Morgane Austern is a postdoctoral researcher at Microsoft Research New-England. She obtained her Ph.D in Statistics from Columbia University in 2019, where she worked under the supervision of Peter Orbanz and Arian Maleki. She is interested in problems in probability and statistics that are motivated by machine learning. Notably, her research focuses on developing probability tools for modern machine learning estimators, and on establishing the properties of learning algorithms for structured and dependent data.
Talk: Asymptotics of learning on dependent and structured random objects
A link to this Zoom talk will be sent to the Stats Seminar list serv
Abstract: Classical statistical inference relies on numerous tools from probability theory to study the properties of estimators. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting. Firstly, we consider distributionally "structured" and dependent random object-i.e random objects whose distribution are invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory. Secondly by building on these results, we establish the asymptotic distribution of the cross-validated risk with the number of folds allowed to grow at an arbitrary rate. Using this, we study the statistical speed-up of cross validation compared to a train-test split procedure, which reveals surprising results even when used on simple estimators.