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====== Projects ======

* [[world:markovchains|Click here to switch back to the Markov chain course website]]

^ Link to the paper                                                                                                              ^ Title                                                                                                                                       ^ Authors                                                                  ^ Associated team (2 students per project). To register, please double click on the table and fill your name together with your classmate's name.  ^ Comments  ^
| [[https://arxiv.org/pdf/2004.10850.pdf|paper 1]]                                                                               | **A probabilistic approach to convex (φ)-entropy decay for Markov chains**                                                                  | Giovanni Conforti                                                        |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2412.17997.pdf|paper 2]]                                                                               | **Shifted Composition III: Local Error Framework for KL Divergence**                                                                        | Jason M. Altschuler & Sinho Chewi                                        |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2011.10985.pdf|paper 3]]                                                                               | **A probability approximation framework: Markov process approach**                                                                          | Peng Chen, Qi‑Man Shao & Lihu Xu                                         |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/1801.07815.pdf|paper 4]]                                                                               | **Multivariate approximations in Wasserstein distance by Stein’s method and Bismut’s formula**                                              | Xiao Fang, Qi‑Man Shao & Lihu Xu                                         |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2102.04923.pdf|paper 5]]                                                                               | **Berry–Es̈een Bounds for Multivariate Nonlinear Statistics with Applications to M‑estimators and Stochastic Gradient Descent Algorithms**  | Qi‑Man Shao & Zhuo‐Song Zhang                                            |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2308.16196.pdf|paper 6]]                                                                               | **Asymptotically unbiased approximation of the QSD of diffusion processes with a decreasing time step Euler scheme**                        | Fabien Panloup & Julien Reygner                                          |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2412.09087.pdf|paper 7]]                                                                               | **General Markovian randomized equilibrium existence and construction in zero‑sum Dynkin games for diffusions**                             | Sören Christensen & Kristoffer Lindensjö                                 | Améthyste Bichard, Maxime Cros                                                                                                                   |           |
| [[https://arxiv.org/pdf/2504.01247.pdf|paper 8]]                                                                               | **On spectral gap decomposition for Markov chains**                                                                                         | Qian Qin                                                                 |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2410.08423.pdf|paper 9]]                                                                               | **A phase transition in sampling from Restricted Boltzmann Machines**                                                                       | Youngwoo Kwon, Qian Qin, Guanyang Wang & Yuchen Wei                      | Clémence Audibert, Simon Gabet                                                                                                                   |           |
| [[https://arxiv.org/pdf/2312.12782.pdf|paper 10]]                                                                              | **Spectral gap bounds for reversible hybrid Gibbs chains**                                                                                  | Qian Qin, Nianqiao Ju & Guanyang Wang                                    |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2201.12500.pdf|paper 11]]                                                                              | **Analysis of two‑component Gibbs samplers using the theory of two projections**                                                            | Qian Qin                                                                 |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/1810.08826.pdf|paper 12]]                                                                              | **Wasserstein‑based methods for convergence complexity analysis of MCMC with applications**                                                 | Qian Qin & James P. Hobert                                               |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2411.09514.pdf|paper 13]]                                                                              | **On importance sampling and independent Metropolis‑Hastings with an unbounded weight function**                                            | George Deligiannidis, Pierre E. Jacob, El Mahdi Khribch & Guanyang Wang  |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2501.18548.pdf|paper 14]]                                                                              | **The No‑Underrun Sampler: A Locally‑Adaptive, Gradient‑Free MCMC Method**                                                                  | Nawaf Bou‑Rabee, Bob Carpenter, Sifan Liu & Stefan Oberdörster           |                                                                                                                                                  |           |
| [[https://proceedings.neurips.cc/paper_files/paper/2024/file/99fecf765ecf62c3e3175ef2278f3315-Paper-Conference.pdf|paper 15]]  | **Deep Learning for Computing Convergence Rates of Markov Chains**                                                                          | Y Qu et al.                                                              |                                                                                                                                                  |           |
| [[https://arxiv.org/pdf/2506.22258.pdf|paper 16]]                                                                              | **Mixing Time Bounds for the Gibbs Sampler under Isoperimetry**                                                                             | Alexander Goyal, George Deligiannidis & Nikolas Kantas                   | Andreas Mignon et Adrien Chivet                                                                                                                  |           |
| [[https://arxiv.org/pdf/2102.00366.pdf|paper 17]]                                                                              | **Metropolis–Hastings transition kernel couplings**                                                                                         | John O’Leary & Guanyang Wang                                             |  Paul Bastin, Cherif Belkacemi                                                                                                                   |           |

====== Instructions ======
  * A short summary (5 pages max) of the paper is requested before the defense by sending an email to Alain and Randal, one week before the defense. You can add technical appendix (with no limitation size) if needed. 
  * The defense will be 20 minutes long per project + questions. Exact dates will be given later (probably thursday, 22 january of 29 january). 
  * Be as pedagogical as possible, you can highlight a particular proof that interests you if you find it interesting. 
  * Please read the <color /yellow>{{ :world:guidelinesmda.pdf |guidelines for the report}}</color>.    
  * If there is any question, please contact [[alain.durmus@polytechnique.edu|Alain Durmus]] or [[randal.douc@polytechnique.edu|Randal Douc]].

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