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

• Final Report Year: 2024

Final Report Abstract

Graphical models have become a popular tool for describing dependence networks. Their main feature is a graphical representation of the dependencies, which can be easily understood and interpreted. However, research on graphical models has been focused on a limited selection of distributions, such as Gauß or Ising data. A general framework for graphical models, especially in high-dimensional settings, is missing. Although this project could not establish an entirely satisfactory framework yet, it made three major contributions: a complete graphical-model-based pipeline for the selection of depth normalization in genomics, a novel approach to tuning-parameter calibration, and theories for nested regularizers.

Publications

• Tuning parameter calibration for personalized prediction in medicine. Electronic Journal of Statistics, 15(2).
  Huang, Shih-Ting; Düren, Yannick; Hellton, Kristoffer H. & Lederer, Johannes
  
• Depth normalization of small RNA sequencing: using data and biology to select a suitable method. Nucleic Acids Research, 50(10), e56-e56.
  Düren, Yannick; Lederer, Johannes & Qin, Li-Xuan
  
• Lag selection and estimation of stable parameters for multiple autoregressive processes through convex programming.
  Somnath Chakraborty, Johannes Lederer & Rainer von Sachs