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Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…
This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances,…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
Uncertainty estimation has been extensively studied in recent literature, which can usually be classified as aleatoric uncertainty and epistemic uncertainty. In current aleatoric uncertainty estimation frameworks, it is often neglected that…
Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…
Aleatoric (data) and epistemic (knowledge) uncertainty are textbook components of Uncertainty Quantification. Jointly estimating these components has been shown to be problematic and non-trivial. As a result, there are multiple ways to…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
The treatment of both aleatory and epistemic uncertainty by recent methods often requires an high computational effort. In this abstract, we propose a numerical sampling method allowing to lighten the computational burden of treating the…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the…
This paper addresses a significant gap in explainable AI: the necessity of interpreting epistemic uncertainty in model explanations. Although current methods mainly focus on explaining predictions, with some including uncertainty, they fail…
The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…
Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic…
Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response…
Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can…
Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…