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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.

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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



  • 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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