Structure and Randomness of Continuous-Time, Discrete-Event Processes
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifi...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer-Verlag
2017
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| Online Access: | http://hdl.handle.net/1721.1/111635 |
| _version_ | 1811069734683148288 |
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| author | Crutchfield, James P Marzen, Sarah E. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Crutchfield, James P Marzen, Sarah E. |
| author_sort | Crutchfield, James P |
| collection | MIT |
| description | Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ϵ-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes. |
| first_indexed | 2024-09-23T08:15:06Z |
| format | Article |
| id | mit-1721.1/111635 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:15:06Z |
| publishDate | 2017 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1116352022-09-30T08:37:16Z Structure and Randomness of Continuous-Time, Discrete-Event Processes Crutchfield, James P Marzen, Sarah E. Massachusetts Institute of Technology. Department of Physics Marzen, Sarah E. Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process’ intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models—memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects (ϵ-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes. 2017-09-25T18:08:22Z 2018-06-03T05:00:09Z 2017-08 2017-04 2017-09-23T04:44:13Z Article http://purl.org/eprint/type/JournalArticle 0022-4715 1572-9613 http://hdl.handle.net/1721.1/111635 Marzen, Sarah E., and Crutchfield, James P. “Structure and Randomness of Continuous-Time, Discrete-Event Processes.” Journal of Statistical Physics 169, 2 (August 2017): 303–315 © 2017 Springer Science+Business Media, LLC en http://dx.doi.org/10.1007/s10955-017-1859-y Journal of Statistical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media, LLC application/pdf Springer-Verlag Springer US |
| spellingShingle | Crutchfield, James P Marzen, Sarah E. Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title | Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title_full | Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title_fullStr | Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title_full_unstemmed | Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title_short | Structure and Randomness of Continuous-Time, Discrete-Event Processes |
| title_sort | structure and randomness of continuous time discrete event processes |
| url | http://hdl.handle.net/1721.1/111635 |
| work_keys_str_mv | AT crutchfieldjamesp structureandrandomnessofcontinuoustimediscreteeventprocesses AT marzensarahe structureandrandomnessofcontinuoustimediscreteeventprocesses |