Learning Mixtures of Ranking Models

TL;DR

This paper introduces the first polynomial-time algorithm with theoretical guarantees for learning the parameters of a mixture of two Mallows models, using tensor decomposition to identify the top-k prefix in ranking data.

Contribution

It provides the first provably correct polynomial-time method for learning parameters of a two-component Mallows mixture model, addressing previous gaps in identifiability and algorithmic guarantees.

Findings

Algorithm is polynomial-time and provably correct.

Successfully learns parameters of a two-Mallows mixture.

Addresses identifiability issues in mixture models.

Abstract

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.