Publications associées à Distance de Wasserstein

Discrete Optimal Transport with Independent Marginals is #P-Hard

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

We study the computational complexity of the optimal transport problem that evaluates the Wasser- stein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in th ...

2023

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...

EPFL2022

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Bahar Taskesen

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

2023

COVID-19: data-driven dynamic asset allocation in times of pandemic

Anna Timonina-Farkas

The COVID-19 pandemic has demonstrated the importance and value of multi-period asset allocation strategies responding to rapid changes in market behavior. In this article, we formulate and solve a multi-stage stochastic optimization problem, choosing the ...

AMER INST MATHEMATICAL SCIENCES-AIMS2021

Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case

Valentin Hartmann

We consider the problem of finding an optimal transport plan between an absolutely continuous measure and a finitely supported measure of the same total mass when the transport cost is the unsquared Euclidean distance. We may think of this problem as close ...

SPRINGER HEIDELBERG2020

Scalable Stochastic Optimization: Scenario Reduction with Guarantees

Kilian Schindler

Stochastic optimization is a popular modeling paradigm for decision-making under uncertainty and has a wide spectrum of applications in management science, economics and engineering. However, the stochastic optimization models one faces in practice are int ...

EPFL2020

Context Mover's Distance & Barycenters: Optimal Transport of Contexts for Building Representations

Martin Jaggi, Aymeric Daphnis Kévin Dieuleveut, Sidak Pal Singh, Andreas Hug

We present a framework for building unsupervised representations of entities and their compositions, where each entity is viewed as a probability distribution rather than a vector embedding. In particular, this distribution is supported over the contexts w ...

ADDISON-WESLEY PUBL CO2020

An objective comparison of detection and segmentation algorithms for artefacts in clinical endoscopy

Georges Wagnières, Xiaokang Wang, Sharib Ali

We present a comprehensive analysis of the submissions to the first edition of the Endoscopy Artefact Detection challenge (EAD). Using crowd-sourcing, this initiative is a step towards understanding the limitations of existing state-of-the-art computer vis ...

Nature Research2020

Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

Victor Panaretos, Yoav Zemel, Valentina Masarotto

Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loeve expansion. These operators may themselves be subject to variation, for instance in contexts wh ...

2019

Procrustes Metrics and Optimal Transport for Covariance Operators

Valentina Masarotto

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019