Epsilon-machine

With a direct measure of an ε'''-machine’s complexity, the theory gives a computation-theoretic foundation to the notions of model optimality and, most importantly, a measure of the computational complexity of estimated models.

The ϵ'''-machine is the organization of the process, or at least of the part of it which is relevant to our measurements. It leads to a natural measure of the statistical complexity of processes, namely the amount of information needed to specify the state of the ϵ'''-machine. […] Using the ϵ'''-machine, we see that the causal states always form a Markov process. This is satisfying ideologically, and has interesting information-theoretic and ergodic consequences.

These predictors, called ε-machines, are a subset of a well known statistical model class called the Hidden Markov Model (HMM). Despite being a subset, ε-machines have several important advantages over traditional HMMs. This dissertation illustrates these advantages by applying ε-machines to several problems in computer security: anomaly-based intrusion detection in High Performance Computing (HPC) environments, automated protocol reverse engineering, and structural drift.

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. […] The intrinsic underlying structure of the system is modeled by an epsilon-machine and its causal states.