Variational and Information Flows in Machine Learning and Optimal Transport
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Beschreibung
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.
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.
Gives an overview over a rapidly developing field Provides a basis for lectures and seminars on the topic Includes recent novel ideas
Autor*in
Wuchen Li
Themen in »Variational and Information Flows in Machine Learning and Optimal Transport«
Wasserstein Spaces Generalized Normalizing Flows Mean Field Games Optimal Transport Markov Chain
Stimmen zu »Variational and Information Flows in Machine Learning and Optimal Transport«
“This book is a collection of four short monographs exploring the theoretical foundations of optimal transport and its connections with machine learning. Each part can be read independently, but together they form a coherent and well-structured overview of the field. I would recommend this volume both as an accessible entry point for researchers with a strong theoretical background wishing to explore applications in machine learning, and as a rigorous theoretical reference for graduate students in data science or applied mathematics.” (Ronan Herry, zbMATH 1576.49001, 2026)
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