Variational and Information Flows in Machine Learning and Optimal Transport

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 flow