Learning mixtures of permutations: Groups of pairwise comparisons and combinatorial method of moments
针对Mallows混合模型，提出一种多项式时间算法，在样本复杂度与噪声依赖上达到最优，通过成对比较组模拟无噪声查询实现。
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 logn, 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.