A General Framework for Graphical Models

• Applicant: Professor Dr. Johannes Lederer
• Subject Area: Mathematics
• Term: from 2020 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 451920280

Network structures, such as the microbial communities of our gut, the connections among the different regions of our brains, and the regulation networks in cells, are essential to our health and well-being. A promising way to describe such interactive structures mathematically is graphical modeling, which yields visuals that can be easily interpreted. However, standard representatives of graphical models, such as Ising and Gaussian models, are limited to very specific types of data, and the potential of graphical modeling for count data, heavy-tailed data, and other types of data that are common in practice remains largely unexplored. We will establish a new and more flexible class of graphical models and develop corresponding theories, estimators, and algorithms. By devising and applying novel penalization and optimization strategies, we will be able to make effective use of the increasingly large and complex datasets that represent the glut of data produced by modern technology. We will also prepare user-friendly software that will make our results useful to the scientific community at large.

• DFG Programme: Research Grants