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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY:Compressible priors for high-dimensional statistic
s - Prof. Volkan Cevher\, EPFL
DTSTART;TZID=Europe/London:20140611T110000
DTEND;TZID=Europe/London:20140611T120000
UID:TALK52846AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52846
DESCRIPTION:We develop a principled way of identifying probabi
lity distributions whose independent and identical
ly distributed (iid) realizations are compressible
\, i.e.\, can be approximated as sparse. We focus
on the context of Gaussian random underdetermined
linear regression (GULR) problems\, where compress
ibilityis known to ensure the success of estimator
s exploiting sparse regularization. We prove that
many of the conventional priors revolving around p
robabilistic interpretations of the p-norm (p<=1)
regularization algorithms are in fact incompressib
le in the limit of large problem sizes. To show th
is\, we identify nontrivial undersampling regions
in GULR where the simple least squares solution al
most surely outperforms an oracle sparse solution\
, when the data is generated from a prior such as
the Laplace distribution. We provide rules of thum
b to characterize large families of compressible a
nd incompressible priors based on their second and
fourth moments. Generalized Gaussians and general
ized Pareto distributions serve as running example
s for concreteness. We then conclude with a study
of the statistics of wavelet coefficients of natur
al images in the context of compressible priors.\n
LOCATION:LR5\, Cambridge University Engineering Department
CONTACT:Prof. Ramji Venkataramanan
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