arXiv Machine Learning
Jun 25

Sample complexity of unbalanced entropic OT

arXiv:2606. 24987v1 Announce Type: cross Abstract: Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon
arXiv Machine Learning
Jun 5

Variational Entropic Optimal Transport

arXiv:2602. 02241v2 Announce Type: replace Abstract: Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem.

By Roman Dyachenko, Nikita Gushchin, Kirill Sokolov, Petr Mokrov, Evgeny Burnaev, Alexander Korotin
arXiv Statistics ML
Aug 27

Continuum-marginal optimal transport: a mesh-free kernel method

The paper introduces a mesh‑free kernel method for continuum‑marginal optimal transport, aiming to recover the minimum‑energy velocity field that reproduces a continuous family of probability marginals. By embedding the weak continuity equation into a reproducing kernel Hilbert space, the authors obtain a sample‑only objective that eliminates spatial discretization. The velocity is represented via a linear‑in‑parameters dictionary or neural network and optimized with mini‑batch stochastic techniques, achieving accurate drift recovery and marginal consistency in synthetic experiments, and the framework also extends to the Nelson problem of stochastic optimal transport.

By Yumiharu Nakano
arXiv AI
Jun 16

Optimal Transport for Machine Learners

arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.

By Gabriel Peyr\'e