Related papers: Minimax Robust Quickest Change Detection using Was…
This paper presents a novel distribution-agnostic Wasserstein distance-based estimation framework. The goal is to determine an optimal map combining prior estimate with measurement likelihood such that posterior estimation error optimally…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…
We consider decision-making problems involving the optimization of linear objective functions with uncertain coefficients. The probability distribution of the coefficients--which are assumed to be stochastic in nature--is unknown to the…
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 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…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
In this paper, we propose a distributionally robust safety verification method for Markov decision processes where only an ambiguous transition kernel is available instead of the precise transition kernel. We define the ambiguity set around…
This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…
Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before…
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…
This paper considers the design of a minimax test for two hypotheses where the actual probability densities of the observations are located in neighborhoods obtained by placing a bound on the relative entropy between actual and nominal…
Contaminations are a key concern in modern statistical learning, as small but systematic perturbations of all datapoints can substantially alter estimation results. Here, we study Wasserstein-$r$ contaminations ($r\ge 1$) in an $\ell_q$…
Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…
We address the computational challenge of finding the robust sequential change-point detection procedures when the pre- and post-change distributions are not completely specified. Earlier works [veeravalli 1994] and [Unnikrishnan 2011]…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…