\documentclass[11pt]{article}
\setlength{\oddsidemargin}{0.0truein}
\setlength{\evensidemargin}{0.0truein}
\setlength{\textwidth}{6.5truein}
\setlength{\topmargin}{0.0truein}
\setlength{\textheight}{9.0truein} \setlength{\headsep}{0.0truein}
\setlength{\headheight}{0.0truein} \setlength{\topskip}{10.0pt}
\setlength{\parskip}{5mm}
\usepackage{url}
\begin{document}

\begin{center}
  \textbf{\textsc{STANFORD UNIVERSITY}}\\[5pt]
  \textbf{\textsc{DEPARTMENT OF STATISTICS}}\\[5pt]
  \Large{\textbf\textsc{{DEPARTMENTAL SEMINAR}}}
\end{center}

\begin{center}
  4:15 p.m., Tuesday, May 30, 2006\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
\end{center}

\begin{center}
  \textsl{Hui Zou}\\
School of Statistics,  University of Minnesota
\end{center}

\begin{center}
  \textbf{The Adaptive Lasso and Its Oracle Properties    } 
\end{center}

\noindent
The lasso (or $\ell_1$ penalization) is famous for its ability to 
automatically produce a sparse subset model. It has been shown
that the $\ell_1$ penalization approach can discover the "right" 
sparse representation of the model under certain conditions (e.g.,
orthogonal design). The LARS algorithm (Efron, Hastie, Johnstone 
and Tibshirani 2004, Annals of Stat.) further facilitates the 
applications of the lasso in practice. The $\ell_1$ shrinkage 
method now seems to become {\it the default choice} for building 
a sparse model. 

\noindent
In this talk, we first show a necessary condition for the lasso
variable selection to be consistent. We present some examples in
which the lasso is inconsistent for variable selection. In the
second part of the talk, we propose a new version of the lasso,
called the adaptive lasso, where adaptive weights are used for
penalizing different coefficients in the $\ell_1$ penalty. We show
that the adaptive lasso is consistent in variable selection, and 
in addition, it possesses the oracle properties using the language 
in Fan and Li (2001, JASA). A new oracle inequality is
derived to show that the adaptive lasso shrinkage is near minimax
optimal in the sense of Donoho and Johnstone (1994, Biometrika).
As a byproduct of our analysis, Breiman's nonnegative garotte is
shown to be consistent for variable selection. 

\noindent
If time permits, we will also discuss the extension of the adaptive
lasso in generalized linear models, survival models and the 
support vector machines.



\end{document}