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SUMMARY:Distance Shrinkage and Euclidean Embedding via Regularized Kernel 
 Estimation - Ming Yuan (U. of Wisconsin)
DTSTART:20160524T130000Z
DTEND:20160524T140000Z
UID:TALK65861@talks.cam.ac.uk
CONTACT:Quentin Berthet
DESCRIPTION:Although recovering an Euclidean distance matrix from noisy ob
 servations is a common problem in practice\, how well this could be done r
 emains largely unknown. To fill in this void\, we study a simple distance 
 matrix estimate based upon the so-called regularized kernel estimate. We s
 how that such an estimate can be characterized as simply applying a consta
 nt amount of shrinkage to all observed pairwise distances. This fact allow
 s us to establish risk bounds for the estimate implying that the true dist
 ances can be estimated consistently in an average sense as the number of o
 bjects increases. In addition\, such a characterization suggests an effici
 ent algorithm to compute the distance matrix estimator\, as an alternative
  to the usual second order cone programming known not to scale well for la
 rge problems.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge.
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