the MIC Seminar

The Mathematics, Information and Computation (MIC) Seminar runs at irregular intervals and covers specific aspects at the interface of applied maths, information theory and theory of computation.

Schedule Spring 17

Date & Time Speaker Title Room
Mar 21, 2:30pm Liza Rebrova (U Michigan) Local and global obstructions for the random matrix norm regularization CDS 650

Abstracts

Liza Rebrova: Local and Global obstructions for the random matrix norm regularization

We study large n by n random matrices A with i.i.d. entries. If the distribution of the entries have mean zero and at least gaussian decay, then the operator norm ||A|| is at most of order sqrt(n) with high probability. However, for the distributions with heavier tails we cannot expect the same norm bound any more. So, we are motivated by the question: under what conditions operator norm of a heavy-tailed matrix can be improved by modifying just a small fraction of its entries (a small sub-matrix of A)? I will explain why this happens exactly when the entries of A have zero mean and bounded variance. I will also discuss the almost optimal dependence between the size of the removed sub-matrix and the resulting operator norm that we’ve obtained. This is a joint work with Roman Vershynin, inspired by the methods developed recently by Can Le and R. Vershynin and in our joint work with Konstantin Tikhomirov. Room: Center for Data Science, NYU, 60 5th ave, room 650 Time: 2:30pm-3:30pm.