Adversarial Top-K Ranking

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We study the top-K ranking problem where the goal is to recover the set of top-K ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are two population sets, and pairwise comparison samples drawn from one of the populations follow the standard Bradley-Terry-Luce model (i.e., the chance of item i beating item j is proportional to the relative score of item i to item j), while in the other population, the corresponding chance is inversely proportional to the relative score. When the relative size of the two populations is known, we characterize the minimax limit on the sample size required (up to a constant) for reliably identifying the top-K items, and demonstrate how it scales with the relative size. Moreover, by leveraging a tensor decomposition method for disambiguating mixture distributions, we extend our result to the more realistic scenario, in which the relative population size is unknown, thus establishing an upper bound on the fundamental limit of the sample size for recovering the top-K set.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2017-04
Language
English
Article Type
Article; Proceedings Paper
Keywords

LATENT VARIABLE MODELS

Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.63, no.4, pp.2201 - 2225

ISSN
0018-9448
DOI
10.1109/TIT.2017.2659660
URI
http://hdl.handle.net/10203/223598
Appears in Collection
EE-Journal Papers(저널논문)
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