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Gradient flows for sampling and their deterministic interacting particle approximations
Multi angle
Authors : Slepčev, Dejan (Author of the conference)
CIRM (Publisher )
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
Additional resources :
https://www.cirm-math.fr/RepOrga/3049/Slides/Dejan_Slepcev_CIRM.pdf
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/RepOrga/3049/Slides/Dejan_Slepcev_CIRM.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 30/04/2024 Conference Date : 11/04/2024 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Analysis and its Applications ; Numerical Analysis & Scientific Computing ; PDE Format : MP4 (.mp4) - HD Video Time : 00:48:23 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-04-11_Slepcev.mp4 
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Information on the Event
Event Title : Aggregation-Diffusion Equations & Collective Behavior: Analysis, Numerics and Applications / Conférence Chaire Jean Morlet: Equations d'agrégation-diffusion et comportement collectif: Analyse, schémas numériques et applicationsEvent Organizers : Carrillo, José Antonio ; Esposito, Antonio ; Gómez-Castro, David ; Nouri, Anne Dates : 08/04/2024 - 12/04/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3049.html
Citation Data
DOI : 10.24350/CIRM.V.20160203Cite this video as: 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 |
See Also
- [Multi angle] Suppression of chemotactic blow-up by buoyancy / Author of the conference Yao, Yao.
- [Multi angle] Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems / Author of the conference Savaré, Giuseppe.
- [Multi angle] Global existence and boundedness for chemotaxis models with local sensing / Author of the conference Laurençot, Philippe.
- [Multi angle] Dynamics of strategic agents and algorithms as PDEs / Author of the conference Hoffmann, Franca.
Bibliography
- 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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