On aggregation in ranking median regression

In the present era of personalized customer services and rec-ommender systems, predicting the preferences of an individual over a set of items indexed by [n] = {1, ⋯, n}, n ≥ 1, based on its characteristics, modelled as a r.v. X say, is an ubiquitous issue. Though easy to state, this predictive problem referered to as ranking median regression (RMR in short) is very difficult to solve in practice. The major challenge lies in the fact that, here, the (discrete) output space is the symmetric group S_n, composed of all permutations of [n], of explosive cardinality n!, and which is not a subset of a vector space. It is thus far from straightforward to build (non parametric) predictive rules taking their values in S_n, except by means of ranking aggregation techniques implemented at a local level, as proposed in [1] or [2]. However, such local learning techniques exhibit high instability and it is the main goal of this paper to investigate to which extent Kemeny ranking aggregation of randomized RMR rules may remedy this drawback. Beyond a theoretical analysis establishing its validity, the relevance of this novel ensemble learning technique is supported by experimental results.