Event

Content:

The lecture focuses on modelling statistical objects (random vectors, random matrices and random graphs) in high dimensions. It deals with concentration inequalities that limit the fluctuations of such objects as well as complexity measures for quantities and functions. The theory is transferred to well-known and widespread applications such as neighbourhood detection in networks, statistical learning theory and LASSO.

Learning objectives:

Students are able to

• name and justify statistical properties of high-dimensional objects (vectors, matrices, functions).
• describe and explain differences in the behaviour between low- and high-dimensional random objects.
• name procedures for assess uncertainties in statistical models and apply them in simple examples.
• decide well-founded which modeling of high-dimensional structures is best suited in a specific situation.
• transform data into lower dimensions and quantify approximation errors.
• understand basic proofs in high-dimensional statistics using examples.
• develop, implement and evaluate smaller simulations in a programming language of their choice.