[Numpy-discussion] N dimensional dichotomy optimization

[Gael Varoquaux]

On Tue, Nov 23, 2010 at 04:33:00PM +0100, Sebastian Walter wrote:
> At first glance it looks as if a relaxation is simply not possible:
> either there are additional rows or not.
> But with some technical transformations it is possible to reformulate
> the problem into a form that allows the relaxation of the integer
> constraint in a natural way.

> Maybe this is also possible in your case?

Well, given that it is a cross-validation score that I am optimizing,
there is not simple algorithm giving this score, so it's not obvious at
all that there is a possible relaxation. A road to follow would be to
find an oracle giving empirical risk after estimation of the penalized
problem, and try to relax this oracle. That's two steps further than I am
(I apologize if the above paragraph is incomprehensible, I am getting too
much in the technivalities of my problem.

> Otherwise, well, let me know if you find a working solution ;)

Nelder-Mead seems to be working fine, so far. It will take a few weeks
(or more) to have a real insight on what works and what doesn't.

Thanks for your input,

Gael