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.
- 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.
- 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
- 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
Part 2 - OT in generative models (ABC, GAN)
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)
- please email one of us if you wish to be added to the reading group mailing list.