Graph-based machine learning for detection tasks on complex systems

Recent technological advances have increased our capacity to monitor many aspects of daily life or natural phenomena by collecting and analyzing data in real-time coming from multiple data sources. For example, public transportation systems monitor passenger affluence and delays at the level of each station to improve commuting; modern geological hazard monitoring systems raise early alarms for events such as earthquakes.This thesis focuses on the detection of changes in the data-generating distributions associated with a set of agents belonging to a complex system. In many applications, the underlying structure, frequently modeled as a graph between agents, holds essential information about how the system reacts to changes.Building on this intuition, the thesis mainly explores two research questions: how can a graph detection task effectively leverage the information encoded in the graph topology? And how can classical detection methods be extended to non-parametric settings where the available data is indexed by graph nodes or accessed online?The main tool used throughout this thesis is non-parametric likelihood-ratio estimation, which allows a machine learning perspective on classical detection techniques and enriches their domain of applicability. The thesis contributes with new techniques enabling more flexible detection algorithms in both offline and online settings.