Magnitude-preserving ranking algorithms

This paper studies the learning problem of ranking when one wishes not just to accurately predict pairwise ordering but also preserve the magnitude of the preferences or the difference between ratings, a problem motivated by its key importance in the design of search engines, movie recommendation, and other similar ranking systems. We describe and analyze several algorithms for this problem and give stability bounds for their generalization error, extending previously known stability results to non-bipartite ranking and magnitude of preference-preserving algorithms. We also report the results of experiments comparing these algorithms on several datasets and compare these results with those obtained using an algorithm minimizing the pairwise misranking error and standard regression.