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Anomaly Ranking as Supervised Bipartite Ranking
Authors: Stephan Clémençon and Sylvain Robbiano
Conference: Proceedings of the 31st International Conference on Machine Learning (ICML-14)
Abstract: The Mass Volume (MV) curve is a visual tool to evaluate the performance of a scoring function with regard to its capacity to rank data in the same order as the underlying den- sity function. Anomaly ranking refers to the unsupervised learning task which consists in building a scoring function, based on unla- beled data, with a MV curve as low as pos- sible at any point. In this paper, it is proved that, in the case where the data generat- ing probability distribution has compact sup- port, anomaly ranking is equivalent to (su- pervised) bipartite ranking, where the goal is to discriminate between the underlying prob- ability distribution and the uniform distribu- tion with same support. In this situation, the MV curve can be then seen as a simple trans- form of the corresponding ROC curve. Ex- ploiting this view, we then show how to use bipartite ranking algorithms, possibly com- bined with random sampling, to solve the MV curve minimization problem. Numeri- cal experiments based on a variety of bipar- tite ranking algorithms well-documented in the literature are displayed in order to illus- trate the relevance of our approach.
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