Groups and interactions in data, networks and biology

Variational methods for geometric statistical inference problems

Florian Theil

University of Warwick

The estimation of geometric shapes such as tracks or surfaces in data sets creates significant mathematical challenges because one tries to identify an infinite dimensional object based on a finite number of measurements. We present a simple variational framework for which the estimators can be shown to converge to minimizers of certain functionals as the number of data points increases.