On the Generative Nature of Prediction

Given an observed stochastic process, computational mechanics provides an explicit and efficient method of constructing a minimal hidden Markov model within the class of max-imally predictive models. Here, the corresponding so-called ε-machine encodes the mech-anisms of prediction. We propose an alternative notion of predictive models in terms of a hidden Markov model capable of generating the underlying stochastic process. A comparison of these two notions of prediction reveals that our approach is less restrictive and thereby allows for predictive models that are more concise than the ε-machine