Outlier and Novelty Detection for Functional Data: a Semiparametric BayesianApproach

A novelty detection model can be seen as a supervised classifier, trained on a fully- labeled training set, that allows for the presence of new classes in the test set not previously observed among the training units. When dealing with functional data, this requires learning the main patterns for the curves in the known classes, whilst being able to isolate signals that possess distinctive characteristics in the unlabeled set. In order to tackle this challenging problem, we propose a two-stage Bayesian semi-parametric novelty detector [2]. In the first stage, robust estimates are extracted from the training set via the Minimum Regularized Covariance Determinant (MRCD) estimator [1]. In the second stage, such information is employed to elicit informative priors within a Bayesian mixture of known groups plus a novelty term. To reflect the lack of knowledge on the latter component, we resort to a Dirichlet Process mixture model, thus overcoming the problematic a-priori specification of the expected number of novelties that may be present in the test set. The described methodology is applied to a spectroscopic dataset within a food authenticity study.