Vignettes

hdim

Networks

Network models describe connections among entities in a system. Such models are used across many scientific disciplines, including economy, sociology, biology, medicine, and physics. We develop general frameworks for network models and investigate their properties in specific applications. For example, we study data that describe social environments, gene-gene interactions, and brain connectivity.

hdim

High-dimensional Data

Modern technology can collect data at very fine resolutions. This means that in contemporary data sets, the number of observed parameters is typically much larger than the number of samples. To obtain good estimates in such settings, all information about the data needs to be incorporated, and the methods need to be carefully calibrated. We develop corresponding tools, and we equip these tools with efficient algorithms and sound theoretical frameworks.

concentration

Empirical Processes

Empirical processes are a pivotal concept in mathematical statistics. We are especially interested in concentration bounds for empirical processes. Classical examples are Bernstein’s and Höffding’s inequalities. In our research, we develop new bounds that relax the assumptions on the underlying model. These bounds serve as a theoretical basis for evaluating statistical methods, both in classical as well as high-dimensional settings.