Learning Mixtures of Ranking Models

This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a {\em Mallows Mixture Model}. Despite being widely studied, current heuristics for this problem do not have theoretical guarantees and can get stuck in bad local optima. We present the first polynomial time algorithm which provably learns the parameters of a mixture of two Mallows models. A key component of our algorithm is a novel use of tensor decomposition techniques to learn the top-$k$ prefix in both the rankings. Before this work, even the question of {\em identifiability} in the case of a mixture of two Mallows models was unresolved.