MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

On the Generative Nature of Prediction

Wolfgang Löhr and Nihat Ay


Given an observed stochastic process, computational mechanics provides an explicit and efficient method of constructing a minimal hidden Markov model within the class of maximally predictive models. Here, the corresponding so-called "-machine encodes the mechanisms 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 $\varepsilon$-machine.

hidden Markov models, computational mechanics, $\varepsilon$-machines, observable operator models, prediction, epsilon-machines

Related publications

2009 Repository Open Access
Wolfgang Löhr and Nihat Ay

On the generative nature of prediction

In: Advances in complex systems, 12 (2009) 2, pp. 169-194