Title: A computationally efficient non-parametric signal estimation approach for ranking data
Authors: Michael Georg Schimek - Medical University of Graz (Austria) [presenting]
Luca Vitale - University of Salerno (Italy)
Bastian Pfeifer - Medical University of Graz (Austria)
Michele La Rocca - University of Salerno (Italy)
Abstract: The ranking of items is widely used to rate their relative quality or relevance across multiple lists of assessments. Typically, the list length $p$ is in the thousands and the number of lists $n<<p$. Our interest, beyond classical rank aggregation, is to estimate the, usually unobservable, latent signals that inform a consensus ranking. Under the only assumption of independent assessments, we introduce indirect inference via convex optimisation in combination with computationally efficient Poisson Bootstrap. The mathematical formulation of the signal estimation problem is based on pairwise comparisons of all items with respect to their rank positions. The order relations are represented by a system of inequalities for optimisation. The transitivity property of rank scales allows us to reduce substantially the number of constraints associated with the full set of item comparisons. The key idea is the successive reduction of the ranker-induced errors until optimal latent signal estimates are obtained. Its advantage is a substantial reduction in the computational burden and the possibility to handle n<<p data problems. The power of this novel approach is demonstrated in a large bio-medical data problem.