Learning Mixtures of Plackett-Luce Models

Understand

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 $k\geq 2$, 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 $k\leq\lfloor\frac {m-2} 2\rfloor!$.
• 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.