Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes
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Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes

  • Author(s): Marzen, Sarah E.
  • Crutchfield, James P.
  • et al.

Published Web Location

https://arxiv.org/pdf/1611.01099.pdf
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Abstract

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the {\epsilon}-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models. Our information-theoretic analysis leads to new expressions for the entropy rate and the rates of related information measures for these very general continuous-time process classes.

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