In this paper, we consider mixtures of two Mallows models for top-$k$ 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-$k$ 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-$k$ 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.

本文主要研究包含两种Mallows模型的混合模型，用于对包含专家和非专家评委的异质性选民群体进行排名。在此基础上，针对数据中的噪声和非专家评委造成的影响，对Borda算法进行了改进，以便能够更好地还原“专家排名”的排名。

基于Mallows模型的同心混合模型用于top-$k$排名:采样与可识别性