Re: [eigen] Does anyone know of a good l1-solver? |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Does anyone know of a good l1-solver?*From*: Márton Danóczy <marton78@xxxxxxxxx>*Date*: Tue, 17 Apr 2012 15:27:15 +0200*Dkim-signature*: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :content-type; bh=9y3ejJtDUJSBeTRfqniipAr5zkdhT6UmpG2czLTDUfo=; b=dCXnhysHiWuluWf4bGLwWcy451EQ29NBIOjEdzDvYpvJgh3f5tDSxouYBQZj0w/HE0 4TdKmRyqdZrgayXZSiV6vhlF5HOboijHGaiujaQoMsTaipbAOQAxwsxMmX4Of7w5ljtJ pyqpiAcjU/96VksWrJYchUDhBlJ+sEX/BROs+MIjNu9b2lBZ8a10M+vBElOMONGSHUhY uGgW7E1zVrZTTdbgfQ6/J9zvxbHooSRIFLi45SMxUjsU73OqN7gI+Szw/Xip3kxJKUj+ TnqE0/ZHC64g1SzzvbX0nrSOGqtwqWDHwT6QFkIzoBIe/hGg9++oWswHfjcjlPXheTcy Bktg==

Hi Anil, you mentioning L1 magic and primal-dual solvers makes me guess that you actually want to solve argmin ||Ax-b||^2_2 + a ||x||_1? That is, quadratic loss with L1-penalty, aka LASSO? In this case, I can recommend the orthant-wise limited-memory quasi-Newton (OWLQN) algorithm. Actually, it can solve f(Ax-b) + ||W x||_1, where f is a smooth convex loss and W is diagonal. There is a good implementation as part of the libBFGS [2] library. I have taken this implementation and eigenified it, if you (or somebody else) is interested, I can send it per Email. Or even push it to Eigen/unsupported? I have used it from MATLAB in the past (there's also a mex file wrapper) and found it to work ok, as long as there are not too many variables (then, convergence can be slow). A better behaved method is DAL [3], however, to my knowledge, there is only a MATLAB implementation. In case your loss function is really 1-norm, I think the standard method is called "column generation" but I have never used it. [1]: http://nlp.stanford.edu/~pupochik/papers/andrew07scalable.pdf [2]: http://www.chokkan.org/software/liblbfgs/ [3]: http://www.ibis.t.u-tokyo.ac.jp/ryotat/dal/ HTH, Marton On 17 April 2012 14:38, cr.anil@xxxxxxxxx <cr.anil@xxxxxxxxx> wrote: >> Either that, or maybe find x, s.t. ||Ax - b||_1=min ? >> > Yes this is what I want to solve although I want to add a l2 regulariser > sometime later to this. > >> Do you know anything about A? (sparse, square, symmetric, rank-deficient, >> ill-conditioned, ...) >> > No. A is a dense matrix and full rank but I do know that it has 6 columns > and 3N rows. > >> Anyways, afaik, Eigen itself does not provide L1-solvers, so you need to >> find an external library anyways (or find an algorithm and implement it). It >> is quite easy to interact with other libraries by using Eigen's Map and >> .data() functionality. > > Hmmm... I thought it would be nice if there was a efficient library which > did this since I run the optimisation in a loop. > > Also is the primal dual technique the most efficient for this problem? > That's what I found in a matlab library called l1 magic. > > Anil

**Follow-Ups**:**Re: [eigen] Does anyone know of a good l1-solver?***From:*Rodrigo Benenson

**References**:**[eigen] Does anyone know of a good l1-solver?***From:*cr.anil@xxxxxxxxx

**Re: [eigen] Does anyone know of a good l1-solver?***From:*Helmut Jarausch

**Re: [eigen] Does anyone know of a good l1-solver?***From:*Markus Moll

**Re: [eigen] Does anyone know of a good l1-solver?***From:*Christoph Hertzberg

**Re: [eigen] Does anyone know of a good l1-solver?***From:*cr.anil@xxxxxxxxx

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