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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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\begin{center}
  4:15pm, Tuesday, May 15, 2007\\
  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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\begin{center}
  \textsl{Rob Tibshirani} \\
  Department of Statistics\\
Stanford University
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\begin{center}
  \subsection*{Pathwise coordinate optimization}
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I consider ``one-at-a-time'' coordinate-wise descent algorithms 
for a class of convex optimization problems. An algorithm of this 
kind has been proposed for the L$_1$-penalized regression (lasso) 
in the literature, but it seems to have been largely ignored.  
Indeed, it seems that coordinate-wise algorithms are not  often 
used  in convex optimization.  

I show that this algorithm is very 
competitive with the well known LARS (or homotopy) procedure in 
large lasso problems, and that it can be applied to related 
methods such as the garotte and elastic net. It turns out that 
coordinate-wise descent does not work in the ``fused lasso'' 
however, so we derive a generalized  algorithm that yields the 
solution in much less time that a standard convex optimizer. 
Finally we generalize the  procedure to the two-dimensional 
fused lasso, and demonstrate its performance on some image 
smoothing problems.  

This is joint work wth Jerome Friedman and Trevor Hastie  
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