Variational and Information Flows in Machine Learning and Optimal Transport / / by Wuchen Li, Bernhard Schmitzer, Gabriele Steidl, François-Xavier Vialard, Christian Wald
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| Autore: |
Li Wuchen
|
| Titolo: |
Variational and Information Flows in Machine Learning and Optimal Transport / / by Wuchen Li, Bernhard Schmitzer, Gabriele Steidl, François-Xavier Vialard, Christian Wald
|
| Pubblicazione: | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025 |
| Edizione: | 1st ed. 2025. |
| Descrizione fisica: | 1 online resource (433 pages) |
| Disciplina: | 515.35 |
| Soggetto topico: | Differential equations |
| Mathematical optimization | |
| Calculus of variations | |
| Differential Equations | |
| Calculus of Variations and Optimization | |
| Altri autori: |
SchmitzerBernhard
SteidlGabriele
VialardFrançois-Xavier
WaldChristian
|
| Nota di contenuto: | - 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. |
| Sommario/riassunto: | 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. . |
| Titolo autorizzato: | Variational and Information Flows in Machine Learning and Optimal Transport |
| ISBN: | 3-031-92731-1 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9911015963203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Oberwolfach Seminars, . 2296-5041 ; ; 56