no code implementations • 6 Feb 2024 • Alexander Kolesov, Petr Mokrov, Igor Udovichenko, Milena Gazdieva, Gudmund Pammer, Evgeny Burnaev, Alexander Korotin
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions.
no code implementations • 2 Oct 2023 • Alexander Kolesov, Petr Mokrov, Igor Udovichenko, Milena Gazdieva, Gudmund Pammer, Anastasis Kratsios, Evgeny Burnaev, Alexander Korotin
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties.
1 code implementation • NeurIPS 2023 • Nikita Gushchin, Alexander Kolesov, Petr Mokrov, Polina Karpikova, Andrey Spiridonov, Evgeny Burnaev, Alexander Korotin
We fill this gap and propose a novel way to create pairs of probability distributions for which the ground truth OT solution is known by the construction.
1 code implementation • 12 Apr 2023 • Petr Mokrov, Alexander Korotin, Alexander Kolesov, Nikita Gushchin, Evgeny Burnaev
Energy-based models (EBMs) are known in the Machine Learning community for decades.
no code implementations • 30 May 2022 • Arip Asadulaev, Alexander Korotin, Vage Egiazarian, Petr Mokrov, Evgeny Burnaev
We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals.
3 code implementations • NeurIPS 2021 • Petr Mokrov, Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Evgeny Burnaev
Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space.