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 PlackettLuce 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 and Murphy (2008) , while achieving competitive statistical efficiency.
Zhao et al. REF showed that a mixture of k PlackettLuce models is generically identifiable provided that k ≤ n−2 2 ! and gave a generalized method of moments algorithm that they proved is consistent -meaning that as the number of samples goes to infinity, the algorithm recovers the true parameters.
Learning Mixtures of Plackett-Luce Models
ArXiv
ArXiv
Mathematics Computer Science