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# Learning Mixtures of Plackett-Luce Models

*Proceedings of The 33rd International Conference on Machine Learning*, PMLR 48:2906-2914, 2016.

#### Abstract

In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any k≥2, the mixture of k Plackett-Luce models for no more than 2k-1 alternatives is non-identifiable and this bound is tight for k=2. For generic identifiability, we prove that the mixture of k Plackett-Luce models over m alternatives is \em generically identifiable if k≤⌊\frac m-2 2⌋!. We also propose an efficient generalized method of moments (GMM) algorithm to learn the mixture of two Plackett-Luce models and show that the algorithm is consistent. Our experiments show that our GMM algorithm is significantly faster than the EMM algorithm by Gormley & Murphy (2008), while achieving competitive statistical efficiency.