Minimax Rates and Efficient Algorithms for Noisy Sorting

Cheng Mao; Jonathan Weed; Philippe Rigollet

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arXiv · 1710.10388

Minimax Rates and Efficient Algorithms for Noisy Sorting

Cheng Mao·Jonathan Weed·Philippe Rigollet

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Abstract

There has been a recent surge of interest in studying permutation-based models for ranking from pairwise comparison data. Despite being structurally richer and more robust than parametric ranking models, permutation-based models are less well understood statistically and generally lack efficient learning algorithms. In this work, we study a prototype of permutation-based ranking models, namely, the noisy sorting model. We establish the optimal rates of learning the model under two sampling procedures. Furthermore, we provide a fast algorithm to achieve near-optimal rates if the observations are sampled independently. Along the way, we discover properties of the symmetric group which are of theoretical interest.

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BibTeX RIS

Cheng Mao, Jonathan Weed, Philippe Rigollet. 2017-10-28. Minimax Rates and Efficient Algorithms for Noisy Sorting. https://arxiv.org/abs/1710.10388

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