Administration/Data Management

• Applicant: Professor Dr. Axel Munk
• Co-Applicant: Professor Dr. Lutz Dümbgen
• Subject Area: Mathematics
• Term: from 2008 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 40095828

A basic challenge for statistics at the interface of different sciences is the developmentof methods for the analysis of massive data sets, complex data structures and highdimensionalpredictors. The objectives of this German-Swiss research group are specific developmentand analysis of statistical regularization methods for complex data structures as they mayoccur 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. Aims and scope of the research group. Our primary goal in this research group is to develop and analyze regularization methods for complex data structures in a unifying way from a statistical perspective. Particular emphasis is on regularization methods based on qualitative constraints, i.e. taking into account prior information about the geometric shape of certain model parameters or structural assumptions such as additivity or monotonicity. On the one hand we focus on different data models in various fields of application where we will develop specifically tailored regularization methods according to the needs in these subject matters. On the other hand, our fundamental claim is that statistical regularization via qualitative constraints reveals a unifying principle for a modeling process which is flexible enough to explain important data features but also specific enough to control the prediction or classification error in highly complex data structures. We aim at understanding their methodological commonalities on a broader scale. Our group consists of researchers having dealt with regularization techniques from various perspectives and in various disciplines for a long time, in particular from the perspective of statistics, numerical analysis, machine learning, pattern recognition, and econometrics. All of us cooperated already with some members of this group for a certain time, and in April 2008 we have been started to work all together at this ambitious project. In this second funding proposal three new colleagues (Gerard van den Berg, Tatyana Krivobokova, Ulrike Schneider) have been integrated. Each project is driven by a real substantial application problem. In many cases the same data set is tackled from various perspectives within different projects (e.g. the labor market data provided by B. Fitzenberger’s group or the microscopy data by S. Hell’s group). Various data projects from associated research groups from various fields of applications, such as biophysics, econometrics, medical imaging or molecular biology significantly enhance the practical merits of this Research group. We claim that statistical regularization procedures with structural or qualitative constraints allow a consistent methodical perspective and solution strategy while dealing with those subject fields.

• DFG Programme: Research Units
• Subproject of: FOR 916: Statistical Regularisation and Qualitative Constraints - Inference, Algorithms, Asymptotics and Applications
• International Connection: Switzerland