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CATEGORIES:Statistics
SUMMARY:Efficient sparse recovery with no assumption on th
e dictionary - Alexander (Sasha) Tsybakov (CREST e
t Université Paris)
DTSTART;TZID=Europe/London:20080425T140000
DTEND;TZID=Europe/London:20080425T150000
UID:TALK11781AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/11781
DESCRIPTION:Methods of sparse statistical estimation are mainl
y of the two types. Some of them\, like the BIC\,
enjoy nice theoretical properties without any assu
mption on the dictionary but are computationally i
nfeasible starting from relatively modest dimensio
ns p. Others\, like the Lasso or Dantzig selector\
, are easily realizable for very large p but their
theoretical performance is conditioned by severe
restrictions on the dictionary. The aim of this ta
lk is to propose a new method of sparse recovery i
n regression\, density and classification models r
ealizing a compromise between theoretical properti
es and computational efficiency. The theoretical p
erformance of the method is comparable with that o
f the BIC in terms of sparsity oracle inequalities
for the prediction risk. No assumption on the dic
tionary is required\, except for the standard norm
alization. At the same time\, the method is comput
ationally feasible for relatively large dimensions
p. It is constructed using the exponential weight
ing with suitably chosen priors\, and its analysis
is based on the PAC-Bayesian ideas in statistical
learning. In particular\, we obtain some new PAC-
Bayesian bounds with leading constant 1 and we dev
elop a general technique to derive sparsity oracle
inequalities from the PAC-Bayesian bounds. This i
s a joint work with Arnak Dalalyan. \n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:
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