Abstract
The causal states of computational mechanics define the minimal sufficient (prescient) memory for a given stationary stochastic process. They induce the ε-machine which is a hidden Markov model (HMM) generating the process. The ε-machine is, however, not the minimal generative HMM and minimal internal state entropy of a generative HMM is a tighter upper bound for excess entropy than provided by statistical complexity. We propose a notion of prediction that does not require sufficiency. The corresponding models can be substantially smaller than the ε-machine and are closely related to generative HMMs.
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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Löhr, W., Ay, N. (2009). Non-sufficient Memories That Are Sufficient for Prediction. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_25
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DOI: https://doi.org/10.1007/978-3-642-02466-5_25
Publisher Name: Springer, Berlin, Heidelberg
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