In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we propose a polynomial-time algorithm that learns a Mallows mixture of permutations on $n$ elements with the optimal sample complexity that is proportional to $\log n$, improving upon previous results that scale polynomially with $n$. In the high-noise regime, we characterize the optimal dependency of the sample complexity on the noise parameter. Both objectives are accomplished by first studying demixing permutations under a noiseless query model using groups of pairwise comparisons, which can be viewed as moments of the mixing distribution, and then extending these results to the noisy Mallows model by simulating the noiseless oracle.

中文翻译：

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学习混合排列：成对比较组和矩的组合方法

在秩聚合等应用中，当种群表现出异质性时，经常使用排列的混合模型。在这项工作中，我们研究了广泛使用的 Mallows 混合模型。在高维设置中，我们提出了一种多项式时间算法，该算法可以学习 $n$ 元素上的 Mallows 排列组合，其最佳样本复杂度与 $\log n$ 成正比，改进了先前以多项式方式缩放的结果n$。在高噪声状态下，我们表征了样本复杂度对噪声参数的最佳依赖性。这两个目标都是通过首先使用成对比较组在无噪声查询模型下研究去混合排列来实现的，这可以看作是混合分布的时刻，