Sorting from Noisy Information
Mark Braverman, Elchanan Mossel

TL;DR
This paper develops polynomial-time algorithms for inferring an unknown order from noisy comparison and permutation data, demonstrating that maximum likelihood solutions closely approximate the true order, with applications in ranking systems.
Contribution
It introduces efficient algorithms for maximum likelihood estimation in noisy ranking models, specifically for noisy comparisons and noisy order data, with proven proximity to the true permutation.
Findings
Algorithms solve ranking problems with high probability
Maximum likelihood solutions are close to true order
Applicable to sports and search ranking scenarios
Abstract
This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) on elements denoted by . We assume that information is generated in a way correlated with . The goal is to find a maximum likelihood given the information observed. We will consider two different types of observations: noisy comparisons and noisy orders. The data in Noisy orders are permutations given from an exponential distribution correlated with \pi (this is also called the Mallow's model). The data in Noisy Comparisons is a signal given for each pair of elements which is correlated with their true ordering. In this paper we present polynomial time algorithms for solving both problems with high probability. As part of our proof we show that for both models the maximum likelihood solution is close to the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
