Learning mixtures of permutations: Groups of pairwise comparisons and combinatorial method of moments

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