Mathematical challenges in high-dimensional statistics

Sara van de Geer (ETH Zürich)
Waaier 2, 10:15 - 11:15

A statistical model is called high-dimensional if the number of parameters p is larger than the number of observations n (for instance p = 104, n = 100). An important example is the linear model, where Y = + error, the output Y being an n-vector, the input X an (n×p)-matrix, and β ∈ ℝp being a vector of unknown coefficients. A popular way to deal with the situation is to fit the parameters using an appropriate loss function (for instance least squares) in combination with 1-regularization, i.e., large values of j=1p|βj| are penalized. The study of the theoretical properties of the fitted parameters leads to many mathematical challenges. We will discuss concentration and contraction inequalities for random elements in high-dimensional spaces, the size of convex bodies, sparse approximations and restricted eigenvalues.

Sara van de Geer (Ph.D. 1987 at the University of Leiden) has been working in Tilburg, Amsterdam, Bristol, Utrecht, Toulouse and Leiden, and is from 2005 full professor at the ETH Zürich. Her current area of research is statistical theory for high-dimensional data.