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Optimal Transport in Statistics Reading Group

Term 2, MS Teams, Tuesdays in week 3,5,7 and 9 from 14:00-15:30.

contact the organisers for a link to join the Team, or find it by searching for Optimal Transport in your MS Teams

About: Following the classical formulation of optimal transport (OT) problem by Monge and Kantorovich and the recent breakthroughs in computational OT, there has recently been a significant number of works applying OT for statistics. We started a 'Math-Stat' joint exploration of OT as a tool for solving real-world problems in 2020 and will continue in this academic year. While we focused on more fundamental aspects in the last two terms, we will go more applied this year. Topics of interest include sliced and projected Wasserstein distances in data science, applications of OT in Bayesian and classical inverse problems as well as statistical methods.


Term 2:

  • Week 3 (26/1) A survey of the Schroedinger problem and some of its connections to optimal transport, Christian Leonard, DCDS A, 34(4), 2014, Arxiv by Marie-Therese
  • Week 5 (9/2) Schroedinger Bridge Samplers, 2019 Arxiv by Giorgos
  • Week 7 (23/2) OT Flows: Fast and Accurate Continuous Normalizing Flows via Optimal Transport, Onken, Fung, Li and Rhutotto 2019 Arxiv by Rafa
  • Week 9 (9/3) Maximum Stein Discrepancy Estimators, Barp, Briol, Duncan, Girolami, Mackey, 2019 Arxiv by Rito

Term 1:

  • Week 4 (27/10): Projection Robust Wasserstein Distance and Riemannian Optimization by Lin, Fan, Ho, Cuturi and Jordon Arxiv by Marie-Therese Wolfram
  • Week 6 (10/11): Adversirial Regularisers in Inverse Problems by Lunz, Oektem and Schoenlieb Arxiv by Florian Theil
  • Week 8 (24/11): Gibbs Flows for Approximate Transport with Applications in Bayesian Computation, by Heng, Doucet and Pokern Arxiv by Rito Dutta
  • Week 10(8/12): Sinkhorn EM: An Expectation Maximization Algorithm Based on Entropic Optimal Transport, by Mena, Nejatbakhsh, Varol and Nils-Weed Arxiv by Francesca Crucinio

Schedule for term 3:

Week 4 (13th of May): section 5 of Garcia Trillos and Sanz-Alonso

Week 5 (20th of May): JKO paper (link)

Week 6 (27th of May): Maximum mean discrepancy gradient flow (link)

Week 7 (3rd of June): Gradient flows (link)

Week 8 (10th of June): Wasserstein Variational Inference, Ambrogioni et al 2018 (link)

Week 9 (17th of June): Fisher information regularization schemes for Wasserstein Gradient flows, Li et al 2020 (link)

Week 10 (24th of June): Particle flow Bayes' rule, Chen et al 2020 (link)

Schedule for term 2:

Week 16: Marie-Therese Wolfram - Intro to OT, Chapter 1 of Santanbrogio

Week 17: Rito Dutta - Remaining of Chapter 1 of Santanbrogio

Week 18: Florian Theil - Minimal flows, chapter 4 of Santanbrogio

Week 19 (03/02): Wasserstein Spaces, chapter 5 of Santanbrogio

Week 20 (10/02): Wasserstein Spaces, chapter 5 of Santanbrogio

Week 21 (17/02): Part 1 - Numerical methods, chapter 6 of Santanbrogio (or chapter 4 of Peyre and Cuturi)

Part 2 - OT in generative models (ABC, GAN)

Relevant papers: GAN with Wasserstein, ABC with Wasserstein, GAN, likelihood free inference, normalizing flows

Week 22 (24/02): Part 1 - Other numerical methods, chapter 4 of Peyre and Cuturi

Part 2 - Inference via low-dimensional couplings (Spantini's paper)

Week 23 (02/03): Part 1 - Continuation of OT (chapter to decide)

Part 2 - Continuous-time diffusion processes and MCMC

Week 24 (09/03): Part1 - Continuation of OT (chapter to decide)

Part 2 - Gradient Flows and MCMC (Garcia Trillos paper)

Organisers: Marie-Therese Wolfram (Dept. of Mathematics), Ritabrata (Rito) Dutta (Dept. of Statistics), Susana Gomes (Dept. of Mathematics)

- please email one of us if you wish to be added to the reading group mailing list.