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.

翻译：深度生成学习不仅可用于生成具有输入数据统计特征的新数据，还可通过基于重构质量区分正常与异常实例来实现异常检测。本文探讨了三种无监督深度生成模型——具有高斯、伯努利和玻尔兹曼先验的变分自编码器——在检测商业航班飞行操作数据（由多变量时间序列构成）中异常情况时的性能。由于机器学习应用中对离散变量模型的需求，以及基于两级量子系统的量子设备集成要求此类模型，我们设计了两种离散潜变量变分自编码器模型，一种采用因式分解伯努利先验，另一种采用受限玻尔兹曼机作为先验。采用相对简单（可经典或量子力学方式增强）采样技术进行受限玻尔兹曼机负相演化的受限玻尔兹曼机先验离散潜变量变分自编码器，其性能优于伯努利离散潜变量变分自编码器，并与具有连续潜空间的高斯模型相当。我们的研究表明，离散深度生成模型在异常检测任务中与其高斯对应模型相比具有竞争力。此外，采用受限玻尔兹曼机先验的离散潜变量变分自编码器可通过将其生成过程外包给从量子退火器或门模型设备获得的量子态测量结果，轻松实现与量子采样的集成。