Clustering and Inference From Pairwise Comparisons
Abstract
Given a set of pairwise comparisons, the classical ranking problem computes a single ranking that best represents the preferences of all users. In this paper, we study the problem of inferring individual preferences, arising in the context of making personalized recommendations. In particular, we assume users form clusters; users of the same cluster provide similar pairwise comparisons for the items according to the Bradley-Terry model. We propose an efficient algorithm to estimate the preference for each user: first, compute the net-win vector for each user using the comparisons; second, cluster the users based on the net-win vectors; third, estimate a single preference for each cluster separately. We show that the net-win vectors are much less noisy than the high dimensional vectors of pairwise comparisons, therefore our algorithm can cluster the users reliably. Moreover, we show that, when a cluster is only approximately correct, the maximum likelihood estimation for the Bradley-Terry model is still close to the true preference.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 15, 2015
- Source ID
- 10.1145/2796314.2745887
Entities
People
- Bruce Hajek
- Jiaming Xu
- Laurent Massoulie
- Marc Lelarge
- Rayadurgam Srikant
- Rui Wu
Organizations
- Air Force Office of Scientific Research
- Institut National de Recherche en Informatique et en Automatique
- University of Illinois Urbana–Champaign