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SUMMARY:Graph Total Variation for Inverse Problems with Highly Correlated 
 Designs - Rebecca Willett (University of Wisconsin-Madison)
DTSTART:20180321T090000Z
DTEND:20180321T100000Z
UID:TALK102724@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Garvesh Raskutti		(University of Wisconsin)\
 , Yuan Li		(University of Wisconsin)        <br></span><br>Sparse high-dim
 ensional linear regression and inverse problems have received substantial 
 attention over the past two decades. Much of this work assumes that explan
 atory variables are only mildly correlated. However\, in modern applicatio
 ns ranging from functional MRI to genome-wide association studies\, we obs
 erve highly correlated explanatory variables and associated design matrice
 s that do not exhibit key properties (such as the restricted eigenvalue co
 ndition). In this talk\, I will describe novel methods for robust sparse l
 inear regression in these settings. Using side information about the stren
 gth of correlations among explanatory variables\, we form a graph with edg
 e weights corresponding to pairwise correlations. This graph is used to de
 fine a graph total variation regularizer that promotes similar weights for
  correlated explanatory variables. I will show how the graph structure enc
 apsulated by this regularizer interacts with correlated design matrices to
  yield provably a ccurate estimates. The proposed approach outperforms sta
 ndard methods in a variety of experiments on simulated and real fMRI data.
   <br><span><br>This is joint work with Yuan Li and Garvesh Raskutti.</spa
 n>
LOCATION:Seminar Room 1\, Newton Institute
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