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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, May 27, 2003}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Rob Tibshirani}
\centerline{\sl Stanford University}
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\centerline{\bf Stagewise algorithms and the lasso}
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Abstract:

The Lasso (Tibshirani 1996) is  a  method for regularizing least squares
regression via L1 constraints. The  LAR (Least angle regression)
algorithm of (Efron et al 2003) provides an efficient method for
computing the entire sequence of Lasso solutions. In the process,
the LAR algorithm also provides a conceptual link between the Lasso and
Forward Stagewise regression. The latter strategy is an important
component in adaptive regression procedures like boosting, and hence
this link helps us understand how boosting works.

In this talk we derive the criterion that is optimized by Forward
Stagewise regression: it features  a  minimimum L1 arc-length penalty.
We also characterize problems for which the coefficient curves for Lasso
are monotone as a function of the L1 norm; this is the situation where
all three procedures (LAR, Lasso, and Forward Stagewise) coincide.

This is joint work with Trevor Hastie, Jonathan Taylor, and Guenther
Walther.


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