Learning Rankings via Convex Hull Separation

Abstract

We propose efficient algorithms for learning ranking functions from or- der constraints between sets—i.e. classes—of training samples. Our al- gorithms may be used for maximizing the generalized Wilcoxon Mann Whitney statistic that accounts for the partial ordering of the classes: spe- cial cases include maximizing the area under the ROC curve for binary classification and its generalization for ordinal regression. Experiments on public benchmarks indicate that: (a) the proposed algorithm is at least as accurate as the current state-of-the-art; (b) computationally, it is sev- eral orders of magnitude faster and—unlike current methods—it is easily able to handle even large datasets with over 20,000 samples.