'Did something just break-' -- A Stream-Learning View on Monitoring: the Geometry and Causes of Change
Monitoring systems analyze live data to detect and characterize anomalies and failures, enabling informed decision-making. As systems become increasingly complex, the ability to capture interactions among multiple features in real time is growing in importance across domains. In this tutorial, we approach monitoring through the lens of data streams, concept drift, and explainability. We begin with methods for automatically detecting anomalous behavior and then turn to machine-assisted analysis techniques that provide insight into observed changes, including their geometry and potential root causes. We cover both practical algorithms and theoretical foundations, and place particular emphasis on two complementary perspectives on data shift explainability: (1) the geometry of change, which introduces optimal transport as a model of data shift and leverages Wasserstein distances to characterize distributional changes; and (2) the causality of change, which extends computational causal methods for actionable root-cause analysis. Finally, we demonstrate an end-to-end workflow for critical infrastructure applications.
