High-Dimensional Model Selection With Network Data: Methods, Theories, and Software

• Applicant: Professor Dr. Johannes Lederer
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541176257

Networks are ubiquitous in our lives: think of social networks, power grids, and the internet. Nevertheless, statistical model selection based on network data still needs much development. Two main challenges are that many networks have high-dimensional parameter spaces but are observed only once. This project tries to approach these two challenges. We devise estimators that can handle many parameters yet require only a single observation of the network, and we establish mathematical guarantees for this property. We then show how to calibrate the estimators' tuning parameters in a computationally efficient and statistically sound way. We finally devise efficient algorithms and implement our estimators in user-friendly software. In sum, the results of this project yield new theoretical and conceptual insights into model selection with network data but might also be of substantial interest to applied researchers in biology, finance, sociology, and beyond.

• DFG Programme: Research Grants