A Margin-based MLE for Crowdsourced Partial Ranking

TL;DR

This paper introduces a margin-based MLE framework for learning probabilistic partial orders from crowdsourced pairwise comparisons, effectively capturing inherent data ambiguity and improving ranking accuracy.

Contribution

It proposes a novel convex optimization approach for partial order modeling using margin-based MLE, extending traditional models with theoretical analysis and empirical validation.

Findings

The models outperform traditional algorithms on simulated data.

The framework effectively captures data ambiguity in crowdsourced rankings.

Theoretical guarantees are provided for the proposed models.

Abstract

A preference order or ranking aggregated from pairwise comparison data is commonly understood as a strict total order. However, in real-world scenarios, some items are intrinsically ambiguous in comparisons, which may very well be an inherent uncertainty of the data. In this case, the conventional total order ranking can not capture such uncertainty with mere global ranking or utility scores. In this paper, we are specifically interested in the recent surge in crowdsourcing applications to predict partial but more accurate (i.e., making less incorrect statements) orders rather than complete ones. To do so, we propose a novel framework to learn some probabilistic models of partial orders as a \emph{margin-based Maximum Likelihood Estimate} (MLE) method. We prove that the induced MLE is a joint convex optimization problem with respect to all the parameters, including the global ranking scores and margin parameter. Moreover, three kinds of generalized linear models are studied, including the basic uniform model, Bradley-Terry model, and Thurstone-Mosteller model, equipped with some theoretical analysis on FDR and Power control for the proposed methods. The validity of these models are supported by experiments with both simulated and real-world datasets, which shows that the proposed models exhibit improvements compared with traditional state-of-the-art algorithms.