Ημερομηνία: Πέμπτη 3 Οκτωβρίου
Ώρα: 13:00
Τόπος: Αίθουσα Γ32
Oμιλητής: Van Vu (Yale, USA)
Τίτλος: New matrix perturbation bounds via contour analysis
Περίληψη: Matrix perturbation bounds (such as Weyl and Davis-Kahan) are among the most frequently used tools in many branches of mathematics, statistics, and theoretical computer science.
Most of the classical results in this area are optimal, in the worst case analysis. However, in modern applications, both the ground and the nose matrices frequently have extra structural properties. For instance, it is often assumed that the ground matrix is essentially low rank, and the nose matrix is random or pseudo-random. It is of fundamental interest to see if one can improve upon the classical theory under these modern and popular assumptions.
We aim to systematically rebuild a part of perturbation theory, adapting to these modern assumptions. We will do this using a method called "contour expansion". which maybe of independent interest.
With this method, we are able to exploit the skewness among the leading eigenvectors of the ground matrix and the noise matrix (which is significant when the two matrices are uncorrelated) to our advantage. This has lead to a number of quantitative improvements over the classical results in well-known problems, which, in turn, has direct applications in data science and theoretical computer science.
Joined work with Phuc Tran (Yale).