  Deep generative learning cannot only be used for generating new data with
statistical characteristics derived from input data but also for anomaly
detection, by separating nominal and anomalous instances based on their
reconstruction quality. In this paper, we explore the performance of three
unsupervised deep generative models -- variational autoencoders (VAEs) with
Gaussian, Bernoulli, and Boltzmann priors -- in detecting anomalies in
flight-operations data of commercial flights consisting of multivariate time
series. We devised two VAE models with discrete latent variables (DVAEs), one
with a factorized Bernoulli prior and one with a restricted Boltzmann machine
(RBM) as prior, because of the demand for discrete-variable models in
machine-learning applications and because the integration of quantum devices
based on two-level quantum systems requires such models. The DVAE with RBM
prior, using a relatively simple -- and classically or quantum-mechanically
enhanceable -- sampling technique for the evolution of the RBM's negative
phase, performed better than the Bernoulli DVAE and on par with the Gaussian
model, which has a continuous latent space. Our studies demonstrate the
competitiveness of a discrete deep generative model with its Gaussian
counterpart on anomaly-detection tasks. Moreover, the DVAE model with RBM prior
can be easily integrated with quantum sampling by outsourcing its generative
process to measurements of quantum states obtained from a quantum annealer or
gate-model device.
