A basic challenge for statistics at the interface of different sciences is the development of methods for the analysis of massive data sets, complex data structures and high-dimensional predictors. The objectives of this German-Swiss research group are specific development and analysis of statistical regularization methods for complex data structures as they may occur in different fields of application. In the foreground, there are methods in which regularization is given by qualitative constraints on the structure or geometry of data models.
Our basic hypothesis is that statistical regularization by qualitative constraints produces a consistent methodology for modeling of data structures which, on the one hand, is flexible enough to identify and scientifically utilize main structural features of data, but, on the other hand, specific enough to control prediction and classification error. Our research group consists of scientists who have been pursuing this objective for a long time from the perspective of different disciplines (statistics, numerical analysis, machine learning, pattern recognition, imaging, econometrics).
All of us cooperated already with some members of this group for a certain time, and now we start to work all together at this ambitious project. Each of the 14 sub-projects examines some aspects of this methodological target. In cooperation with other members, specific application problems are being studied which can originate directly from the research group or be brought up by associated groups. At the same time, we are working on diverse problems from the fields of systems biology, medical event-time analysis, astrophysics, atmospheric research, forest sciences, materials sciences, job market policy, biophotonics, medical image processing and empirical finance. Statistical regularization procedures with structural or qualitative constraints allow a consistent methodical perspective and solution strategy while dealing with those subject fields.