On the Generative Nature of Prediction
Wolfgang Löhr and Nihat Ay
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Submission date: 04. Feb. 2008 (revised version: September 2008)
published in: Advances in complex systems, 12 (2009) 2, p. 169-194
DOI number (of the published article): 10.1142/S0219525909002143
Keywords and phrases: hidden Markov models, computational mechanics, $\varepsilon$-machines, observable operator models, prediction, epsilon-machines
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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 -machine.