Speakers
Kevin Schnelli (KTH Stockholm)
Minicourse on Random Matrices
Radoslav Harman (Comenius University in Bratislava)
Minicourse on Optimal Experimental Design
Randolf Altmeyer (University of Cambridge)
Research talk: “Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models”
Mini Courses
Kevin Schnelli: “Edge universality for random matrices”
Random matrix theory has become a very active field of research during the past decades. Its study connects mathematics with many branches of science such as statistics, physics and computer
science. Part I of the minicourse introduces Wigner matrices and the Gaussian invariant ensembles. We will study the empirical eigenvalue distribution of these models by deriving Wigner’s semicircle law.
Moreover, we will discuss further random matrix models such as the Wishart ensembles or sample covariance models, as well as adjacency matrices of random graphs. In Part II, we will introduce
some basic tools (Stieltjes transform, Green function, Stein’s lemma, cumulant expansions) used to study Wigner’s law on different spectral scales and establish rigidity estimates for the eigenvalues. In
Part III, we look at the extremal eigenvalues of some random matrix ensembles. We show that the rescaled fluctuations of the extremal eigenvalues are (often) universal and are thence described by
the Tracy-Widom laws. Finally, we outline some applications to signal detection problems. Reading suggestion: Chapter 2, An Introduction to Random Matrices, by G. Anderson, A. Guionnet, O. Zeitouni (Cambridge University Press).
Radoslav Harman: “An Introduction to the Optimum Design of Experiments”
Optimum design of experiments is a rich research field at the intersection of mathematics, statistics, optimization and computer science. I will split the introductory course into 3 parts. Part I: Statistical models, information matrices, optimality criteria. Exact designs of experiments. Known optimal exact designs for specific models. Algorithms for computing optimal or nearly-optimal exact designs with demonstrations in R. Part II: Approximate design of experiments. Caratheodory theorem and the ”equivalence” theorem. Known optimal approximate designs for specific models. Algorithms
for computing optimal approximate designs with demonstrations in R. Part III: Brief discussion on the extensions of optimal design to multivariate observations, nonlinear models and the models with
correlated observations. Relations to other fields: Enclosing ellipsoids and the outlier detection in multivariate data. Spectral graph theory and the design of well-connected networks. In the course, I will not follow any particular book, but a readable introduction to the topic is Atkinson, Donev, Tobias: ”Optimum Experimental Design, with SAS”, Oxford University Press 2007.
Venue
1’308 Erwin Schrödinger-Zentrum,
Rudower Chaussee 26, 12489 Berlin
Program
Thursday, January 12, 2023
- 9:00-10:30 Minicourse on random matrices, Part I
- 10:30-11:00 Coffee break
- 11:00-12:30 Minicourse on optimal experimental design, Part I
- 12:30-14:00 Lunch break
- 14:00-15:30 Minicourse on random matrices, Part II
- 15:30-16:00 Coffee break
- 16:00-17:00 Research talk via Zoom on “Polynomial time guarantees for sampling based posterior inference in high-dimensional generalised linear models” [Randolf Altmeyer, University of Cambridge]
- 19:00 Conference dinner, Ratskeller Köpenick
Friday, January 13, 2023
- 9:00-10:30 Minicourse on random matrices, Part III
- 10:30-11:00 Coffee break
- 11:00-12:30 Minicourse on optimal experimental design, Part II
- 12:30-14:00 Lunch break
- 14:00-15:30 Minicourse on optimal experimental design, Part III
- 16:00-20:00 Guided tour through the Bundestag