[Ml-stat-talks] FW: IDeAS Seminar on Thursday 4/19/12 - Joseph Henry Room - 3PM

Amit Singer amits at math.Princeton.EDU
Tue Apr 17 23:39:13 EDT 2012


There will be an IDeAS Seminar on Thursday 4/19/12 at 3:00 pm in the Joseph
Henry Room - Jadwin Hall - 1 floor.  (Details below)

Date:  Thursday, 4/19/12

Seminar:  IDeAS Seminar

Place:  Joseph Henry Room - Jadwin Hall 1st floor (NOTE THE CHANGE IN ROOM)

Speaker:Michael McCoy, California Institute of Technology

Title: Random geometry meets data analysis: Sharp recovery bounds for convex
deconvolution 

Abstract:
Consider the common situation where observed data consists of the
superposition of two signals. Some examples include: an image of the night
sky containing both stars and galaxies; a communications message with
impulsive noise; and a low rank matrix obscured by sparse corruptions.
Deconvolution is the problem of determining the constituent signals from
their superposition. A fundamental question is "When is deconvolution
possible with a tractable algorithm?" We describe a convex optimization
framework for deconvolution, and provide a geometric characterization of
success in this framework. This geometric viewpoint, coupled with a natural
incoherence model, leads us into the realm of random geometry. A powerful
result from spherical integral geometry yields an exact formula for the
probability that our program succeeds. This formula leads to simple summary
statistics that reveal sharp phase transitions between success and failure,
and important theoretical properties of convex regularizers. We apply our
results to deconvolving the superposition of sparse vectors in random bases,
a stylized robust communications protocol, and determining a low rank matrix
corrupted by a matrix that is sparse in a random basis. We show that
empirical results closely match our theoretical bounds. Joint work with Joel
Tropp 



 
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