[Ml-stat-talks] Fwd: IDeAS Seminar Wed. 4/10/13 @ 3:45 pm

Philippe Rigollet rigollet at princeton.edu
Mon Apr 8 11:58:44 EDT 2013

Hello again,

another interesting talk by Matan Gavish, a student of David Donoho at Stanford. Note that this IDeAS seminar will take place on Wednesday.


Date: April 10 - IDeAS Seminar

Room: 102A McDonnell Hall @ 3:45 pm

Speaker: Matan Gavish, Stanford University
Title: Minimax Risk of Matrix Denoising by Singular Value Thresholding
Abstract: In matrix denoising, we estimate an unknown real m-by-n matrix X from a single noisy measurement Y=X+Z, where Z is assumed to have i.i.d normal entries. A popular matrix denoising scheme is Singular Value Thresholding (SVT), which applies soft thresholding (with a common threshold) to each of the singular values of the data matrix Y. I'll show an explicit formula for the minimax MSE of SVT over matrices of rank <= r, and the corresponding optimal location for the threshold of SVT. I will also compare the minimax MSE of SVT to the minimax MSE over all possible matrix denoisers. For example, for n=m, we will see that SVT is no more than a factor of 3 suboptimal. Matrix denoising is connected to compressed sensing of matrices: there is empirical evidence that the minimax formula I'll present accurately predicts the phase transition of matrix recovery from Gaussian measurements. Joint work with David Donoho.

Valerie Marino
Program Secretary
Program in Applied & Computational Mathematics
Tel: 609-258-3703
Fax: 609-258-1735

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