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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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  4:15 p.m., Tuesday, February 20, 2007\\
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  Sequoia Hall Room 200\\
  (Cookies at 3:45 in 1st Floor Lounge)
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  \textsl{Saharon Rosset} \\
  Data Analytics Group\\
  IBM T.J. Watson Research Center
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  \subsection*{$\ell_1$ regularization in infinite dimensional feature spaces}
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\noindent

We discuss the problem of fitting $\ell_1$ regularized prediction
models in infinite (possibly non-countable) dimensional feature
spaces. Our main contributions are: a. Deriving a generalization of
$\ell_1$ regularization based on measures which can be applied in
non-countable feature spaces; b. Proving that the sparsity property
of $\ell_1$ regularization is maintained in infinite dimensions; c.
Devising a path-following algorithm that can generate the set of
regularized  solutions in ``nice'' feature spaces; and d. Presenting
an example of penalized spline models where this path following
algorithm is computationally feasible, and gives encouraging
empirical results.

Joint work with Grzegorz Swirszcz, Nathan Srebro and Ji Zhu


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