Understand
Optimal transport tools (OTT-JAX) is a Python toolbox that can solve optimal transport problems between point clouds and histograms.
- The toolbox builds on various JAX features, such as automatic and custom reverse mode differentiation, vectorization, just-in-time compilation and accelerators support.
- The toolbox covers elementary computations, such as the resolution of the regularized OT problem, and more advanced extensions, such as barycenters, Gromov-Wasserstein, low-rank solvers, estimation of convex maps, differentiable generalizations of quantiles and ranks, and approximate OT between Gaussian mixtures.
- The toolbox code is available at \texttt{https://github.com/ott-jax/ott}
Built on
On the transfer of masses (in russian)
Leonid Kantorovich · 1942
Earlier work this paper cites.
Tres observaciones sobre el algebra lineal
Garrett Birkhoff · 1946
Earlier work this paper cites.
Network flows
Ravindra K Ahuja, Thomas L Magnanti, and James B Orlin · 1988
Earlier work this paper cites.
Ranking via sinkhorn propagation
Ryan Prescott Adams and Richard S Zemel · 2011
Earlier work this paper cites.
Gromov–Wasserstein distances and the metric approach to object matching
Facundo Mémoli · 2011
Earlier work this paper cites.
Similar
Sinkhorn distances: lightspeed computation of optimal transport
Marco Cuturi · 2013
Cited alongside, same era.
On the rate of convergence in Wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
Cited alongside, same era.
Wasserstein barycentric coordinates: histogram regression using optimal transport
Nicolas Bonneel, Gabriel Peyré, and Marco Cuturi · 2016
Cited alongside, same era.
Input convex neural networks
Brandon Amos, Lei Xu, and J Zico Kolter · 2017
Cited alongside, same era.
Differential properties of sinkhorn approximation for learning with wasserstein distance
Giulia Luise, Alessandro Rudi, Massimiliano Pontil, and Carlo Ciliberto · 2018
Cited alongside, same era.
Low-rank sinkhorn factorization
Meyer Scetbon, Marco Cuturi, and Gabriel Peyré
Cited in the paper.
Linear-time gromov wasserstein distances using low rank couplings and costs
Meyer Scetbon, Gabriel Peyré, and Marco Cuturi
Cited in the paper.
Then
Differentiable ranking and sorting using optimal transport
Marco Cuturi, Olivier Teboul, and Jean-Philippe Vert · 2019
Later among the works it cites.
Sample complexity of sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
Later among the works it cites.
Statistical bounds for entropic optimal transport: Sample complexity and the central limit theorem
Gonzalo Mena and Jonathan Niles-Weed · 2019
Later among the works it cites.
Supervised quantile normalization for low rank matrix factorization
Marco Cuturi, Olivier Teboul, Jonathan Niles-Weed, and Jean-Philippe Vert · 2020
Later among the works it cites.
A wasserstein-type distance in the space of gaussian mixture models
Julie Delon and Agnes Desolneux · 2020
Later among the works it cites.
Beyond the bibliography
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…