English
Trajectory inference with Schrödinger bridges - lecture 2
Multi angle
Auteurs : Chizat, Lénaïc (Auteur de la Conférence)
CIRM (Editeur )
49M29 - Multiplier methods
62M05 - Markov processes: estimation
60-08
Ressources complémentaires :
http://smai.emath.fr/cemracs/cemracs22/slides/slides_chizat
CIRM (Editeur )
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Résumé :
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
Codes MSC : Keywords : Schrödinger bridge; entropic optimal transport; relative entropy minimization; mean-field Langevin
49M29 - Multiplier methods
62M05 - Markov processes: estimation
60-08
Ressources complémentaires :
http://smai.emath.fr/cemracs/cemracs22/slides/slides_chizat
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/08/2022 Date de captation : 20/07/2022 Sous collection : Research School arXiv category : Optimization and Control ; Machine Learning Domaine : Control Theory & Optimization ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 01:01:34 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-07-20_Chizat_2.mp4 
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Informations sur la Rencontre
Nom de la rencontre : CEMRACS: Transport in Physics, Biology and Urban Traffic / CEMRACS: Transport en physique, biologie et traffic urbainOrganisateurs de la rencontre : Franck, Emmanuel ; Hivert, Helene ; Latu, Guillaume ; Leman, Hélène ; Maury, Bertrand ; Mehrenberger, Michel ; Navoret, Laurent Dates : 18/07/2022 - 22/07/2022 Année de la rencontre : 2022 URL Congrès : http://smai.emath.fr/cemracs/cemracs22/s...
Données de citation
DOI : 10.24350/CIRM.V.19941003Citer cette vidéo: Chizat, Lénaïc (2022). Trajectory inference with Schrödinger bridges - lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19941003 URI : http://dx.doi.org/10.24350/CIRM.V.19941003 |
Voir aussi
- [Multi angle] Trajectory inference with Schrödinger bridges - lecture 3 / Auteur de la Conférence Chizat, Lénaïc.
- [Multi angle] Integro-differential models of evolutionary adaptation in changing environments - lecture 2 / Auteur de la Conférence Mirrahimi, Sepideh.
- [Multi angle] Numerical methods and uncertainty quantification for kinetic equations - lecture2 / Auteur de la Conférence Dimarco, Giacomo.
- [Multi angle] Introduction to optimal transport theory - lecture 2 / Auteur de la Conférence Santambriogio, Filippo.
- [Multi angle] Trajectory inference with Schrödinger bridges - lecture 1 / Auteur de la Conférence Chizat, Lénaïc.
- [Multi angle] Integro-differential models of evolutionary adaptation in changing environments - lecture 1 / Auteur de la Conférence Mirrahimi, Sepideh.
- [Multi angle] Numerical methods and uncertainty quantification for kinetic equations - lecture 1 / Auteur de la Conférence Dimarco, Giacomo.
- [Multi angle] Introduction to optimal transport theory - lecture 1 / Auteur de la Conférence Santambriogio, Filippo.
Bibliographie
- 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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