This work provides uncertainty intervals for semantic latent variables in disentangled latent spaces.
problem Challenges in providing meaningful uncertainty quantification for semantic information in disentangled latent spaces.
method Uses quantile regression to output heuristic uncertainty intervals, calibrates these intervals to contain true latent values, and propagates them through the generator.
result Reliably communicates semantically meaningful, principled, and instance-adaptive uncertainty in image super-resolution and image completion.
Method converts neural networks to function space for better uncertainty quantification.
problem Lack of uncertainty estimates and difficulty in incorporating new data in deep neural networks.
method Dual parameterization to convert from weight space to function space, enabling sparse representation.
result Compact and principled way to capture uncertainty and incorporate new data.
Simple neural net outperforms complex uncertainty methods.
problem Reliable uncertainty estimation from deterministic models.
method A simple baseline using a single softmax neural net with residual connections and spectral normalization.
result Simple neural net outperforms DUQ and SNGP on uncertainty prediction.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
A novel double-space tensor-product RKHS framework for hybrid uncertainty sensitivity analysis.
problem Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses.
method A novel double-space tensor-product RKHS framework for sensitivity analysis under hybrid uncertainty.
result Concurrent double Möbius inversion orthogonally decomposes global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions.
UACQR improves CQR by separating aleatoric and epistemic uncertainties.
problem Ineffective CQR for problems with varying quantile regressor performance.
method Integrates aleatoric and epistemic uncertainties in CQR.
result UACQR provides stronger conditional coverage in simulated and real-world data.
The paper proves uncertainty principles on Finsler measure spaces.
problem Uncertainty principles on Finsler measure spaces.
method Analyzes Lp-uncertainty principles on Finsler measure spaces with bounded curvatures. result Sharp Lp-uncertainty principles are proven and characterized. Paper tackles uncertainties in reduced-order modeling of complex systems.
problem Model-form uncertainties in reduced-order modeling of complex systems.
method Combines Riemannian projection and retraction operators on a subset of the Stiefel manifold with an information-theoretic formulation.
result Identifies and quantifies the impact of model-form uncertainties on inferred operators.
New method calibrates neural network uncertainty for medical images.
problem Uncalibrated probabilistic outputs from deep neural networks in medical diagnosis.
method Functional space variational inference for Bayesian neural networks.
result Better calibrated uncertainty estimates at lower computational cost.
Optimizes latent space of VAEs using decoder uncertainty to generate valid objects.
problem Lack of robustness in optimizing VAE latent space for black-box properties.
method Importance sampling-based estimator of decoder epistemic uncertainty to guide optimization.
result Improves trade-off between black-box objective and validity of generated samples.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
A new method for estimating uncertainty in deep neural networks.
problem Challenges in uncertainty estimation in deep neural networks, especially with increased complexity.
method Decompose tasks into representation learning and state space model for uncertainty estimation.
result The proposed method can estimate predictive distributions on top of existing neural networks.
A method constructs a stochastic surrogate from dimensionality reduction results for high-dimensional uncertainty quantification.
problem High-dimensional uncertainty quantification with physics-based models.
method Constructs a stochastic surrogate model from dimensionality reduction results.
result Preserves convenience of sequential dimensionality reduction and Gaussian process regression while overcoming limitations.
Robust SVM optimization in Banach spaces tackles classification uncertainty.
problem Binary classification in Banach spaces with uncertainty.
method Generalization of SVM results to Banach spaces, Representer Theorem, strong duality, Nash equilibrium formulation.
result Generalization of SVM results to Banach spaces, including Representer Theorem and strong duality.
Efficiently quantifies uncertainty in DeepONets for function spaces.
problem Uncertainty quantification in deep operator networks.
method Randomized prior ensembles for frequentist inference.
result Improved robustness and accuracy, reliable uncertainty estimates, out-of-distribution detection, and model bias quantification.
BayesIMP combines multiple causal graphs to estimate average treatment effects with uncertainty.
problem Uncertainty quantification in causal inference from multiple datasets.
method Bayesian Interventional Mean Processes (BayesIMP) integrating probabilistic integration and kernel mean embeddings.
result Improvements in average treatment effect estimation over state-of-the-art methods.
F-PACOH improves meta-learners' reliability in uncertain regions.
problem Overconfident uncertainty estimates in meta-learning.
method Meta-learning priors as stochastic processes in function space, directly steering predictions towards high epistemic uncertainty.
result Significantly outperforms other meta-learners in Bayesian Optimization.
δ-CLUE generates diverse explanations for model uncertainty.
problem Lack of constraints in generating explanations for uncertainty estimates.
method Augmenting CLUE approach to provide a set of plausible explanations.
result Returns a set of diverse inputs that yield confident predictions.
Density-Regression improves deep uncertainty estimation with faster inference.
problem Efficient uncertainty estimation under distribution shifts with modern deep models.
method Leverages density function for fast inference and distance-aware feature space.
result Density-Regression achieves competitive uncertainty estimation performance.
FisherNet extends Autoencoder using Fisher information for better data reconstruction.
problem Data reconstruction accuracy and model scalability in high-dimensional latent spaces.
method Introduces FisherNet architecture that uses Fisher information to quantify and account for latent space uncertainty.
result FisherNet produces more accurate reconstructions and scales better with latent space dimensions compared to VAE.
The paper proposes a method for better uncertainty estimation in neural networks.
problem Estimating predictive uncertainty in neural networks is crucial but challenging.
method The paper proposes a function-space variational inference method to infer a posterior distribution over functions.
result The proposed method leads to state-of-the-art uncertainty estimation and predictive performance.
Unified deep sequential and state-space models for robust option pricing with uncertainty.
problem Combining robustness to noise and uncertainty measurement in option pricing models.
method Unscattered reservoir smoother (URS) integrating deep sequential and state-space models.
result URS achieves competitive forecasting accuracy and uncertainty measurement in noisy datasets.
Framework for uncertainty estimation in training parameters.
problem Estimating uncertainty in training parameters.
method Marginalizing hyperparameters as random variables, investigating various forms of marginalisation.
result Some marginalisations can reliably estimate uncertainty without extensive tuning.
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
NP-PROV separates mean and variance spaces to improve function uncertainty.
problem Neural Processes fail on out-of-domain tasks due to shared latent space uncertainty.
method Separates mean and variance into function-value-related and position-related latent spaces.
result NP-PROV achieves state-of-the-art likelihood with bounded variance in drifts.
New GP-based method improves uncertainty quantification for causal functions.
problem Challenges in quantifying uncertainty for causal effects, especially for entire functions.
method GP-based approach using inner-product of observational functions in RKHS, with tractable posterior moments and calibration.
result Improves uncertainty quantification while maintaining causal effect estimation performance.
Sharp uncertainty principle for nodal sets in singular spaces.
problem Estimating the size of nodal sets in non-smooth spaces.
method Uncertainty principle applied to eigenfunctions in metric measure spaces with synthetic Ricci curvature bounds.
result New lower bounds on nodal set sizes in non-smooth spaces.
The paper develops scalable variational inference for Bayesian neural networks under model and parameter uncertainty.
problem Combining structural and parameter uncertainties in scalable Bayesian neural networks.
method Adapted variational inference with reparametrization for model space constraints.
result Comparable accuracy with sparse inference compared to ordinary BNNs.
Study examines time-varying betas and their volatility in bank interest income and expense margins.
problem Understanding the variability of bank betas and their impact on net interest margins.
method Used state-space methods to estimate time-varying betas and conditional volatility.
result Substantial variation in interest income and expense betas, leading to varying net interest margin coefficients.
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, fac…
Framework disentangles deep feature uncertainty for efficient inference.
problem Inference-time uncertainty estimation for reliable decision-making.
method Uncertainty-Guided Inference-Time Selection framework.
result Significantly tighter prediction intervals and 60% compute reduction.
A new model improves uncertainty estimation in deep learning.
problem Deep Kernel Learning (DKL) produces unreliable uncertainty estimates.
method Proposed a bi-Lipschitz constraint to preserve distances in feature space.
result DUE model outperforms previous DKL and other methods in uncertainty quality.
This paper tackles high-dimensional uncertainty quantification with semi-supervised learning.
problem High-dimensional uncertainty quantification due to the curse of dimensionality.
method Autoencoder for dimension reduction, DFN for mapping and reconstruction, GP for surrogate modeling, semi-supervised learning for accuracy.
result The framework effectively reduces uncertainty quantification and reliability analysis for high-dimensional problems.
Mathematical foundation for phylogenetic tree uncertainty quantification.
problem Uncertainty in evolutionary relationships between species.
method Introducing the Wald space as a subset of symmetric positive definite matrices, studying its topology and structure, and proposing a new numerical method for geodesics and curvature.
result Wald space has a topology of disjoint open cubes, is contractible, and is a Whitney stratified space of type (A).
Method combines LD and Fermat Distance for neural network uncertainty.
problem Measuring uncertainty in neural network predictions.
method Statistical Depth (LD) combined with Fermat Distance.
result Effective uncertainty estimation without impacting original model performance.
As machine learning systems get widely adopted for high-stake decisions, quantifying uncertainty over predictions becomes crucial. While modern neural networks are making remarkable gains in terms of predictive accuracy, characterizing uncertainty over the parameters of these models is challenging because of the high d…
GAPA method provides efficient uncertainty quantification for pretrained networks.
problem Reliable uncertainty estimates for pretrained models are challenging.
method Post-hoc Gaussian Process Activations (GAPA) method that shifts Bayesian modeling from weights to activations.
result GAPA method provides efficient uncertainty quantification without altering the backbone's predictions.
Bayesian uncertainty quantification is flawed, according to new research.
problem Flawed interpretation of Bayesian uncertainty quantification.
method Discussion of Bayesian updating and optimization-based perspective, proposing measures of quality.
result Bayesian uncertainty quantification is not coherent with optimization-based perspective.
Framework estimates multiple plausible solutions with uncertainty measures.
problem Machine learning models need to propose multiple plausible solutions with meaningful uncertainty.
method Discrete latent variables model one-to-many mappings, allowing effective conditional probability estimation.
result Framework outperforms state-of-the-art in uncertainty estimation and is practical.
CRUDE calibrates regression uncertainty without assuming specific error distributions.
problem Uncalibrated uncertainty estimates in regression models, especially for modern predictive tasks.
method CRUDE assumes error distributions have a constant shape, shifted and scaled by predicted mean and standard deviation.
result CRUDE produces sharper, better calibrated, and more accurate uncertainty estimates than existing methods.
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological…
Data assimilation for subsurface flow using latent diffusion models shows that ensemble Kalman methods may overestimate posterior uncertainty, while Monte Carlo sampling is more reliable.
problem Data assimilation for subsurface flow
method Ensemble Kalman smoother and Markov chain Monte Carlo sampling
result Monte Carlo sampling is more reliable than ensemble Kalman methods
New methods improve uncertainty explanations for models.
problem Improving interpretation of uncertainty estimates from probabilistic models.
method Developed new methods to generate diverse and global explanations for uncertain model predictions.
result Generated diverse and global explanations for uncertain model predictions, addressing previous limitations.
Combines neural networks with variational inference for better uncertainty quantification.
problem Overconfident predictions from traditional neural networks and time-consuming Bayesian optimization.
method VIFO (Variational Inference on the Final-Layer Output) using neural networks to learn mean and variance.
result VIFO provides a good tradeoff in run time and uncertainty quantification, especially for out of distribution data.
The paper introduces algorithms for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models defined on metric spaces.
method Proposes conformal and kNN prediction algorithms for metric spaces.
result Both algorithms provide finite-sample guarantees and improve local coverage calibration.
We give explicit solutions for utility maximization of terminal wealth problem u(XT) in the presence of Knightian uncertainty in continuous time [0,T] in a complete market. We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space o…
Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confi…