Multivariate Spearman's rho for aggregating ranks using copulas
This addresses rank aggregation problems in information retrieval and recommendation systems, but is an incremental extension of existing correlation methods.
The paper tackles rank aggregation from multiple ranked lists, including cases with only extreme ranks (best/worst elements), by developing a non-parametric estimator based on multivariate Spearman's rho using copulas. It demonstrates good performance on MQ2007 and MQ2008 benchmarks.
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 by the average value and generalise Spearman's ρto 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 ρis 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.