Concentric mixtures of Mallows models for top-$k$ rankings: sampling and identifiability
Abstract
In this paper, we consider mixtures of two Mallows models for top- rankings, both with the same location parameter but with different scale parameters, i.e., a mixture of concentric Mallows models. This situation arises when we have a heterogeneous population of voters formed by two homogeneous populations, one of which is a subpopulation of expert voters while the other includes the non-expert voters. We propose efficient sampling algorithms for Mallows top- rankings. We show the identifiability of both components, and the learnability of their respective parameters in this setting by, first, bounding the sample complexity for the Borda algorithm with top- rankings and second, proposing polynomial time algorithm for the separation of the rankings in each component. Finally, since the rank aggregation will suffer from a large amount of noise introduced by the non-expert voters, we adapt the Borda algorithm to be able to recover the ground truth consensus ranking which is especially consistent with the expert rankings.
Keywords
Cite
@article{arxiv.2010.14260,
title = {Concentric mixtures of Mallows models for top-$k$ rankings: sampling and identifiability},
author = {Collas Fabien and Irurozki Ekhine},
journal= {arXiv preprint arXiv:2010.14260},
year = {2020}
}