Workshop: High-dimensional problems in statistics

This workshop is organized by the members of the Seminar for Statistics (SfS) P. Buehlmann, S. van de Geer and H.R. Kuensch.

Date: September 19-23, 2011
Place: Institute for Mathematical Research, ETH Zuerich

Modern statistical theory concerns the estimation of objects in complex parameter spaces, for example a space of regression functions with a huge number of variables, or a collection of convex sets in image analysis, etc. A key point is the way one describes smoothness. For example, smoothness may sparsity, e.g. in the number of coefficients in a wavelet expansion, or the dimension of a manifold. A main theme in this workshop is adapting to unknown smoothness, using penalty based methods which are computationally feasible for high-dimensional problems. There will be many connections with analysis and approximation theory. There are also quite a few further apparent relations with other branches of mathematics. For example, concentration inequalities from probability theory are nowadays a main statistical tool. As another example, statistics uses and extends various techniques from optimization theory (e.g., convex optimization, exponential weighting, interior point methods). Moreover, from the algorithmic point of view, statistical problems have clear relations with e.g. compressing and learning algorithms in computer science. There will be two subthemes. The first is "Graphical modeling and causal inference", with important connections to the theory of sparse (random) graphs, discrete optimization including randomized algorithms, and sparse approximation. The second subtheme is "Statistical and stochastic modeling in biology", inspired by the high-throughput technology in molecular biology or bio-medicine, and systems biology, where often advanced mathematical modeling or statistical signal extraction are needed for meaningful complexity reduction or efficient extraction of information.