基于成对比较的在线排名聚合的随机迭代方法
Stochastic Iterative Methods for Online Rank Aggregation from Pairwise Comparisons
AI总结：
本文提出基于随机梯度下降的在线排名聚合方法，在低内存条件下从成对比较中恢复潜在排名，并通过理论证明和实验分析了完全、部分及噪声观测下的收敛性与噪声容忍度。
摘要：
在本文中，我们考虑大规模排名问题，其中给定一组（可能是非冗余的）成对比较，并希望得到由这些比较所解释的潜在排名。我们表明，可以利用随机梯度下降方法在低内存运算的条件下收敛到一个能够揭示潜在排名的解。我们引入了该方法的几种变体，当成对比较存在噪声时（即某些比较不符合潜在排名），这些变体在速度和收敛性之间提供了权衡。我们证明了几乎必然收敛的理论结果，并研究了包括完全观测、部分观测和噪声观测在内的几种情形。我们的实证结果给出了关于所需观测数量以及这些测量中可容忍噪声程度的见解。
英文摘要：
In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent approaches can be leveraged to offer convergence to a solution that reveals the underlying ranking while requiring low-memory operations. We introduce several variations of this approach that offer a tradeoff in speed and convergence when the pairwise comparisons are noisy (i.e., some comparisons do not respect the underlying ranking). We prove theoretical results for convergence almost surely and study several regimes including those with full observations, partial observations, and noisy observations. Our empirical results give insights into the number of observations required as well as how much noise in those measurements can be tolerated.
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。
