English
Gradient flows for sampling and their deterministic interacting particle approximations
Multi angle
Auteurs : Slepčev, Dejan (Auteur de la Conférence)
CIRM (Editeur )
45M05 - Asymptotics
62D05 - Sampling theory, sample surveys
82C21 - Dynamic continuum models (systems of particles, etc.)
35Q70 - PDEs in connection with mechanics of particles and systems
35Q62 - PDEs in connection with statistics
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3049/Slides/Dejan_Slepcev_CIRM.pdf
CIRM (Editeur )
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Résumé :
Motivated by the task of sampling measures in high dimensions we will discuss a number of gradient flows in the spaces of measures, including the Wasserstein gradient flows of Maximum Mean Discrepancy and Hellinger gradient flows of relative entropy, the Stein Variational Gradient Descent and a new projected dynamic gradient flows. For all the flows we will consider their deterministic interacting-particle approximations. The talk is highlight some of the properties of the flows and indicate their differences. In particular we will discuss how well can the interacting particles approximate the target measures.The talk is based on joint works wit Anna Korba, Lantian Xu, Sangmin Park, Yulong Lu, and Lihan Wang.
Keywords : Gradient flow; sampling; nonlocal equations; interacting particle systems
Codes MSC : Keywords : Gradient flow; sampling; nonlocal equations; interacting particle systems
45M05 - Asymptotics
62D05 - Sampling theory, sample surveys
82C21 - Dynamic continuum models (systems of particles, etc.)
35Q70 - PDEs in connection with mechanics of particles and systems
35Q62 - PDEs in connection with statistics
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3049/Slides/Dejan_Slepcev_CIRM.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 30/04/2024 Date de captation : 11/04/2024 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : Analysis and its Applications ; Numerical Analysis & Scientific Computing ; PDE Format : MP4 (.mp4) - HD Durée : 00:48:23 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-04-11_Slepcev.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Aggregation-Diffusion Equations & Collective Behavior: Analysis, Numerics and Applications / Conférence Chaire Jean Morlet: Equations d'agrégation-diffusion et comportement collectif: Analyse, schémas numériques et applicationsOrganisateurs de la rencontre : Carrillo, José Antonio ; Esposito, Antonio ; Gómez-Castro, David ; Nouri, Anne Dates : 08/04/2024 - 12/04/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3049.html
Données de citation
DOI : 10.24350/CIRM.V.20160203Citer cette vidéo: Slepčev, Dejan (2024). Gradient flows for sampling and their deterministic interacting particle approximations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20160203 URI : http://dx.doi.org/10.24350/CIRM.V.20160203 |
Voir aussi
- [Multi angle] Suppression of chemotactic blow-up by buoyancy / Auteur de la Conférence Yao, Yao.
- [Multi angle] Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems / Auteur de la Conférence Savaré, Giuseppe.
- [Multi angle] Global existence and boundedness for chemotaxis models with local sensing / Auteur de la Conférence Laurençot, Philippe.
- [Multi angle] Dynamics of strategic agents and algorithms as PDEs / Auteur de la Conférence Hoffmann, Franca.
Bibliographie
- LU, Yulong, SLEPČEV, Dejan, et WANG, Lihan. Birth–death dynamics for sampling: global convergence, approximations and their asymptotics. Nonlinearity, 2023, vol. 36, no 11, p. 5731. - http://dx.doi.org/10.1088/1361-6544/acf988
- PARK, Sangmin et SLEPČEV, Dejan. Geometry and analytic properties of the sliced Wasserstein space. arXiv preprint arXiv:2311.05134, 2023. - https://arxiv.org/abs/2311.05134
- XU, Lantian, KORBA, Anna, et SLEPCEV, Dejan. Accurate quantization of measures via interacting particle-based optimization. In : International Conference on Machine Learning. PMLR, 2022. p. 24576-24595. - https://proceedings.mlr.press/v162/xu22d.html
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