A better CORN loss function

[hoangmit]

I don't see the discussion in the main CORN repo, thus I post it here.

The complexity and memory of the current CORN loss function is O(N * K) where N is the number of examples, and K is the number of ranks.

I think it can be computed in O(N) (or O(N * log(K)) if you are lazy). This is better for large K e.g. the age dataset.

Basically, you just need to sort by the label values. The 2 sum loops can be collapsed into one, as log(f(x)) and log(1-f(x)) are unchanged. Just telescope the the indicator function as the training subsets are subsets of each others.

[hoangmit]

My bad, the f(x) in each loop is not the same.