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Variational and information flows in machine learning and optimal transport / Wuchen Li, Bernhard Schmitzer, Gabriele Steidl, François-Xavier Vialard, Christian Wald

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Oberwolfach seminars ; volume 56Publisher: Cham : Birkhäuser, 2025Description: 1 Online-Ressource (xiv, 254 Seiten)ISBN:
  • 9783031927317
Subject(s): Additional physical formats: 9783031927300 | 9783031927324 | Erscheint auch als: Variational and information flows in machine learning and optimal transport. Druck-Ausgabe. Cham : Birkhäuser, 2025. xiv, 254 SeitenDDC classification:
  • 515.35 23
MSC: MSC: 49-02 | 76D55 | 49Q22 | 49Q10 | 49N90DOI: DOI: 10.1007/978-3-031-92731-7Online resources: Summary: This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on “Computational Variational Flows in Machine Learning and Optimal Transport”. Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.Summary: Contents: 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.PPN: PPN: 1931458855Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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