We introduce Neural Contextual Anomaly Detection (NCAD), a framework for anomaly detection on time series that scales seamlessly from the unsupervised to supervised setting, and is applicable to both univariate and multivariate time series. This is achieved by combining recent developments in representation learning for multivariate time series, with techniques for deep anomaly detection originally developed for computer vision that we tailor to the time series setting. Our window-based approach facilitates learning the boundary between normal and anomalous classes by injecting generic synthetic anomalies into the available data. NCAD can effectively take advantage of domain knowledge and of any available training labels. We demonstrate empirically on standard benchmark datasets that our approach obtains a state-of-the-art performance in the supervised, semi-supervised, and unsupervised settings.

Bayesian statistical inference loses predictive optimality when generative models are misspecified.Working within an existing coherent loss-based generalisation of Bayesian inference, we show existing Modular/Cut-model inference is coherent, and write down a new family of Semi-Modular Inference (SMI) schemes, indexed by an influence parameter, with Bayesian inference and Cut-models as special cases. We give a meta-learning criterion and estimation procedure to choose the inference scheme. This returns Bayesian inference when there is no misspecification.The framework applies naturally to Multi-modular models. Cut-model inference allows directed information flow from well-specified modules to misspecified modules, but not vice versa. An existing alternative power posterior method gives tunable but undirected control of information flow, improving prediction in some settings. In contrast, SMI allows \emph{tunable and directed} information flow between modules.We illustrate our methods on two standard test cases from the literature and a motivating archaeological data set.