"parallel" multinomial logit

[paolo-losi]

Hi Fabian,

I'm working on a dense problem (n_samples=1000, n_features=32000)
for which classical formulation of ordinal logistic regression is somewhat
too constrained.

As an alternative I was considering standard multinomial logit
with the constraint that the sigmoid functions should be parallel.

This would be less restricted than ordinal logistic regression since
the "slopes" of the sigmoids would be allowed to be different
while avoiding any crossing of the curves.

The questions are:

1. Do you thing such an optimization target loss would be useful?
   Would it be in scope with minirank? Are you aware of any
   paper related to this approach?

2. Since manual derivation of gradient and hessian is quite heavy and
   error prone, is there any automatic differentiation framework that you
   have tested or you would suggest? Have you done any experiment
   with automatic differentiation?

3. While being definitely out of scope for minirank. I would be nice to have
   a l2 penalized logistic package for dense/sparse problems based on
   pytron solving multinomial logit (with/without parallel constraint) and
   ordinal regression based on pytron ...

Thanks!
Paolo