Informational and Causal Architecture of Continuous-time Renewal Processes |
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| Authors: | Sarah Marzen James P Crutchfield |
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| Institution: | 1.Physics of Living Systems Group, Department of Physics,Massachusetts Institute of Technology,Cambridge,USA;2.Department of Physics,University of California at Berkeley,Berkeley,USA;3.Complexity Sciences Center and Department of Physics,University of California at Davis,Davis,USA |
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| Abstract: | We introduce the minimal maximally predictive models (\(\epsilon \text{-machines }\)) of processes generated by certain hidden semi-Markov models. Their causal states are either discrete, mixed, or continuous random variables and causal-state transitions are described by partial differential equations. As an application, we present a complete analysis of the \(\epsilon \text{-machines }\) of continuous-time renewal processes. This leads to closed-form expressions for their entropy rate, statistical complexity, excess entropy, and differential information anatomy rates. |
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