Robust Novelty Detection with Single-Class MPM

Gert Lanckriet
(Professors Laurent El Ghaoui and Michael I. Jordan)
(NSF) IIS-9988642 and (ONR) MURI N00014-00-1-0637

In this project we consider the problem of novelty detection, presenting an algorithm that aims to find a minimal region in input space containing a fraction alpha of the probability mass underlying a data set. This algorithm, the "single-class minimax probability 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 assumptions. 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.

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