Systems and methods that use probabilistic grammatical inference and statistical data analysis techniques to characterize the behavior of systems in terms of a low dimensional set of summary variables and, on the basis of these models, detect anomalous behaviors are disclosed. The disclosed information-theoretic system and method exploit the properties of information to deduce a structure for information flow and management. The properties of information can provide a fundamental basis for the decomposition of systems and hence a structure for the transmission and combination of observations at the desired levels of resolution (e.g., component, subsystem, system).