Robust Novelty Detection with Single-Class MPM

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Laurent Ghaoui, Michael Jordan, Gert Lanckriet


the "single-class minimax probabil(cid:173)

In this paper we consider the problem of novelty detection, pre(cid:173) senting an algorithm that aims to find a minimal region in input space containing a fraction 0: of the probability mass underlying a data set. This algorithm- ity machine (MPM)" - is built on a distribution-free methodology that minimizes the worst-case probability of a data point falling outside of a convex set, given only the mean and covariance matrix of the distribution and making no further distributional assump(cid:173) tions. We present a robust approach to estimating the mean and covariance matrix within the general two-class MPM setting, and show how this approach specializes to the single-class problem. We provide empirical results comparing the single-class MPM to the single-class SVM and a two-class SVM method.