Martin Burger: Modern regularization methods in inverse problems and data science

This talk discusses recent developments on variational methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and further discuss the derivation of quantitative estimates respectively needed ingredients such as Bregman distances for convex variational and iterative methods. In addition to the approach developed for inverse problems we will also discuss analogous regularization in machine learning and work out some connections to the classical regularization theory. In particular we will discuss a reinterpretation of machine learning problems in the framework of regularization theory and a reinterpretation of variational methods for inverse problems in the framework of risk minimization. Slides: https://www.mathunion.org/fileadmin/IMU/ICM2022/Presentation-slides/180-Martin%20Burger.pdf