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Ryan Tibshirani introduced once a more general type of Lasso, where the regularizer is $$\parallel D \alpha \parallel_1$$ instead of $\parallel \alpha \parallel_1$. See paper

However, there is nearly no discussion about this form and I wonder why since its a great way to deal with derivative smoothness regularizers.

  • Is there an easy way I overlooked to transform a general Lasso to the standard Lasso form?

  • Which algorithm can be used for the gen. lasso? Currently I only tested quadratic programs, but this is quite slow.

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  • $\begingroup$ The main topic of that paper you linked to is answering the two bullets in your question! The answers are: 1) in general no, and 2) yes, but it's generally slower than algorithms for the standard lasso. See another paper by Ryan Tibshirani for an application to "derivative smoothness" regularization: arxiv.org/abs/1304.2986 $\endgroup$
    – vqv
    Commented Nov 28, 2013 at 18:07
  • $\begingroup$ Wow! Thank you so much for the hint to the paper! Looks very interesting. I will definitely take a close look on it. As for the General Lasso Form, I ended up using the "split bregman" method to compute the solution of a "general lasso" problem. In most cases it is much faster then a quadratic program. $\endgroup$
    – mojovski
    Commented Nov 29, 2013 at 21:20
  • $\begingroup$ Add "Is there an easy way I overlooked to transform a general Lasso to the standard Lasso form?" - am I wrong in thinking that using D=diag(1,p) (a diagonal matrix with 1 values on diagonal) leads to a starndard Lasso form? $\endgroup$
    – Marta Karas
    Commented Feb 25, 2016 at 15:13
  • $\begingroup$ @Marta, yes, but you dont choose D usually. Its set by the applicaiton. When D is not diagonal, then its not a standard Lasso.:) $\endgroup$
    – mojovski
    Commented Feb 26, 2016 at 8:28

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Partially answered in comments:

The main topic of that paper you linked to is answering the two bullets in your question! The answers are: 1) in general no, and 2) yes, but it's generally slower than algorithms for the standard lasso. See another paper by Ryan Tibshirani for an application to "derivative smoothness" regularization: https://arxiv.org/abs/1304.2986 – vqv

( Wow! Thank you so much for the hint to the paper! Looks very interesting. I will definitely take a close look on it. As for the General Lasso Form, I ended up using the "split bregman" method to compute the solution of a "general lasso" problem. In most cases it is much faster then a quadratic program. – mojovski )

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