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Trajectory inference with Schrödinger bridges - lecture 1

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Authors : Chizat, Lénaïc (Author of the conference)
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 :
49M29 - Multiplier methods
62M05 - Markov processes: estimation
60-08
Additional resources :
http://smai.emath.fr/cemracs/cemracs22/slides/slides_chizat

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : 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

Information on the Event

Event Title : CEMRACS: Transport in Physics, Biology and Urban Traffic / CEMRACS: Transport en physique, biologie et traffic urbain
Event 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.19940403
Cite 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

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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