Multivariate Spearman’s rho for rank aggregation

We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Our main contribution is the derivation of a nonparametric 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 or worst elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman’s ρ. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008.