How to Trust Generative Probabilistic Models for Time-Series Data?

Generative machine learning methods deliver unprecedented quality in the fields of computer vision and natural language processing. When comparing models for these task, the user can fast and reliably judge generated data with her bare eye-for humans, it is easy to decide whether an image or a paragraph of text is realistic. However, generative models for time series data from natural or social processes are largely unexplored, partially due to a lack of reliable and practical quality measures. In this work, measures for the evaluation of generative models for time series data are studied-in total, over 1000 models are trained and analyzed. The well-established maximum mean discrepancy (MMD) and our novel proposal: the Hausdorff discrepancy (HD) are considered for quantifying the disagreement between the sample distribution of each generated data set and the ground truth data. While MMD relies on the distance between mean-vectors in an implicit high-dimensional feature space, the proposed HD relies on intuitive and explainable geometric properties of a ""typical"" sample. Both discrepancies are instantiated for three underlying distance measures, namely Euclidean, dynamic time warping, and Frechét distance. The discrepancies are applied to evaluate samples from generative adversarial networks, variational autoencoders, and Markov random fields. Experiments on real-world energy prices and humidity measurements suggest, that considering a single score is insufficient for judging the quality of a generative model.