Ranking Recovery from Limited Comparisons using Low-Rank Matrix Completion

TL;DR

This paper introduces a low-rank matrix completion approach to rank aggregation from limited, noisy pairwise comparisons, improving preference estimation accuracy over existing methods.

Contribution

It develops a novel matrix completion-based algorithm for rank aggregation that effectively handles partial and noisy comparison data.

Findings

Outperforms state-of-the-art methods in simulations

Accurately recovers preferences from limited data

Effective on real-world comparison datasets

Abstract

This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix form. We then use tools from matrix completion, which has served as a major component in the low-rank completion solution of the Netflix challenge, to construct the preference of the different objects. In our approach, the data of multiple comparisons is used to create an estimate of the probability of object i to win (or be chosen) over object j, where only a partial set of comparisons between N objects is known. The data is then transformed into a matrix form for which the noiseless solution has a known rank of one. An alternating minimization algorithm, in which the target matrix takes a bilinear form, is then used in combination with maximum likelihood estimation for both factors. The reconstructed matrix is used to obtain the true underlying preference intensity. This work demonstrates the improvement of our proposed algorithm over the current state-of-the-art in both simulated scenarios and real data.