  After being trained on a fully-labeled training set, where the observations
are grouped into a certain number of known classes, novelty detection methods
aim to classify the instances of an unlabeled test set while allowing for the
presence of previously unseen classes. These models are valuable in many areas,
ranging from social network and food adulteration analyses to biology, where an
evolving population may be present. In this paper, we focus on a two-stage
Bayesian semiparametric novelty detector, also known as Brand, recently
introduced in the literature. Leveraging on a model-based mixture
representation, Brand allows clustering the test observations into known
training terms or a single novelty term. Furthermore, the novelty term is
modeled with a Dirichlet Process mixture model to flexibly capture any
departure from the known patterns. Brand was originally estimated using MCMC
schemes, which are prohibitively costly when applied to high-dimensional data.
To scale up Brand applicability to large datasets, we propose to resort to a
variational Bayes approach, providing an efficient algorithm for posterior
approximation. We demonstrate a significant gain in efficiency and excellent
classification performance with thorough simulation studies. Finally, to
showcase its applicability, we perform a novelty detection analysis using the
openly-available Statlog dataset, a large collection of satellite imaging
spectra, to search for novel soil types.
