Learning Dependencies and Localizing Anomalies with Neural Rosenblatt Transform

Multivariate time series anomaly localization remains relatively understudied, despite its importance for diagnosing anomalies in many real-world complex systems. Existing models may result in ambiguous per-series anomaly scores, mainly due to inaccurate modeling of cross-series dependencies. Furthermore, methods focused on dependency learning typically do not address anomaly localization and are mostly designed for continuous-valued time series, limiting their applicability to mixed continuous–discrete settings common in real-world systems. To address these limitations, **NeuralRos** is proposed to jointly learn cross-series dependencies and localize anomalies in mixed-type multivariate time series. NeuralRos reformulates the Rosenblatt transformation from a diagnostic tool into a learning mechanism, combining a learnable variable ordering with neural conditional distribution models to capture cross-series dependencies. Two complementary localization scores are derived: a likelihood-based score from the learned normal conditional distributions and a Rosenblatt-based score from deviations of the transformed variables from their theoretical behavior. Experiments on synthetic and real-world datasets demonstrate the effectiveness of NeuralRos across both tasks.