Machine Learning of Inverse Problems: Statistical Inference and Stochastic Optimization

• Applicants: Professor Dr. Jan Johannes; Professor Dr. Enno Mammen
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 568957765

In this project, questions of mathematical statistics and machine learning for statistical inverse problems are examined from different perspectives. On the one hand, complex inverse problems are examined in which non-linear relationships occur in different ways. On the other hand, modern methods of machine learning, e.g. Generative Adversarial Networks and Random Forests, are being introduced as promising new methods of statistical inference of inverse problems. The aim is in particular to build new statistical methods optimal in some sense and quantify their convergence rates as measures of their accuracy. This question naturally leads to the study of model selection procedures, which are also examined in an abstract context in the project. Another point of the project is the algorithmic use of gradient-free stochastic optimization methods, in particular in view to our approach of statistical inverse problems. The project addresses four different interrelated research subjects: (A) Generative models for inverse problems; (B) Statistics of inverse problems under nonlinearity; (C) Gradient-free stochastic optimization; (D) Model selection under structural assumptions.

• DFG Programme: Research Grants
• International Connection: France
• Cooperation Partners: Professorin Cristina Butucea; Professor Alexandre Tsybakov