Computing Parametric Ranking Models via Rank-Breaking

Rank breaking is a methodology introduced by Azari Soufiani et al. (2013a) for applying a Generalized Method of Moments (GMM) algorithm to the estimation of parametric ranking models. Breaking takes full rankings and breaks, or splits them up, into counts for pairs of alternatives that occur in particular positions (e.g., first place and second place, second place and third place). GMMs are of interest because they can achieve significant speed-up relative to maximum likelihood approaches and comparable statistical efficiency. We characterize the breakings for which the estimator is consistent for random utility models (RUMs) including Plackett-Luce and Normal-RUM, develop a general sufficient condition for a full breaking to be the only consistent breaking, and provide a trichotomy theorem in regard to single-edge breakings. Experimental results are presented to show the computational efficiency along with statistical performance of the proposed method.