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With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in…
We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein…
Uncertainty quantification is essential for the reliable deployment of machine learning models to high-stakes application domains. Uncertainty quantification is all the more challenging when training distribution and test distribution are…
Robustness studies of black-box models is recognized as a necessary task for numerical models based on structural equations and predictive models learned from data. These studies must assess the model's robustness to possible…
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,…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
Deep neural networks have proven to be extremely powerful, however, they are also vulnerable to adversarial attacks which can cause hazardous incorrect predictions in safety-critical applications. Certified robustness via randomized…