The world is witnessing an explosion in abundance of "complicated data" with geometric structure and a growing need for its statistical analysis. In the last century, substantial progress had largely focused on suitably linearizing such data and subjecting it to classical statistical methods. With the advent of increased computational power, more involved novel intrinsic methodology has been developed. This has led on the one hand to design of highly sophisticated new statistical descriptors (e.g. in persistent homology), and on the other hand to discovery of non-Euclidean limiting behaviors of such descriptors. The latter has linked geometry and statistics in an unanticipated and quite unprecedented way. This currently evolving new field "Statistics of Data with Geometric Structure" requires intense collaboration across mathematical disciplines that have been traditionally rather remote: statistics, probability, optimization, and machine learning on one side, and combinatorics, topology and geometry, on the other side. To foster this development we will bring together specialists from the varying disciplines to discuss fundamental questions.
The one-week workshop will consist of plenary overview and highlight talks. The overview talks aim to introduce all workshop participants to the core themes of the workshop, while the highlight talks will point out recent cutting-edge research and identify open areas, including major perceived challenges. This is particularly important to enable all participants to join the discussions and share knowledge as well as ideas.
Overview talks will be planned on these areas
- Statistics on manifolds;
- Optimization on manifolds;
- Manifold learning;
- Persistent homology.