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We study the problem of rank aggregation: given a set of ranked lists, wewant to form a consensus ranking. Furthermore, we consider the case of extremelists: i.e., only the rank of the best or worst elements are known. We imputemissing ranks by the average value and generalise Spearman's \rho to extremeranks. Our main contribution is the derivation of a non-parametric estimatorfor rank aggregation based on multivariate extensions of Spearman's \rho, whichmeasures correlation between a set of ranked lists. Multivariate Spearman's\rho is defined using copulas, and we show that the geometric mean ofnormalised ranks maximises multivariate correlation. Motivated by this, wepropose a weighted geometric mean approach for learning to rank which has aclosed form least squares solution. When only the best or worst elements of aranked list are known, we impute the missing ranks by the average value,allowing us to apply Spearman's \rho. Finally, we demonstrate good performanceon the rank aggregation benchmarks MQ2007 and MQ2008.

Multivariate Spearman's rho for aggregating ranks using copulas