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  \textbf{\Large{\textsc{STANFORD UNIVERSITY}}}\\[5pt]
  \textbf{\Large{\textsc{DEPARTMENT OF STATISTICS}}}\\[5pt]
  \Large{\textsc{DEPARTMENTAL SEMINAR}}
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  %% Time of talk, Weekday, Date of talk\\
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  4:15 p.m., Tuesday, February 26th, 2008\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Philippe Rigollet} \\
  Georgia Tech
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  \subsection*{Stochastic convex optimization using mirror averaging algorithms}
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\noindent
Several statistical problems where the goal is to minimize an unknown  
convex risk function, can be formulated in the general framework of  
stochastic convex optimization. For example the problem of model  
selection and more generally of aggregation can be treated using the  
machinery of stochastic optimization in several frameworks including  
density estimation, regression and convex classification. We describe  
a family of general algorithms called "mirror averaging algorithms"  
that yield an estimator (or a classifier) which attains optimal rates  
of model selection in several interesting cases. The theoretical  
results are presented in the form of exact oracle inequalities similar  
to those employed in optimization theory. The practical performance of  
the algorithms is illustrated on several real and artificial examples  
and compared to standard estimators or classifiers.
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