Publications associées à Théorie du transport

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, ...

2021

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

Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

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

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

GOT: An Optimal Transport framework for Graph comparison

Pascal Frossard, Mireille El Gheche, Hermina Petric Maretic, Giovanni Chierchia

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Regularization via Mass Transportation

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

A disaggregate choice-based approach to find epsilon-equilibria of oligopolistic markets

Michel Bierlaire, Virginie Janine Camille Lurkin, Stefano Bortolomiol

We present a general framework to find epsilon-equilibrium solutions of oligopolistic markets in which demand is modeled at the disaggregate level using discrete choice models. Consumer choices are modeled according to random utility theory, and the choice ...

2019

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Théorie du transport

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

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

Forward-Backward Splitting for Optimal Transport Based Problems

Minimum energy adaptive structures – All-In-One problem formulation

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

Procrustes Metrics and Optimal Transport for Covariance Operators

Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

GOT: An Optimal Transport framework for Graph comparison

Regularization via Mass Transportation

A disaggregate choice-based approach to find epsilon-equilibria of oligopolistic markets

Graph Chatbot

Chattez avec Graph Search

A disaggregate choice-based approach to find epsilon-equilibria of oligopolistic markets

Procrustes Metrics and Optimal Transport for Covariance Operators

Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

GOT: An Optimal Transport framework for Graph comparison

Minimum energy adaptive structures – All-In-One problem formulation

Forward-Backward Splitting for Optimal Transport Based Problems

Regularization via Mass Transportation

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

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

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