Certifiable Metric One Class Learning with adversarially trained Lipschitz Classifier

Louis Béthune, Mathieu Serrurier

Abstract: We propose a new Novelty Detection and One Class classifier, based on the smoothness properties of orthogonal neural network, and on the properties of Hinge Kantorovich Rubinstein (HKR) function. The classifier benefits from robustness certificates against $l2$-attacks thanks to the Lipschitz constraint, whilst the HKR loss allows to provably approximate the signed distance function to the boundary of the distribution: the normality score induces by the classifier has a meaningful interpretation in term of distance to the support. Finally, gradient steps in the input space allows free generation of samples from the one class in a fashion that reminds GAN or VAE.