Learning Mixtures of Ranking Models
This solves a foundational problem in ranking data analysis for heterogeneous populations, addressing a previously unresolved identifiability issue.
The authors tackled the problem of learning parameters for a mixture of two Mallows ranking models, which lacked theoretical guarantees and could get stuck in local optima, by developing the first polynomial-time algorithm that provably learns these parameters.
This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a 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 identifiability in the case of a mixture of two Mallows models was unresolved.