Shahar Mendelson is a Professor at the Australian National University and a Guest Professor at the University of Vienna. He studies high dimensional phenomena, focusing mainly on the connections between Statistical Learning Theory, Empirical Processes Theory and Asymptotic Geometric Analysis. He is an editor of the journal Mathematical Statistics and Learning.
May 13, 2021 at 15:00 in this link: meet.google.com/umd-afzc-jfe
Shahar Mendelson, Australian National University and University of Vienna
The small-ball method and (some of) its applications
Abstract:
I will present three seemingly unrelated problems – one in Asymptotic Geometric Analysis; one in random matrices theory; and one in statistics – that turn out to be very closely related: the solution to all of them is based on finding a nontrivial lower bound on the infimum of the same nonnegative random process. As it happens, the standard way of controlling that process (and the way all three problems have been studied previously) involves a natural, two-sided concentration argument.
I will explain why, despite its popularity, the two-sided concentration argument is very restrictive and often terribly loose; and I will suggest an alternative – the small-ball method – which leads to sharp estimates and holds under minimal restriction.