2020/09/14 by Cheng Mao, Yihong Wu, Mao, Cheng +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Census and Population Estimation #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2009.06784
openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.