I am learning about the "pairwise approach" for learning to rank. As far as I understood, the training output is a partial ranking function $r$ that:

  • given given some query $q$ and two document $d_i$ and $d_j$
  • predicts whether $$r(d_i)>r(d_j)$$ or not

However, for a IR system to work, the ranking should be absolute.

The natural question next is how to construct the absolute rank using only the partial ranks output by $r$?

But partial ranks does not guarantee absolute rank. For example

$$r(x)>r(y), r(y)>r(z), r(z)>r(x)$$ gives a cycle.

I guess I am misunderstanding about how pairwise approach works for IR system. Can anyone correct me?


1 Answer 1


Creating a total ranking from pairwise comparisons that don’t necessarily follow the axioms or rational preferences would certainly require some optimization, and you would need to compute a quadratic number of such comparisons in order to produce a ranking.

There is however one trick to do this easily: if the function that classifies whether one element is ranked above the other is linear in all the features, you can, intuitively, compare each element to a null element (i.e. just apply the decision function to the element alone), get a score assigned to them, and sort them by this score.

So, intuitively, your linear classifier would be something like this: element 1 is above element 2 if: F(el1 – el2)>0 [function has to be symmetrical, thus there can't be a non-zero threshold] --> F(el1) – F(el2) >0 (only when F is linear!!!) Which implies that el1 > el2 iff F(el1)>F(el2)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.