arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1602.04567cs.IRcs.ITcs.LGmath.ITstat.ML
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对抗性最佳- $K$排名

Adversarial Top-$K$ Ranking

Korea Advanced Institute of Science and Technology(韩国科学技术院);National University of Singapore(新加坡国立大学)

Changho Suh, Vincent Y. F. Tan, Renbo Zhao

摘要:

我们研究的顶部- $K$排名的问题,其目标是恢复一组顶部- $K$排名项目出一个大的项目集合的基础上部分显示的偏好。我们考虑一个对抗性众包设置,其中有两个群体集,并且从其中一个群体中抽取的成对比较样本遵循标准Bradley-Terry-Luce模型(即,项目$i$击败项目$j$的机会与项目$i$对项目$j$的相对分数成正比),而在另一个群体中,相应的机会与相对分数成反比。当两个群体的相对大小是已知的,我们的特征所需的样本量的最小最大限度(直到一个常数)可靠地确定前$K$项目,并证明它如何与相对大小的规模。此外,通过利用张量分解方法来消除混合分布的歧义,我们将我们的结果扩展到更现实的情况下,其中的相对人口规模是未知的,从而建立一个上限的基本限制的样本大小恢复顶部$K$集。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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