一组对象的排序：基于图的最小二乘方法
Ranking a set of objects: a graph based least-square approach
摘要：
我们考虑的问题，排名$N$对象从一组嘈杂的成对比较提供了一群平等的工人。我们假设，物体被赋予了内在的品质，一个物体优于另一个物体的概率只取决于两个竞争者的品质之间的差异。我们提出了一类非自适应排名算法，依赖于最小二乘优化标准的质量估计。这种算法被证明是渐近最优的（即，它们要求$O(\frac{N}{ε^2}\log \frac{N}δ)$比较为$(ε, δ)$ -PAC）。数值结果表明，我们的计划是非常有效的，也在许多非渐近的情况下表现出类似的最大似然算法的性能。此外，我们展示了如何将它们扩展到自适应方案，并在真实世界的数据集上进行测试。
英文摘要：
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object is preferred to another depends only on the difference between the qualities of the two competitors. We propose a class of non-adaptive ranking algorithms that rely on a least-squares optimization criterion for the estimation of qualities. Such algorithms are shown to be asymptotically optimal (i.e., they require $O(\frac{N}{ε^2}\log \frac{N}δ)$ comparisons to be $(ε, δ)$-PAC). Numerical results show that our schemes are very efficient also in many non-asymptotic scenarios exhibiting a performance similar to the maximum-likelihood algorithm. Moreover, we show how they can be extended to adaptive schemes and test them on real-world datasets.
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