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SUMMARY:Efficient sparse recovery with no assumption on the dictionary - A
 lexander (Sasha) Tsybakov (CREST et Université Paris)
DTSTART:20080425T130000Z
DTEND:20080425T140000Z
UID:TALK11781@talks.cam.ac.uk
CONTACT:8047
DESCRIPTION:Methods of sparse statistical estimation are mainly of the two
  types. Some of them\, like the BIC\, enjoy nice theoretical properties wi
 thout any assumption on the dictionary but are computationally infeasible 
 starting from relatively modest dimensions p. Others\, like the Lasso or D
 antzig selector\, are easily realizable for very large p but their theoret
 ical performance is conditioned by severe restrictions on the dictionary. 
 The aim of this talk is to propose a new method of sparse recovery in regr
 ession\, density and classification models realizing a compromise between 
 theoretical properties and computational efficiency. The theoretical perfo
 rmance of the method is comparable with that of the BIC in terms of sparsi
 ty oracle inequalities for the prediction risk. No assumption on the dicti
 onary is required\, except for the standard normalization. At the same tim
 e\, the method is computationally feasible for relatively large dimensions
  p. It is constructed using the exponential weighting with suitably chosen
  priors\, and its analysis is based on the PAC-Bayesian ideas in statistic
 al learning. In particular\, we obtain some new PAC-Bayesian bounds with l
 eading constant 1 and we develop a general technique to derive sparsity or
 acle inequalities from the PAC-Bayesian bounds. This is a joint work with 
 Arnak Dalalyan. \n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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