Spring 2012 Seminar Series

DATE: March 22nd
LOCATION: E62-550
TIME: 4:15pm
Reception immediately following in the ORC Conference Room (E40-106)

SPEAKER:
Andrea Montanari

TITLE
Universal limits in high-dimensional statistics

ABSTRACT
Classical statistical thinking is heavily shaped by limit theorems, and most notably the central limit theorem. As an example, the very fact that a `two sigma' event is considered as statistically significant is ultimately related to the central limit theorem. This and similar rules of thumb play in turn a central role in most empirical sciences, from econometrics to high-energy physics. The modern era of high-dimensional data requires to revise radically these notions. This is due to the fact naive limit theorems fail in high dimension. I will discuss a well studied example of this type. Namely, considering a cloud of p i.i.d. points in n dimensions, let P(p,n) denote the convex envelope of these points. How many faces does P(n,p) has when both n and p diverge to infinity? I will prove a universality result, and discuss its connection to high-dimensional linear regression, compressed sensing and message passing algorithms.

 

Based on joint work with David Donoho, Arian Maleki, Mohsen Bayati and Marc Lelarge.