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SUMMARY:Compressible priors for high-dimensional statistics - Prof. Volkan
  Cevher\, EPFL
DTSTART:20140611T100000Z
DTEND:20140611T110000Z
UID:TALK52846@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:We develop a principled way of identifying probability distrib
 utions whose independent and identically distributed (iid) realizations ar
 e compressible\, i.e.\, can be approximated as sparse. We focus on the con
 text of Gaussian random underdetermined linear regression (GULR) problems\
 , where compressibilityis known to ensure the success of estimators exploi
 ting sparse regularization. We prove that many of the conventional priors 
 revolving around probabilistic interpretations of the p-norm (p<=1) regula
 rization algorithms are in fact incompressible in the limit of large probl
 em sizes. To show this\, we identify nontrivial undersampling regions in G
 ULR where the simple least squares solution almost surely outperforms an o
 racle sparse solution\, when the data is generated from a prior such as th
 e Laplace distribution. We provide rules of thumb to characterize large fa
 milies of compressible and incompressible priors based on their second and
  fourth moments. Generalized Gaussians and generalized Pareto distribution
 s serve as running examples for concreteness. We then conclude with a stud
 y of the statistics of wavelet coefficients of natural images in the conte
 xt of compressible priors.\n
LOCATION:LR5\, Cambridge University Engineering Department
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