Learning Mixtures of Plackett-Luce Models

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 generically identifiable if k ≤ ⌊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.