Related papers: Data-driven ambiguity sets with probabilistic guar…
Despite of its importance for safe machine learning, uncertainty quantification for neural networks is far from being solved. State-of-the-art approaches to estimate neural uncertainties are often hybrid, combining parametric models with…
We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
A data-driven MPC scheme is proposed to safely control constrained stochastic linear systems using distributionally robust optimization. Distributionally robust constraints based on the Wasserstein metric are imposed to bound the state…
We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only…
We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
We study the scenario approach for solving chance-constrained optimization in time-coupled dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
Safe control of constrained linear systems under both epistemic and aleatory uncertainties is considered. The aleatory uncertainty characterizes random noises and is modeled by a probability distribution function (PDF) and the epistemic…
The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use…
We present a novel approach for the control of uncertain, linear time-invariant systems, which are perturbed by potentially unbounded, additive disturbances. We propose a \emph{doubly robust} data-driven state-feedback controller to ensure…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…