Related papers: Efficient Distribution Estimation and Uncertainty …
Automated segmentation of BUS images is important for precise lesion delineation and tumor characterization, but is challenged by inherent artifacts and dataset inconsistencies. In this work, we evaluate the use of a modified Residual…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$. We give an exact formula…
Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…
This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called \emph{evidential deep learning} (EDL), in which a single neural network model is trained to learn a meta distribution over the…
We prove existence of strong solutions to a family of some semilinear parabolic free boundary problems by means of elliptic regularization. Existence of solutions is obtained in two steps: we first show some uniform energy estimates and…
We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior…
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…
Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…
We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
The present paper studies the fractional $p$-Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and sign-changing solutions by constructing the suitable…
Uncertainty is an essential consideration for time series forecasting tasks. In this work, we specifically focus on quantifying the uncertainty of traffic forecasting. To achieve this, we develop Deep Spatio-Temporal Uncertainty…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
In machine learning, uncertainty quantification helps assess the reliability of model predictions, which is important in high-stakes scenarios. Traditional approaches often emphasize predictive accuracy, but there is a growing focus on…
The use of deep learning for medical imaging has seen tremendous growth in the research community. One reason for the slow uptake of these systems in the clinical setting is that they are complex, opaque and tend to fail silently. Outside…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential…
Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to…