Related papers: Regularized Wasserstein Means for Aligning Distrib…

Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…

Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the neural network. The design of the model is motivated by a…

We use distributionally-robust optimization for machine learning to mitigate the effect of data poisoning attacks. We provide performance guarantees for the trained model on the original data (not including the poison records) by training…

Domain generalization aims at learning a universal model that performs well on unseen target domains, incorporating knowledge from multiple source domains. In this research, we consider the scenario where different domain shifts occur among…

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…

Given multiple source domains, domain generalization aims at learning a universal model that performs well on any unseen but related target domain. In this work, we focus on the domain generalization scenario where domain shifts occur among…

This paper studies the problem of distribution matching (DM), which is a fundamental machine learning problem seeking to robustly align two probability distributions. Our approach is established on a relaxed formulation, called partial…

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…

Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this…

We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…

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…

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…

We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…

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…

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…

This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…