High-Dimensional Problems in Statistics

September 19 to 23, 2011

Organisers: Sara van de Geer, Peter Bühlmann, Marloes Maathuis and Hans-Rudolf Künsch

This workshop is part of the thematic semester "High Dimensional Approximation, Learning Theory and Stochastic Partial Differential Equations" of fall 2011.

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 be sparsity, e.g. in the number of coefficients in a wavelet expansion, or the dimension of a manifold. An important topic in this workshop is the adaptation 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.
The workshop has as sub-theme "Graphical modeling and causal inference", with important connections to the theory of sparse (random) graphs, discrete optimization including randomized algorithms, and sparse approximation.