  Anomaly detection is a widely studied task for a broad variety of data types;
among them, multiple time series appear frequently in applications, including
for example, power grids and traffic networks. Detecting anomalies for multiple
time series, however, is a challenging subject, owing to the intricate
interdependencies among the constituent series. We hypothesize that anomalies
occur in low density regions of a distribution and explore the use of
normalizing flows for unsupervised anomaly detection, because of their superior
quality in density estimation. Moreover, we propose a novel flow model by
imposing a Bayesian network among constituent series. A Bayesian network is a
directed acyclic graph (DAG) that models causal relationships; it factorizes
the joint probability of the series into the product of easy-to-evaluate
conditional probabilities. We call such a graph-augmented normalizing flow
approach GANF and propose joint estimation of the DAG with flow parameters. We
conduct extensive experiments on real-world datasets and demonstrate the
effectiveness of GANF for density estimation, anomaly detection, and
identification of time series distribution drift.
