Related papers: Wasserstein Contraction of Stochastic Nonlinear Sy…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…
This paper deals with the deterministic particle method for the equation of porous media (with p = 2). We establish a convergence rate in the Wasserstein-2 distance between the approximate solution of the associated nonlinear transport…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…
We establish a general concentration result for the 1-Wasserstein distance between the empirical measure of a sequence of random variables and its expectation. Unlike standard results that rely on independence (e.g., Sanov's theorem) or…
Ranking distributions according to a stochastic order has wide applications in diverse areas. Although stochastic dominance has received much attention, convex order, particularly in general dimensions, has yet to be investigated from a…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
In contextual optimization, a decision-maker leverages contextual information, often referred to as covariates, to better resolve uncertainty and make informed decisions. In this paper, we examine the challenges of contextual…
The effects of treatments are often heterogeneous, depending on the observable characteristics, and it is necessary to exploit such heterogeneity to devise individualized treatment rules (ITRs). Existing estimation methods of such ITRs…
We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of…
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…
Distributionally robust optimization (DRO) is an effective approach for data-driven decision-making in the presence of uncertainty. Geometric uncertainty due to sampling or localized perturbations of data points is captured by Wasserstein…
This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…
Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…