Gradient flows for sampling and their deterministic interacting particle approximations | Vidéo | Carmin.tv

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Gradient flows for sampling and their deterministic interacting particle approximations

By Dejan Slepčev

Appears in collection : Aggregation-Diffusion Equations & Collective Behavior: Analysis, Numerics and Applications / Conférence Chaire Jean Morlet: Equations d'agrégation-diffusion et comportement collectif: Analyse, schémas numériques et applications

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.

Information about the video

Date of recording 11/04/2024
Date of publication 30/04/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20160203
Cite this video Slepčev, Dejan (11/04/2024). Gradient flows for sampling and their deterministic interacting particle approximations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20160203
URL https://dx.doi.org/10.24350/CIRM.V.20160203

Domain(s)

Analysis of PDEs

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

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/3049/Slides/Dejan_Slepcev_CIRM.pdf

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