I finally found a desk and some focus. I addressed Mathieu's
suggestions and added some timings on real data (with a lot of
concessions so that it would run reasonably quick on my machine).

Here's the results: http://nbviewer.ipython.org/7224672

It becomes clear that `tol` still means different things between the
two solvers. I think the convergence plots are interesting, not only
confirming that the solvers work well but it seems that for tall
sparse data, projected gradient is better.

The non-convergence in the first scenario seems data-dependent (it
didn't happen yesterday).

L1 regularization seems all the more helpful on real data, I would
have expected the slowest two curves to be the other way around
though.
Active set becomes unusably slow, which explains the issue re: slow
performance in transform.

Cheers,
Vlad

On Fri, Nov 8, 2013 at 12:48 PM, Gael Varoquaux
<gael.varoqu...@normalesup.org> wrote:
> On Fri, Nov 08, 2013 at 11:56:24AM +0100, Olivier Grisel wrote:
>> In retrospect I would have prefered it named something explicit like
>> "regularization" or "l2_reg" instead of "alpha".
>
> Agreed.
>
>> Still I like the (alpha, l1_ratio) parameterization better over the
>> (l2_reg, l1_reg) parameter set
>
> Absolutely.
>
> G
>
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