[Ml-stat-talks] FW: IDeAS Seminar Wed. 2/22/12 @ 3PM -214 Fine Hall

Amit Singer amits at math.Princeton.EDU
Tue Feb 21 14:48:33 EST 2012

Nikhil Srivastava will give a talk tomorrow about his recent work with Roman
Vershynin. Please see announcement below.   





From: Valerie Marino [mailto:vmarino at math.princeton.edu] 
Sent: Tuesday, February 21, 2012 10:54 AM
To: PACM Grad Students; PACM etc.
Cc: Philippe Rigollet; Amit Singer; E Weinan; Peter Constantin; Phill
Holmes; Nikhil Srivastava; pacmcertif at math.princeton.edu
Subject: IDeAS Seminar Wed. 2/22/12 @ 3PM -214 Fine Hall


Below is the information for the next IDeAS Seminar

Seminar:  IDeAS Seminar

Date: Wednesday 2/22/12

Speaker:  Nikhil Srivastava - Computer Science Dept. Princeton University

Time:  3:00 pm

Place:  214 Fine Hall

Title:   Covariance Estimation for Distributions with 2+eps Moments

Authors and Abstract:
Nikhil Srivastava, Roman Vershynin
We study the minimal sample size N=N(n) that suffices to estimate the
covariance matrix of an n-dimensional distribution by the sample covariance
matrix in the operator norm, and with an arbitrary fixed accuracy. We
establish the optimal bound N = O(n) for every distribution whose
k-dimensional marginals have uniformly bounded 2+\epsilon moments outside
the sphere of radius O(\sqrt{k}). In the specific case of log-concave
distributions, this result provides an alternative approach to the
Kannan-Lovasz-Simonovits problem, which was recently solved by Adamczak,
Litvak, Pajor and Tomczak-Jaegermann. Moreover, a lower estimate on the
covariance matrix holds under a weaker assumption -- uniformly bounded
2+\epsilon moments of one-dimensional marginals. Our argument proceeds by
randomizing the spectral sparsification technique of Batson, Spielman and
Srivastava. The spectral edges of the sample covariance matrix are
controlled via
the Stieltjes transform evaluated at carefully chosen random points.
Valerie Marino
Program Secretary
Program in Applied & Computational Mathematics
Tel: 609-258-3703
Fax: 609-258-1735
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