The Solution Path of the Generalized Lasso

Details The Solution Path of the Generalized Lasso The Solution Path of the Generalized Lasso

2010-05-11

arxiv.org/abs/1005.1971v3

Ann. Statist. Volume 39, Number 3 (2011), 1335-1371

Mathematics

Statistics Theory

32 pages, 10 figures

Scientific paper

We present a path algorithm for the generalized lasso problem. This problem penalizes the $\ell_1$ norm of a matrix $D$ times the coefficient vector, and has a wide range of applications, dictated by the choice of $D$. Our algorithm is based on solving the dual of the generalized lasso, which facilitates computation and conceptual understanding of the path. For $D=I$ (the usual lasso), we draw a connection between our approach and the well-known LARS algorithm. For an arbitrary $D$, we derive an unbiased estimate of the degrees of freedom of the generalized lasso fit. This estimate turns out to be quite intuitive in many applications.

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