A fast algorithm for learning large scale preference relations

We consider the problem of learning the ranking function that maximizes a generalization of the Wilcoxon-Mann-Whitney statistic on training data. Relying on an 2-exact approximation for the error-function, we reduce the computational complexity of each iteration of a conjugate gradient algorithm for learning ranking functions from O(m2), to O(m), where m is the size of the training data. Experiments on public benchmarks for ordinal regression and collaborative filtering show that the proposed algorithm is as accurate as the best available methods in terms of ranking accuracy, when trained on the same data, and is several orders of magnitude faster.