Research Training Group 2088

Discovering structure in complex data: Statistics meets Optimization and Inverse Problems

The efficient extraction of significant information from complex data is one of the grand challenges in applied sciences. Continuously growing capacities for the acquisition and storage of large data sets call for new application-adapted approaches to process data efficiently and to extract the embedded information.
Detecting relevant structural information is often hampered by the complexity of data sets as well as by noisy and indirect measurements.
The RTG 2088 focuses on new mathematical concepts for the efficient reconstruction and classification of relevant structural information in data sets, without reconstructing the entire information inherent in the data. One of the guiding principles of this RTG consists of discovering and rigorously exploiting structural a priori information in order to obtain the desired information.
We aim at utilizing a wide range of a priori knowledge - such as topological structures, probability metrics, sparsity in adaptive dictionaries or natural non-quadratic bending energies - to design numerically and statistically both stable and efficient algorithms for the recovery and classification of information.
Methodologically, we focus on an interplay between approaches in statistics, optimization, and inverse problems. Important solution concepts include generalized regularization techniques, multi-scale methods in harmonic analysis and statistics, statistical inference for topological tructures, nonlinear local and global spectral dimensionality reduction, and cutting-edge, iterative algorithms at the interface of statistics and optimization.

funded by the