论文标题
顶部$ K $排名的绿木匠型号的同心混合物：采样和可识别性
Concentric mixtures of Mallows models for top-$k$ rankings: sampling and identifiability
论文作者
论文摘要
在本文中，我们考虑了两种顶部$ k $排名的摩洛小槌模型的混合物，均具有相同的位置参数，但具有不同的比例参数，即同心钟声模型的混合物。当我们有两个同质人口组成的选民人口异质的情况下，就会出现这种情况，其中一个是对专家选民的亚人群，而另一种则包括非专家选民。我们提出了木狼上$ $ K $排名的有效抽样算法。我们首先将两个组件的可识别性及其在此设置中的可学习性显示，首先将Borda算法的样本复杂性与顶部$ K $排名和第二个界定，并提出了每个组件中排名分离的多项式时间算法。最后，由于等级的聚合将遭受非专家选民引入的大量噪音，因此我们适应了Borda算法，以便能够恢复与专家排名尤其一致的地面真相共识排名。
In this paper, we consider mixtures of two Mallows models for top-$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.
