Term 1, hybrid, Wednesdays 15:00-16:30, Physical locations can be found below.

Teams link: https://teams.microsoft.com/l/team/19%3a4d42e9f334374bdfbb847dbc84711548%40thread.tacv2/conversations?groupId=9ef18898-76da-4ed9-ab3d-f0cdb2377184&tenantId=09bacfbd-47ef-4465-9265-3546f2eaf6bc

Focus: We start by discussing more theoretical aspect in 2021/22, focusing in particular on L1 theory, minimal flows and generalisations of the Wasserstein distance.

2021/2022

Term 1:

• Week 3 (20/10) MB2.23: OT in a Nutshell Part I: About Monge, Kantorovich and Duality Chapter 1.1-1.3 in Optimal Transport for Applied Mathematicians; Marie-Therese
• Week 4 (27/10) MB2.23: OT in a Nutshell Part II: About cycling and convexity Chapter 1.6 and 1.7 in Optimal Transport for Applied Mathematicians, Marie-Therese
• Week 5 (3/11) MB2.24: Brenier Theorem, Rito
• Week 6 (10/11) MB2.24: L1 & L^\infty Theory Chapter 3 in Optimal Transport for Applied Mathematicians, Francesca
• Week 8 (24/11) MB2.24: Extending OT to measures with different and/or infinite mass, Marta. Based on

  - Figalli & Gigli (2010). A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions. Journal de Mathe ́matiques Pures et Appliquées.

  - Guilllen, Mou & Swięch, A. (2019). Coupling Lévy measures and comparison principles for viscosity solutions. Transactions of the American Mathematical Society.

• Week 10 (8/12) MB2.24: OT on Lévy measures and connections to Bayesian Nonparametrics, Marta. Based on
  
  - Catalano, Lavenant, Lijoi, Prünster (2021+). A Wasserstein index of dependence for random measures. arXiv:2109.06646.

2020/2021

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

2019/2020

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.