References

[AP12]

S. A. Abdallah and M. D. Plumbley. A measure of statistical complexity based on predictive information with application to finite spin systems. Physics Letters A, 376(4):275–281, 2012.

[ASBY14]

B. Allen, B. C. Stacey, and Y. Bar-Yam. An information-theoretic formalism for multiscale structure in complex systems. arXiv preprint arXiv:1409.4708, 2014.

[Ama01]

Shun-ichi Amari. Information geometry on hierarchy of probability distributions. Information Theory, IEEE Transactions on, 47(5):1701–1711, 2001.

[BG15]

Pradeep Kr Banerjee and Virgil Griffith. Synergy, redundancy and common information. arXiv preprint arXiv:1509.03706, 2015.

[BRMontufar17]

Pradeep Kr. Banerjee, Johannes Rauh, and Guido Montúfar. Computing the unique information. arXive preprint arXiv:1709.07487, 2017.

[BY04]

Y. Bar-Yam. Multiscale complexity/entropy. Advances in Complex Systems, 7(01):47–63, 2004.

[BG16]

Salman Beigi and Amin Gohari. Phi-entropic measures of correlation. arXiv preprint arXiv:1611.01335, 2016.

[Bel03]

A. J. Bell. The co-information lattice. In S. Makino S. Amari, A. Cichocki and N. Murata, editors, Proc. Fifth Intl. Workshop on Independent Component Analysis and Blind Signal Separation, volume ICA 2003, 921–926. New York, 2003. Springer.

[BROJ13]

Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, and Jürgen Jost. Shared information—new insights and problems in decomposing information in complex systems. In Proceedings of the European Conference on Complex Systems 2012, 251–269. Springer, 2013.

[BRO+14]

Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, Jürgen Jost, and Nihat Ay. Quantifying unique information. Entropy, 16(4):2161–2183, 2014.

[Cal02]

Cristian Calude. Information and Randomness: An Algorithmic Perspective. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2nd edition, 2002. ISBN 3540434666.

[CABE+15]

Chung Chan, Ali Al-Bashabsheh, Javad B Ebrahimi, Tarik Kaced, and Tie Liu. Multivariate mutual information inspired by secret-key agreement. Proceedings of the IEEE, 103(10):1883–1913, 2015.

[CP16]

Daniel Chicharro and Stefano Panzeri. Redundancy and synergy in dual decompositions of mutual information gain and information loss. arXiv preprint arXiv:1612.09522, 2016.

[CRW03]

Matthias Christandl, Renato Renner, and Stefan Wolf. A property of the intrinsic mutual information. In IEEE international symposium on information theory, 258–258. 2003.

[CT06]

Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. Wiley-Interscience, New York, second edition, 2006. ISBN 0471241954.

[CPC10]

Paul Warner Cuff, Haim H Permuter, and Thomas M Cover. Coordination capacity. IEEE Transactions on Information Theory, 56(9):4181–4206, 2010.

[FL17]

Conor Finn and Joseph Lizier. 2017.

[FWA16]

Seth Frey, Paul L Williams, and Dominic K Albino. Information encryption in the expert management of strategic uncertainty. arXiv preprint arXiv:1605.04233, 2016.

[GA17]

Amin Gohari and Venkat Anantharam. Comments on “information-theoretic key agreement of multiple terminals—part i”. IEEE Transactions on Information Theory, 63(8):5440–5442, 2017.

[GGunluK17]

Amin Gohari, Onur Günlü, and Gerhard Kramer. On achieving a positive rate in the source model key agreement problem. arXiv preprint arXiv:1709.05174, 2017.

[GK17]

Allison E Goodwell and Praveen Kumar. Temporal information partitioning: characterizing synergy, uniqueness, and redundancy in interacting environmental variables. Water Resources Research, 53(7):5920–5942, 2017.

[GCJ+14]

Virgil Griffith, Edwin KP Chong, Ryan G James, Christopher J Ellison, and James P Crutchfield. Intersection information based on common randomness. Entropy, 16(4):1985–2000, 2014.

[GK14]

Virgil Griffith and Christof Koch. Quantifying synergistic mutual information. In Guided Self-Organization: Inception, pages 159–190. Springer, 2014.

[GacsKorner73]

Peter Gács and János Körner. Common information is far less than mutual information. Problems of Control and Information Theory, 2(2):149–162, 1973.

[Han75]

T. S. Han. Linear dependence structure of the entropy space. Information and Control, 29:337–368, 1975.

[HSP13]

Malte Harder, Christoph Salge, and Daniel Polani. Bivariate measure of redundant information. Physical Review E, 87(1):012130, 2013.

[Inc17a]

Robin A. A. Ince. Measuring multivariate redundant information with pointwise common change in surprisal. Entropy, 19(7):318, 2017.

[Inc17b]

Robin A. A. Ince. The Partial Entropy Decompostion: decomposing multivariate entropy and mutual information via pointwise common surprisal. arXive preprint arXiv:1702.01591, 2017.

[JEC17]

Ryan G. James, Jeffrey Emenheiser, and James P. Crutchfield. Unique information via dependency constraints. arXiv preprint arXiv:1709.06653, 2017.

[Kri09]

Klaus Krippendorff. Ross ashby’s information theory: a bit of history, some solutions to problems, and what we face today. International Journal of General Systems, 38(2):189–212, 2009.

[KLEG14]

G. R. Kumar, C. T. Li, and A. El Gamal. Exact common information. In Information Theory (ISIT), 2014 IEEE International Symposium on, 161–165. IEEE, 2014.

[LSAgro11]

Frank Lad, Giuseppe Sanfilippo, and Gianna Agrò. Extropy: a complementary dual of entropy. arXiv preprint arXiv:1109.6440, 2011.

[LMPR04]

P. W. Lamberti, M. T. Martin, A. Plastino, and O. A. Rosso. Intensive entropic non-triviality measure. Physica A: Statistical Mechanics and its Applications, 334(1):119–131, 2004.

[LXC10]

Wei Liu, Ge Xu, and Biao Chen. The common information of n dependent random variables. In Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on, 836–843. IEEE, 2010.

[LFW13]

Joseph T Lizier, Benjamin Flecker, and Paul L Williams. Towards a synergy-based approach to measuring information modification. In Artificial Life (ALIFE), 2013 IEEE Symposium on, 43–51. IEEE, 2013.

[Mac03]

David JC MacKay. Information theory, inference and learning algorithms. Cambridge university press, 2003.

[MW97]

Ueli Maurer and Stefan Wolf. The intrinsic conditional mutual information and perfect secrecy. In IEEE international symposium on information theory, 88–88. Citeseer, 1997.

[McG54]

W. J. McGill. Multivariate information transmission. Psychometrika, 19(2):97–116, 1954.

[OBR15]

Eckehard Olbrich, Nils Bertschinger, and Johannes Rauh. Information decomposition and synergy. Entropy, 17(5):3501–3517, 2015.

[PVerdu08]

Daniel P Palomar and Sergio Verdú. Lautum information. IEEE transactions on information theory, 54(3):964–975, 2008.

[PPCP17]

Giuseppe Pica, Eugenio Piasini, Daniel Chicharro, and Stefano Panzeri. Invariant components of synergy, redundancy, and unique information among three variables. arXiv preprint arXiv:1706.08921, 2017.

[RCVW04]

Murali Rao, Yunmei Chen, Baba C Vemuri, and Fei Wang. Cumulative residual entropy: a new measure of information. Information Theory, IEEE Transactions on, 50(6):1220–1228, 2004.

[Rau17]

Johannes Rauh. Secret sharing and shared information. arXiv preprint arXiv:1706.06998, 2017.

[RBO+17]

Johannes Rauh, Pradeep Kr Banerjee, Eckehard Olbrich, Jürgen Jost, and Nils Bertschinger. On extractable shared information. arXiv preprint arXiv:1701.07805, 2017.

[RBOJ14]

Johannes Rauh, Nils Bertschinger, Eckehard Olbrich, and Jurgen Jost. Reconsidering unique information: towards a multivariate information decomposition. In Information Theory (ISIT), 2014 IEEE International Symposium on, 2232–2236. IEEE, 2014.

[RSW03]

Renato Renner, Juraj Skripsky, and Stefan Wolf. A new measure for conditional mutual information and its properties. In IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 259–259. 2003.

[RNE+16]

Fernando Rosas, Vasilis Ntranos, Christopher J Ellison, Sofie Pollin, and Marian Verhelst. Understanding interdependency through complex information sharing. Entropy, 18(2):38, 2016.

[SSB+03]

E. Schneidman, S. Still, M. J. Berry, W. Bialek, and others. Network information and connected correlations. Phys. Rev. Lett., 91(23):238701, 2003.

[TS80]

H. Te Sun. Multiple mutual informations and multiple interactions in frequency data. Information and Control, 46:26–45, 1980.

[TPB00]

Naftali Tishby, Fernando C Pereira, and William Bialek. The information bottleneck method. arXiv preprint physics/0004057, 2000.

[TSE94]

Giulio Tononi, Olaf Sporns, and Gerald M Edelman. A measure for brain complexity: relating functional segregation and integration in the nervous system. Proceedings of the National Academy of Sciences, 91(11):5033–5037, 1994.

[TNG11]

H. Tyagi, P. Narayan, and P. Gupta. When is a function securely computable? Information Theory, IEEE Transactions on, 57(10):6337–6350, 2011.

[VAPelaezM16]

Francisco José Valverde-Albacete and Carmen Peláez-Moreno. The multivariate entropy triangle and applications. In Hybrid Artificial Intelligent Systems, pages 647–658. Springer, 2016.

[VW08]

Sergio Verdu and Tsachy Weissman. The information lost in erasures. Information Theory, IEEE Transactions on, 54(11):5030–5058, 2008.

[VerduW06]

S. Verdú and T. Weissman. Erasure entropy. In Information Theory, 2006 IEEE International Symposium on, 98–102. IEEE, 2006.

[Wat60]

S. Watanabe. Information theoretical analysis of multivariate correlation. IBM Journal of research and development, 4(1):66–82, 1960.

[WB10]

Paul L Williams and Randall D Beer. Nonnegative decomposition of multivariate information. arXiv preprint arXiv:1004.2515, 2010.

[WB11]

Paul L Williams and Randall D Beer. Generalized measures of information transfer. arXiv preprint arXiv:1102.1507, 2011.

[Wyn75]

A. D. Wyner. The common information of two dependent random variables. Information Theory, IEEE Transactions on, 21(2):163–179, 1975.

[Yeu08]

Raymond W Yeung. Information theory and network coding. Springer, 2008.