Multivariate spearman's ρ for aggregating ranks using copulas
Multivariate spearman's ρ for aggregating ranks using copulas
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发表时间：
2016
影响因子：
6
通讯作者：
J. Bedő;Cheng Soon Ong
中科院分区：
文献类型：
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作者：
J. Bedő;Cheng Soon Ong
我们研究排名聚合问题：给定一组排序列表，我们希望形成一个共识排名。此外，我们考虑极端列表的情况：即，只有最好或最差元素的排名是已知的。我们填补缺失的排名，并将斯皮尔曼等级相关系数ρ推广到极端排名。我们的主要贡献是基于斯皮尔曼等级相关系数ρ的多元扩展推导出一种用于排名聚合的非参数估计量，它衡量一组排序列表之间的相关性。多元斯皮尔曼等级相关系数ρ是使用连接函数定义的，并且我们表明归一化排名的几何平均值使多元相关性最大化。受此启发，我们提出一种加权几何平均方法用于学习排序，该方法具有封闭形式的最小二乘解。当只有排序列表中最好的（前k个）或最差的（后k个）元素是已知的时，我们用平均值填补缺失的排名，这使我们能够应用斯皮尔曼等级相关系数ρ。我们讨论了缺失值的乐观和悲观填补，它们分别使相关性最大化和最小化，并展示了其对大学排名聚合的影响。最后，我们在排名聚合基准MQ2007和MQ2008上展示了良好的性能。
We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks and generalise Spearman's ρ to extreme ranks. Our main contribution is the derivation of a non-parametric estimator for rank aggregation based on multivariate extensions of Spearman's ρ, which measures correlation between a set of ranked lists. Multivariate Spearman's ρ is defined using copulas, and we show that the geometric mean of normalised ranks maximises multivariate correlation. Motivated by this, we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution. When only the best (top-k) or worst (bottom-k) elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman's ρ. We discuss an optimistic and pessimistic imputation of missing values, which respectively maximise and minimise correlation, and show its effect on aggregating university rankings. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008.