  We study the problem of ranking a set of items from nonactively chosen
pairwise preferences where each item has feature information with it. We
propose and characterize a very broad class of preference matrices giving rise
to the Feature Low Rank (FLR) model, which subsumes several models ranging from
the classic Bradley-Terry-Luce (BTL) (Bradley and Terry 1952) and Thurstone
(Thurstone 1927) models to the recently proposed blade-chest (Chen and Joachims
2016) and generic low-rank preference (Rajkumar and Agarwal 2016) models. We
use the technique of matrix completion in the presence of side information to
develop the Inductive Pairwise Ranking (IPR) algorithm that provably learns a
good ranking under the FLR model, in a sample-efficient manner. In practice,
through systematic synthetic simulations, we confirm our theoretical findings
regarding improvements in the sample complexity due to the use of feature
information. Moreover, on popular real-world preference learning datasets, with
as less as 10% sampling of the pairwise comparisons, our method recovers a good
ranking.
