Low-algorithmic-complexity entropy-deceiving graphs

Handle URI:
http://hdl.handle.net/10754/625386
Title:
Low-algorithmic-complexity entropy-deceiving graphs
Authors:
Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper ( 0000-0002-9568-5588 )
Abstract:
In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.
KAUST Department:
Biological and Environmental Sciences and Engineering (BESE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Zenil H, Kiani NA, Tegnér J (2017) Low-algorithmic-complexity entropy-deceiving graphs. Physical Review E 96. Available: http://dx.doi.org/10.1103/PhysRevE.96.012308.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
Issue Date:
8-Jul-2017
DOI:
10.1103/PhysRevE.96.012308
Type:
Article
ISSN:
2470-0045; 2470-0053
Sponsors:
N.A.K. was supported by aVinnovaVINNMERfellowship, Stratneuro. H. Z. was supported by the Swedish Research Council (VR).
Additional Links:
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.012308
Appears in Collections:
Articles; Biological and Environmental Sciences and Engineering (BESE) Division; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZenil, Hectoren
dc.contributor.authorKiani, Narsis A.en
dc.contributor.authorTegner, Jesperen
dc.date.accessioned2017-08-23T11:54:06Z-
dc.date.available2017-08-23T11:54:06Z-
dc.date.issued2017-07-08en
dc.identifier.citationZenil H, Kiani NA, Tegnér J (2017) Low-algorithmic-complexity entropy-deceiving graphs. Physical Review E 96. Available: http://dx.doi.org/10.1103/PhysRevE.96.012308.en
dc.identifier.issn2470-0045en
dc.identifier.issn2470-0053en
dc.identifier.doi10.1103/PhysRevE.96.012308en
dc.identifier.urihttp://hdl.handle.net/10754/625386-
dc.description.abstractIn estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.en
dc.description.sponsorshipN.A.K. was supported by aVinnovaVINNMERfellowship, Stratneuro. H. Z. was supported by the Swedish Research Council (VR).en
dc.publisherAmerican Physical Society (APS)en
dc.relation.urlhttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.012308en
dc.rightsArchived with thanks to Physical Review E. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.titleLow-algorithmic-complexity entropy-deceiving graphsen
dc.typeArticleen
dc.contributor.departmentBiological and Environmental Sciences and Engineering (BESE) Divisionen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalPhysical Review Een
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionAlgorithmic Nature Group, LABoRES, Paris, 75006, , Franceen
dc.contributor.institutionDepartment of Computer Science, University of Oxford, Oxford, OX1 3QD, , United Kingdomen
dc.contributor.institutionInformation Dynamics Lab, Unit of Computational Medicine, Department of Medicine Solna, Center for Molecular Medicine, SciLifeLab, Karolinska Institute, Stockholm, 171 76, , Swedenen
kaust.authorTegner, Jesperen
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