Please read our student and staff community guidance on COVID-19
Skip to main content Skip to navigation

Optimal Transport in Statistics Reading Group

Term 3, MS Teams, Wednesdays 14:00-16:00.

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. Hence, a 'Math-Stat' joint exploration of OT as a tool for solving real-world problems is in good time. This reading group will focus on fundamentals of optimal transport, recent developments in computational optimal transport, and finally its applications in statistics, eg. for asymptotic theory, statistical inference, approximate Bayesian computation, etc. We are planning to start with two introductory lectures, on OT by Marie-Therese Wolfram and a review of applications of OT in statistics by Rito. Then onward, each week the focus of the reading group will alternate between:

(i) Fundamentals and computational aspects of OT following the lecture note of Peyre and Cuturi

(ii) Applications of OT in statistical science, through reading articles from statistics.

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.