  Detecting anomalous time series is key for scientific, medical and industrial
tasks, but is challenging due to its inherent unsupervised nature. In recent
years, progress has been made on this task by learning increasingly more
complex features, often using deep neural networks. In this work, we argue that
shallow features suffice when combined with distribution distance measures. Our
approach models each time series as a high dimensional empirical distribution
of features, where each time-point constitutes a single sample. Modeling the
distance between a test time series and the normal training set therefore
requires efficiently measuring the distance between multivariate probability
distributions. We show that by parameterizing each time series using cumulative
Radon features, we are able to efficiently and effectively model the
distribution of normal time series. Our theoretically grounded but
simple-to-implement approach is evaluated on multiple datasets and shown to
achieve better results than established, classical methods as well as complex,
state-of-the-art deep learning methods. Code is provided.
