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Trajectory inference with Schrödinger bridges - lecture 1
Multi angle
Authors : Chizat, Lénaïc (Author of the conference)
CIRM (Publisher )
49M29 - Multiplier methods
62M05 - Markov processes: estimation
60-08
Additional resources :
http://smai.emath.fr/cemracs/cemracs22/slides/slides_chizat
CIRM (Publisher )
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Abstract :
We consider statistical and computation methods to infer trajectories of a stochastic process from snapshots of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data. The goal of this mini-course is to present and understand the estimator proposed by [Lavenant et al. 2020] which searches for the diffusion process that fits the observations with minimal entropy relative to a Wiener process. This estimator comes with consistency guarantees—for a suitable class of ground truth processes—and lends itself to computational methods with global optimality guarantees. Its analysis is the occasion to review important tools from optimal transport and diffusion process theory.
Keywords : Schrödinger bridge; entropic optimal transport; relative entropy minimization; mean-field Langevin
MSC Codes : Keywords : Schrödinger bridge; entropic optimal transport; relative entropy minimization; mean-field Langevin
49M29 - Multiplier methods
62M05 - Markov processes: estimation
60-08
Additional resources :
http://smai.emath.fr/cemracs/cemracs22/slides/slides_chizat
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/08/2022 Conference Date : 19/07/2022 Subseries : Research School arXiv category : Optimization and Control ; Machine Learning Mathematical Area(s) : Control Theory & Optimization ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:59:24 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-07-19_Chizat_1.mp4 
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Information on the Event
Event Title : CEMRACS: Transport in Physics, Biology and Urban Traffic / CEMRACS: Transport en physique, biologie et traffic urbainEvent Organizers : Franck, Emmanuel ; Hivert, Helene ; Latu, Guillaume ; Leman, Hélène ; Maury, Bertrand ; Mehrenberger, Michel ; Navoret, Laurent Dates : 18/07/2022 - 22/07/2022 Event Year : 2022 Event URL : http://smai.emath.fr/cemracs/cemracs22/s...
Citation Data
DOI : 10.24350/CIRM.V.19940403Cite this video as: Chizat, Lénaïc (2022). Trajectory inference with Schrödinger bridges - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19940403 URI : http://dx.doi.org/10.24350/CIRM.V.19940403 |
See Also
- [Multi angle] Trajectory inference with Schrödinger bridges - lecture 3 / Author of the conference Chizat, Lénaïc.
- [Multi angle] Trajectory inference with Schrödinger bridges - lecture 2 / Author of the conference Chizat, Lénaïc.
- [Multi angle] Integro-differential models of evolutionary adaptation in changing environments - lecture 2 / Author of the conference Mirrahimi, Sepideh.
- [Multi angle] Numerical methods and uncertainty quantification for kinetic equations - lecture2 / Author of the conference Dimarco, Giacomo.
- [Multi angle] Introduction to optimal transport theory - lecture 2 / Author of the conference Santambriogio, Filippo.
- [Multi angle] Integro-differential models of evolutionary adaptation in changing environments - lecture 1 / Author of the conference Mirrahimi, Sepideh.
- [Multi angle] Numerical methods and uncertainty quantification for kinetic equations - lecture 1 / Author of the conference Dimarco, Giacomo.
- [Multi angle] Introduction to optimal transport theory - lecture 1 / Author of the conference Santambriogio, Filippo.
Bibliography
- LÉONARD, Christian. A survey of the Schrödinger problem and some of its connections with optimal transport. Discrete and Continuous Dynamical Systems-Series A, 2014, vol. 34, no 4, p. 1533-1574 - http://dx.doi.org/10.3934/dcds.2014.34.1533
- LAVENANT, Hugo, ZHANG, Stephen, KIM, Young-Heon, et al. Towards a mathematical theory of trajectory inference. arXiv preprint arXiv:2102.09204, 2021 - https://doi.org/10.48550/arXiv.2102.09204
- ZHANG, Stephen, CHIZAT, Lénaïc, HEITZ, Matthieu, et al. Trajectory Inference via Mean-field Langevin in Path Space. arXiv preprint arXiv:2205.07146, 2022. - https://doi.org/10.48550/arXiv.2205.07146
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