The paper proposes a scalable framework for uncertainty quantification and propagation in surrogate-based Bayesian inference.
problem Uncertainty in surrogate models and its impact on inference and decision-making.
method Bayesian inference methods for surrogate models with measurement data.
result Scalable framework for uncertainty quantification and propagation in surrogate models.
New method combines ODE filters and numerical quadrature to propagate model uncertainty.
problem Propagation of model uncertainty in ODE solutions with uncertain parameters.
method Combining ODE filters with numerical quadrature.
result Effective propagation of both numerical and parametric uncertainty.
Extended Kalman Filtering (EKF) can be used to propagate and quantify input uncertainty through a Deep Neural Network (DNN) assuming mild hypotheses on the input distribution. This methodology yields results comparable to existing methods of uncertainty propagation for DNNs while lowering the computational overhead con…
Proposes a method to quantify uncertainty in graph neural networks for node classification.
problem Uncertainty in graph neural networks for node classification.
method Bayesian uncertainty propagation (BUP) method embedding GNNs in a Bayesian framework.
result Demonstrates superior performance of the proposed method on benchmark datasets.
A novel method to propagate uncertainty through the soft-thresholding nonlinearity is proposed in this paper. At every layer the current distribution of the target vector is represented as a spike and slab distribution, which represents the probabilities of each variable being zero, or Gaussian-distributed. Using the p…
Unified method for input, data, and model uncertainty in neural networks.
problem Uncertainty in neural network inputs and outputs.
method Propagating uncertainty through inputs using a unified formulation.
result More stable decision boundaries with input noise, and propagation of input uncertainty to model outputs.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
problem Improving accuracy and efficiency in nonlinear uncertainty propagation.
method Preserving mean and covariance, novel heuristics for selecting splitting direction informed by initial uncertainty and nonlinear function properties.
result Improved accuracy and efficiency in uncertainty propagation compared to existing techniques.
SOLBP extends efficient inference to uncertain Bayesian networks.
problem Inference in uncertain Bayesian networks with second-order probabilities.
method Extends Loopy Belief Propagation to second-order Bayesian networks.
result Generates inferences consistent with sum-product networks, more efficient and scalable.
Motivated by the problem of computer-aided detection (CAD) of pulmonary nodules, we introduce methods to propagate and fuse uncertainty information in a multi-stage Bayesian convolutional neural network (CNN) architecture. The question we seek to answer is "can we take advantage of the model uncertainty provided by one…
A standard recipe for spoken language recognition is to apply a Gaussian back-end to i-vectors. This ignores the uncertainty in the i-vector extraction, which could be important especially for short utterances. A recent paper by Cumani, Plchot and Fer proposes a solution to propagate that uncertainty into the backend. …
A new approach estimates propagators for trading risky assets.
problem Estimating price impact kernel from static data for optimal trading.
method Nonparametric estimation of propagator using offline reinforcement learning.
result Pessimistic trading strategy optimises execution costs under uncertainty.
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.
Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for guided wave based damage localization. The performance of these techniques depend on …
Paper presents a method to accurately quantify neural network uncertainty without sampling.
problem Uncertainty quantification in neural networks for reliability and robustness.
method Sample-free moment propagation technique for mean vectors and covariance matrices.
result Analytic solution for covariance of nonlinear activation functions.
Framework for quantifying uncertainty in dynamic processes.
problem Quantifying uncertainty in dynamic stochastic processes.
method Define dynamic uncertainty sets and dynamic robust risk measures.
result Dynamic robust risk measures are time-consistent under specific uncertainty sets.
The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the …
New methods for uncertainty in neural networks with leaky ReLU activations.
problem Uncertainty in feed-forward neural networks with random input perturbations.
method Analytical expressions for PDF and moments of neural network output, linearization of leaky ReLU, Gaussian copula surrogate models.
result Accurate statistical results for large input perturbations, excellent agreement with Monte Carlo simulations.
Framework improves PV forecasting by accounting for missing data uncertainty.
problem Uncertainty from missing data in PV power data.
method Combines stochastic multiple imputation with Rubin's rule.
result Improves prediction interval calibration without sacrificing point prediction accuracy.
We propose a feed-forward inference method applicable to belief and neural networks. In a belief network, the method estimates an approximate factorized posterior of all hidden units given the input. In neural networks the method propagates uncertainty of the input through all the layers. In neural networks with inject…
Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing…
Paper uses PCE to quantify ML model and input uncertainties.
problem Accurately quantify and propagate combined uncertainties in ML predictions.
method Polynomial Chaos Expansion (PCE) for joint input and model uncertainty.
result Efficient and accurate calculation of output variability and sensitivity.
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in f…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal…
A new framework for lightweight BNNs learns heteroscedastic uncertainties efficiently.
problem Learning heteroscedastic uncertainties from BNNs for lightweight networks.
method Embedding heteroscedastic variances into BNN parameters and using moment propagation for inference.
result Improves predictive performance for lightweight BNNs without increasing parameter count.
Proposes a new deep learning model for uncertainty quantification and propagation.
problem High-dimensional uncertainty quantification and propagation problems.
method Integrates U-net with Gaussian Gated Linear Network (GGLN) to create GLU-net.
result Less complex architecture with 44% fewer parameters than existing models.
Graph Posterior Network improves uncertainty estimation for node classification in interdependent graphs.
problem Uncertainty quantification for non-independent node-level predictions in graphs.
method Derives axioms for expected predictive uncertainty, proposes Graph Posterior Network (GPN) which performs Bayesian posterior updates.
result GPN outperforms existing approaches for uncertainty estimation in semi-supervised node classification.
Bayesian model predicts crack evolution on rails with uncertainties.
problem Predicting crack evolution on railways due to complex interactions and uncertainties.
method Robust Bayesian multi-horizon approach with constraints.
result Trade-off between prediction accuracy and constraint compliance.
New method estimates traffic congestion delays using statistical causality.
problem Accurate estimation of traffic congestion delays during accidents.
method Proposes a novel time delay estimation method using lag-specific transfer entropy (TE) and Markov bootstrap techniques.
result Validated the method's efficacy using simulated and real data.
Paper introduces MCRP for estimating feature relevance uncertainty in neural networks.
problem Lack of uncertainty in feature relevance for neural network decisions.
method Monte Carlo Relevance Propagation (MCRP) method.
result Allows deeper understanding of neural networks' perception and reasoning.
Embeddings in machine learning are low-dimensional representations of complex input patterns, with the property that simple geometric operations like Euclidean distances and dot products can be used for classification and comparison tasks. The proposed meta-embeddings are special embeddings that live in more general in…
The paper develops a method to discover causal relations and predict material laws with uncertainty quantification.
problem Discovering causal relations and predicting material laws with uncertainty in civil engineering applications.
method The paper develops a causal discovery algorithm to infer causal relations among time-history data. It uses a deep neural network with dropout layers for uncertainty quantification and propagates predictions through a causal graph.
result The method accurately predicts material laws and quantifies uncertainty, as demonstrated in two numerical examples.
INNs produce interval-valued uncertainty scores for DNNs.
problem Uncertainty quantification in deep neural networks.
method Data-driven interval propagating network using interval arithmetic.
result INNs produce sensible lower and upper bounds for prediction error.
Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we…
Paper improves neural network robustness analysis for safety-critical systems.
problem Uncertainty in neural network outputs for safety-critical systems.
method Unified propagation and partition approaches to provide tighter bounds.
result Proposed algorithms give tighter bounds than existing methods for the same computation time.
Proposes DGCN with trajectory sampling for data-efficient policy search in MBRL.
problem Improving data efficiency in model-based reinforcement learning.
method Combines trajectory sampling and DGCN for uncertainty propagation in probabilistic world models.
result Improves sample-efficiency over other uncertainty propagation methods and probabilistic models.
The paper derives uncertainty quantification for ML models used in metrology.
problem Uncertainty quantification for ML models in metrology applications.
method Analytical expressions for mean and variance of model output are derived for various ML models.
result The derived expressions cover multiple ML models and are validated against Monte Carlo methods.
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the gr…
Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here we introduce methods to characterise different components of uncertainty in suc…
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
problem Efficiently propagating uncertainty in downstream Bayesian analysis without feedback.
method NeVI-Cut combines neural networks and normalizing flows for variational inference.
result NeVI-Cut achieves significant computational gains and higher accuracy than traditional methods.
We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct probabilistic representations for the system states, and put forth an adversarial …
Proposes a framework to quantify uncertainty in multi-step decision-making by LLMs.
problem Uncertainty quantification in multi-step decision-making scenarios of LLMs.
method A principled, information-theoretic framework decomposing uncertainty into internal and extrinsic components, and proposing UProp for efficient extrinsic uncertainty estimation.
result UProp significantly outperforms existing single-turn UQ baselines in multi-step decision-making benchmarks.
The shape of an object is an important characteristic for many vision problems such as segmentation, detection and tracking. Being independent of appearance, it is possible to generalize to a large range of objects from only small amounts of data. However, shapes represented as silhouette images are challenging to mode…
Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described learning". We then introduce a GP framework that solves both, the semi-described and…
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.
Favour speeds up variance estimation in BNNs, making them practical for performance-critical tasks.
problem Slow inference in Bayesian Neural Networks (BNNs) hinders their adoption.
method A fast algorithm for updating a diagonal-plus-low-rank matrix approximation under various operations.
result Favour is as fast as 2-3 inference samples but matches the performance of 10-100 samples.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
problem Incorrect independence assumption in previous work on Gaussian Process uncertainty propagation.
method Proposed a novel piecewise linear approximation to correct the independence assumption in continuous models.
result Corrected the independence assumption in Gaussian Process models for predicting trajectories.
Federated Granger causality learns reliable interactions without sharing data.
problem Uncertainty in federated Granger causality estimates.
method Closed-form covariance recursions and spectral-radius-based convergence conditions.
result Uncertainty depends only on client data statistics and is independent of model parameters.
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.