- Nonparametric and high-dimensional Statistics
- Statistics for stochastic processes
- Statistical inverse problems
- Stochastic (partial) differential equations
|Wintersemester 2021/22||Statistical Learning||Vorlesung|
|Grundlagen der Wahrscheinlichkeitstheorie und Statistik für Studierende der Informatik||Vorlesung|
DASHH is a Helmholtz graduate school involving several partner institutions in Hamburg. In DASHH we harness data, computer and applied mathematical science to advance our understanding of nature. We aim to educate the future generation of data- and information- scientists that will tackle tomorrow’s scientific challenges that come along with large-scale experiments.
- DFG project TR 1349/3-1 "High-dimensional statistics for point and jump processes"
While most of the statistical research for stochastic processes is restricted to one-dimensional or low-dimensional models, an important feature of data sets in modern applications is high dimensionality. The aim of this project is to combine the statistical theory for stochastic processes with high-dimensional statistics to construct and analyse new statistical methods for high-dimensional stochastic processes.
- LD-SODA: \"Lernbasierte Datenanalyse – Stochastik, Optimierung, Dynamik und Approximation\" (Landesforschungsförderung Hamburg)
This research project aims at the mathematical analysis of machine learning methods in sufficient width and depth. On the grounds of the mathematical findings, we further aim to improve existing learning methods, or to develop new ones. In this way, we provide a fundamental account to the construction of more advanced learning algorithms The project is a collaboration between scientists from four mathematical disciplines: Stochastics, Optimization, Dynamical Systems and Approximation.
- DFG Heisenberg professorship TR 1349/4-1 "New Frontiers in Statistics for Stochastic Processes: SPDEs and High-Dimensionality"
Owing to the exploding number of available data and the fast progress in information technology, on the one hand more complex models can be used for data description and on the other hand new methods are necessary to profit from the large amount of data. In the context of statistics for stochastic processes these aspects reflect in two new research directions which recently attracted an increased attention in the mathematical statistics community, namely stochastic partial differential equations (SPDEs) and high-dimensional processes. Due to the high-dimensionality, which is implicit for SPDEs, they require novel approaches at the interface of the innovative fields high-dimensional statistics, stochastic analysis and machine learning.