References
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.
Hamidreza Abin and Amin Gohari. On the source model key agreement problem. IEEE Transactions on Information Theory, 72(8):5317–5334, 2026. doi:10.1109/tit.2026.3691758.
Rudolf Ahlswede and Imre Csiszár. Common randomness in information theory and cryptography. I. Secret sharing. IEEE Transactions on Information Theory, 39(4):1121–1132, 1993. doi:10.1109/18.243431.
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.
Shun-ichi Amari. Information geometry on hierarchy of probability distributions. Information Theory, IEEE Transactions on, 47(5):1701–1711, 2001.
Venkat Anantharam, Amin Gohari, Sudeep Kamath, and Chandra Nair. On maximal correlation, hypercontractivity, and the data processing inequality studied by Erkip and Cover. arXiv preprint arXiv:1304.6133, 2013.
T. W. Anderson and Leo A. Goodman. Statistical inference about Markov chains. The Annals of Mathematical Statistics, 28(1):89–110, 1957. doi:10.1214/aoms/1177707039.
Erdal Arıkan. Source polarization. In 2010 IEEE International Symposium on Information Theory, 899–903. 2010. arXiv:1001.3087, doi:10.1109/ISIT.2010.5513567.
Nihat Ay, Daniel Polani, and Nathaniel Virgo. Information decomposition based on cooperative game theory. Kybernetika, 56(5):979–1014, 2020. arXiv:1910.05979.
Christoph Bandt and Bernd Pompe. Permutation entropy: a natural complexity measure for time series. Physical Review Letters, 88(17):174102, 2002. doi:10.1103/PhysRevLett.88.174102.
Pradeep Kr Banerjee and Virgil Griffith. Synergy, redundancy and common information. arXiv preprint arXiv:1509.03706, 2015.
Pradeep Kr Banerjee, Eckehard Olbrich, Jürgen Jost, and Johannes Rauh. Unique informations and deficiencies. In 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 32–38. IEEE, 2018.
Pradeep Kr. Banerjee, Johannes Rauh, and Guido Montúfar. Computing the unique information. arXive preprint arXiv:1709.07487, 2017.
Y. Bar-Yam. Multiscale complexity/entropy. Advances in Complex Systems, 7(01):47–63, 2004.
Salman Beigi and Amin Gohari. Phi-entropic measures of correlation. arXiv preprint arXiv:1611.01335, 2016.
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.
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.
Nils Bertschinger, Johannes Rauh, Eckehard Olbrich, Jürgen Jost, and Nihat Ay. Quantifying unique information. Entropy, 16(4):2161–2183, 2014.
Chunhua Bian, Chang Qin, Qianli D. Y. Ma, and Qinghong Shen. Modified permutation-entropy analysis of heartbeat dynamics. Physical Review E, 85(2):021906, 2012. doi:10.1103/PhysRevE.85.021906.
Patrick Billingsley. Statistical methods in Markov chains. The Annals of Mathematical Statistics, 32(1):12–40, 1961. doi:10.1214/aoms/1177705136.
Léon Brillouin. The Negentropy Principle of Information. Volume 24. American Institute of Physics, 1953.
Cristian Calude. Information and Randomness: An Algorithmic Perspective. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2nd edition, 2002. ISBN 3540434666.
Deeparnab Chakrabarty, Prateek Jain, and Pravesh Kothari. Provable submodular minimization using wolfe's algorithm. In Advances in Neural Information Processing Systems, volume 27. 2014.
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.
Chung Chan and Tie Liu. Agglomerative info-clustering. arXiv preprint arXiv:1701.04926, 2017.
Anne Chao and Tsung-Jen Shen. Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10(4):429–443, 2003. doi:10.1023/A:1026096204727.
Daniel Chicharro and Stefano Panzeri. Redundancy and synergy in dual decompositions of mutual information gain and information loss. arXiv preprint arXiv:1612.09522, 2016.
Eric Chitambar, Ben Fortescue, and Min-Hsiu Hsieh. Distributions attaining secret key at a rate of the conditional mutual information. In Advances in Cryptology – CRYPTO 2015, volume 9216 of Lecture Notes in Computer Science, 443–462. 2015. doi:10.1007/978-3-662-48000-7_22.
Eric Chitambar, Min-Hsiu Hsieh, and Andreas Winter. The private and public correlation cost of three random variables with collaboration. IEEE Transactions on Information Theory, 62(4):2034–2043, 2016. doi:10.1109/TIT.2016.2530086.
Matthias Christandl, Renato Renner, and Stefan Wolf. A property of the intrinsic mutual information. In IEEE international symposium on information theory, 258–258. 2003.
Ferdinando Cicalese, Luisa Gargano, and Ugo Vaccaro. Minimum-entropy couplings and their applications. IEEE Transactions on Information Theory, 65(6):3436–3451, 2019. doi:10.1109/TIT.2019.2894519.
Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. Wiley-Interscience, New York, second edition, 2006. ISBN 0471241954.
F. H. C. Crick. The origin of the genetic code. Journal of Molecular Biology, 38(3):367–379, 1968. doi:10.1016/0022-2836(68)90392-6.
László Csirmaz. A short proof of the Gács–Körner theorem. 2023. arXiv:2306.14718.
Imre Csiszár and Prakash Narayan. Secrecy capacities for multiple terminals. IEEE Transactions on Information Theory, 50(12):3047–3061, 2004. doi:10.1109/TIT.2004.838380.
Paul Warner Cuff, Haim H Permuter, and Thomas M Cover. Coordination capacity. IEEE Transactions on Information Theory, 56(9):4181–4206, 2010.
Kyle J. A. Down and Pedro A. M. Mediano. A logarithmic decomposition and a signed measure space for entropy. arXiv preprint arXiv:2409.03732, 2024. arXiv:2409.03732.
Abbas El Gamal and Young-Han Kim. Network Information Theory. Cambridge University Press, 2011. doi:10.1017/CBO9781139030687.
Bilal Fadlallah, Badong Chen, Andreas Keil, and José Príncipe. Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information. Physical Review E, 87(2):022911, 2013. doi:10.1103/PhysRevE.87.022911.
C. Finn and J. T. Lizier. Pointwise partial information decomposition using the specificity and ambiguity lattices. Entropy, 20(4):297, 2018.
Conor Finn and Joseph T. Lizier. Generalised measures of multivariate information content. Entropy, 22(2):216, 2020. doi:10.3390/e22020216.
Seth Frey, Paul L Williams, and Dominic K Albino. Information encryption in the expert management of strategic uncertainty. arXiv preprint arXiv:1605.04233, 2016.
Joshua Garland, Ryan G. James, and Elizabeth Bradley. Model-free quantification of time-series predictability. Physical Review E, 90(5):052910, 2014. doi:10.1103/PhysRevE.90.052910.
Nicolas Gisin and Stefan Wolf. Linking classical and quantum key agreement: is there “bound information”? In Advances in Cryptology – CRYPTO 2000, volume 1880 of Lecture Notes in Computer Science, 482–500. 2000. arXiv:quant-ph/0005042.
Naveen Goela. Polarized random variables: maximal correlations and common information. In 2014 IEEE International Symposium on Information Theory, 1643–1647. 2014. doi:10.1109/ISIT.2014.6875112.
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.
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.
Amin Aminzadeh Gohari and Venkat Anantharam. Information-theoretic key agreement of multiple terminals—part I. IEEE Transactions on Information Theory, 56(8):3973–3996, 2010.
Chetan Gohil, Oliver M. Cliff, James M. Shine, Ben D. Fulcher, and Joseph T. Lizier. Cross mutual information. In 2025 IEEE Information Theory Workshop (ITW). 2025. arXiv:2507.15372.
André F. C. Gomes and Mário A. T. Figueiredo. Orders between channels and implications for partial information decomposition. Entropy, 25(7):975, 2023.
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.
Peter Grassberger. Finite sample corrections to entropy and dimension estimates. Physics Letters A, 128(6–7):369–373, 1988. doi:10.1016/0375-9601(88)90193-4.
Peter Grassberger. Entropy estimates from insufficient samplings. 2003. arXiv:physics/0307138.
R. M. Gray and A. D. Wyner. Source coding for a simple network. The Bell System Technical Journal, 53(9):1681–1721, 1974.
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.
Virgil Griffith and Christof Koch. Quantifying synergistic mutual information. In Guided Self-Organization: Inception, pages 159–190. Springer, 2014.
Peter Gács and János Körner. Common information is far less than mutual information. Problems of Control and Information Theory, 2(2):149–162, 1973.
T. S. Han. Linear dependence structure of the entropy space. Information and Control, 29:337–368, 1975.
Malte Harder, Christoph Salge, and Daniel Polani. Bivariate measure of redundant information. Physical Review E, 87(1):012130, 2013.
Robin A. A. Ince. Measuring multivariate redundant information with pointwise common change in surprisal. Entropy, 19(7):318, 2017.
Robin A. A. Ince. The Partial Entropy Decompostion: decomposing multivariate entropy and mutual information via pointwise common surprisal. arXive preprint arXiv:1702.01591, 2017.
Ryan G. James and James P. Crutchfield. Multivariate dependence beyond shannon information. Entropy, 19(10):531, 2017. doi:10.3390/e19100531.
Ryan G. James, Jeffrey Emenheiser, and James P. Crutchfield. Unique information via dependency constraints. arXiv preprint arXiv:1709.06653, 2017.
Ryan G. James, Jeffrey Emenheiser, and James P. Crutchfield. Unique information and secret key agreement. Entropy, 21(1):12, 2019. doi:10.3390/e21010012.
Sudeep Kamath and Venkat Anantharam. A new dual to the Gács-Körner common information defined via the Gray-Wyner system. In 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 1340–1346. IEEE, 2010. doi:10.1109/allerton.2010.5707069.
Dan Kandel, Yossi Matias, Ron Unger, and Peter Winkler. Shuffling biological sequences. Discrete Applied Mathematics, 71(1–3):171–185, 1996. doi:10.1016/S0166-218X(97)81456-4.
Richard W. Katz. On some criteria for estimating the order of a Markov chain. Technometrics, 23(3):243–249, 1981. doi:10.2307/1267787.
Benjamin J. Killian, Joslyn Yundenfreund Kravitz, and Michael K. Gilson. Extraction of configurational entropy from molecular simulations via an expansion approximation. The Journal of Chemical Physics, 127(2):024107, 2007. doi:10.1063/1.2746329.
Michael Kleinman, Alessandro Achille, Stefano Soatto, and Jonathan Kao. Gacs-korner common information variational autoencoder. arXiv preprint arXiv:2205.12239, 2022.
Murat Kocaoglu, Alexandros G. Dimakis, Sriram Vishwanath, and Babak Hassibi. Entropic causal inference. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 31. 2017. doi:10.1609/aaai.v31i1.10674.
Artemy Kolchinsky. A novel approach to the partial information decomposition. Entropy, 24(3):403, 2022.
Artemy Kolchinsky and Bernat Corominas-Murtra. Decomposing information into copying versus transformation. arXiv preprint arXiv:1903.10693, 2019.
Artemy Kolchinsky, Brendan D Tracey, and Steven Van Kuyk. Caveats for information bottleneck in deterministic scenarios. arXiv preprint arXiv:1808.07593, 2018.
Ioannis Kontoyiannis, Paul H. Algoet, Yuri M. Suhov, and Abraham J. Wyner. Nonparametric entropy estimation for stationary processes and random fields, with applications to English text. IEEE Transactions on Information Theory, 44(3):1319–1327, 1998. doi:10.1109/18.669425.
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.
Mariusz Kubkowski and Jan Mielniczuk. Asymptotic distributions of empirical interaction information. Methodology and Computing in Applied Probability, 23(1):291–315, 2020. doi:10.1007/s11009-020-09783-0.
Dimitris Kugiumtzis. Transfer entropy on rank vectors. Journal of Nonlinear Systems and Applications 3(2):73–81, 2012. arXiv:1007.0357.
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.
Frank Lad, Giuseppe Sanfilippo, and Gianna Agrò. Extropy: a complementary dual of entropy. arXiv preprint arXiv:1109.6440, 2011.
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.
H. O. Lancaster. The Chi-Squared Distribution. Wiley, London, 1969.
Alexander Lex, Nils Gehlenborg, Hendrik Strobelt, Romain Vuillemot, and Hanspeter Pfister. Upset: visualization of intersecting sets. IEEE transactions on visualization and computer graphics, 20(12):1983–1992, 2014.
Cheuk Ting Li and Abbas El Gamal. Extended Gray–Wyner system with complementary causal side information. IEEE Transactions on Information Theory, 64(8):5862–5878, 2018. arXiv:1701.03207, doi:10.1109/TIT.2017.2777487.
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.
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.
Aobo Lyu, Andrew Clark, and Netanel Raviv. Explicit formula for partial information decomposition. In 2024 IEEE International Symposium on Information Theory (ISIT), 2329–2334. 2024. arXiv:2402.03554, doi:10.1109/ISIT57864.2024.10619361.
David JC MacKay. Information theory, inference and learning algorithms. Cambridge university press, 2003.
Tobias Mages and Christian Rohner. Decomposing and tracing mutual information by quantifying reachable decision regions. Entropy, 25(7):1014, 2023.
Konstantin Makarychev, Yury Makarychev, Andrei Romashchenko, and Nikolai Vereshchagin. A new class of non-Shannon-type inequalities for entropies. Communications in Information and Systems, 2(2):147–166, 2002. doi:10.4310/CIS.2002.v2.n2.a3.
Abdullah Makkeh, Daniel Chicharro, Dirk Oliver Theis, and Raul Vicente. Introducing a differentiable measure of pointwise shared information. Physical Review E, 103(3):032149, 2021.
Abdullah Makkeh, Dirk Oliver Theis, and Raul Vicente. BROJA-2PID: a robust estimator for bivariate partial information decomposition. Entropy, 20(4):271, 2018. doi:10.3390/e20040271.
Rostislav Matveev and Andrei Romashchenko. Beyond mutual information: extension profiles and shape functions of random variable pairs. 2026. arXiv:2606.23849.
Rostislav Matveev and Andrei Romashchenko. Spectral conditions for the Ingleton inequality. 2026. arXiv:2602.16536.
Ueli Maurer and Stefan Wolf. The intrinsic conditional mutual information and perfect secrecy. In IEEE international symposium on information theory, 88–88. Citeseer, 1997.
Ueli M. Maurer. Secret key agreement by public discussion from common information. IEEE Transactions on Information Theory, 39(3):733–742, 1993. doi:10.1109/18.256484.
W. J. McGill. Multivariate information transmission. Psychometrika, 19(2):97–116, 1954.
George A. Miller. Note on the bias of information estimates. In Henry Quastler, editor, Information Theory in Psychology: Problems and Methods, pages 95–100. Free Press, Glencoe, IL, 1955.
Ilya Nemenman, Fariel Shafee, and William Bialek. Entropy and inference, revisited. In Advances in Neural Information Processing Systems 14, 471–478. MIT Press, 2002. arXiv:physics/0108025.
Xueyan Niu and Christopher J Quinn. A measure of synergy, redundancy, and unique information using information geometry. In 2019 IEEE International Symposium on Information Theory (ISIT), 3127–3131. IEEE, 2019.
Eckehard Olbrich, Nils Bertschinger, and Johannes Rauh. Information decomposition and synergy. Entropy, 17(5):3501–3517, 2015.
Daniel P Palomar and Sergio Verdú. Lautum information. IEEE transactions on information theory, 54(3):964–975, 2008.
Jef Pauwels, Nicolas Gisin, and Renato Renner. Bipartite bound information exists. arXiv preprint arXiv:2607.25838, 2026.
Shawn D. Pethel and Daniel W. Hahs. Exact significance test for Markov order. Physica D: Nonlinear Phenomena, 269:42–47, 2014. arXiv:1302.1500, doi:10.1016/j.physd.2013.11.014.
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.
Dimitris N. Politis and Joseph P. Romano. The stationary bootstrap. Journal of the American Statistical Association, 89(428):1303–1313, 1994. doi:10.1080/01621459.1994.10476870.
Vinod M. Prabhakaran and Manoj M. Prabhakaran. Assisted common information with an application to secure two-party sampling. IEEE Transactions on Information Theory, 60(6):3413–3434, 2014. arXiv:1206.1282, doi:10.1109/TIT.2014.2316011.
Rick Quax, Omri Har-Shemesh, and Peter M. A. Sloot. Quantifying synergistic information using intermediate stochastic variables. Entropy, 19(2):85, 2017. doi:10.3390/e19020085.
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.
Johannes Rauh. Secret sharing and shared information. arXiv preprint arXiv:1706.06998, 2017.
Johannes Rauh, Pradeep Kr Banerjee, Eckehard Olbrich, Jürgen Jost, and Nils Bertschinger. On extractable shared information. arXiv preprint arXiv:1701.07805, 2017.
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.
Johannes Rauh, Maik Schünemann, and Jürgen Jost. Properties of unique information. arXiv preprint arXiv:1912.12505, 2019.
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.
Renato Renner and Stefan Wolf. New bounds in secret-key agreement: the gap between formation and secrecy extraction. In Advances in Cryptology — EUROCRYPT 2003, volume 2656 of Lecture Notes in Computer Science, 562–577. Springer, 2003. doi:10.1007/3-540-39200-9_35.
Fernando Rosas, Vasilis Ntranos, Christopher J Ellison, Sofie Pollin, and Marian Verhelst. Understanding interdependency through complex information sharing. Entropy, 18(2):38, 2016.
Fernando E Rosas, Pedro AM Mediano, Michael Gastpar, and Henrik J Jensen. Quantifying high-order interdependencies via multivariate extensions of the mutual information. Physical Review E, 100(3):032305, 2019.
Fernando E. Rosas, Pedro A. M. Mediano, Borzoo Rassouli, and Adam B. Barrett. An operational information decomposition via synergistic disclosure. Journal of Physics A: Mathematical and Theoretical, 53(48):485001, 2020. doi:10.1088/1751-8121/abb723.
Salman Salamatian, Asaf Cohen, and Muriel Médard. Maximum entropy functions: approximate Gács-Körner for distributed compression. In Information Theory and Applications Workshop (ITA). 2016. arXiv:1604.03877.
E. Schneidman, S. Still, M. J. Berry, W. Bialek, and others. Network information and connected correlations. Phys. Rev. Lett., 91(23):238701, 2003.
Dino Sejdinovic, Arthur Gretton, and Wicher Bergsma. A kernel test for three-variable interactions. In Advances in Neural Information Processing Systems, volume 26. 2013. arXiv:1306.2281.
David Sigtermans. A path-based partial information decomposition. Entropy, 22(9):952, 2020.
Noam Slonim, Gurinder Singh Atwal, Gašper Tkačik, and William Bialek. Information based clustering. arXiv preprint q-bio/0511043, 2005.
Bernd Streitberg. Lancaster interactions revisited. The Annals of Statistics, 18(4):1878–1885, 1990. doi:10.1214/aos/1176347885.
Christopher C. Strelioff, James P. Crutchfield, and Alfred W. Hübler. Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling. Physical Review E, 76(1):011106, 2007. doi:10.1103/PhysRevE.76.011106.
DJ Strouse and David J Schwab. The deterministic information bottleneck. arXiv preprint arXiv:1604.00268, 2016.
H. Te Sun. Multiple mutual informations and multiple interactions in frequency data. Information and Control, 46:26–45, 1980.
Naftali Tishby, Fernando C Pereira, and William Bialek. The information bottleneck method. arXiv preprint physics/0004057, 2000.
Howell Tong. Determination of the order of a Markov chain by Akaike's information criterion. Journal of Applied Probability, 12(3):488–497, 1975. doi:10.2307/3212863.
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.
H. Tyagi, P. Narayan, and P. Gupta. When is a function securely computable? Information Theory, IEEE Transactions on, 57(10):6337–6350, 2011.
Francisco José Valverde-Albacete and Carmen Peláez-Moreno. The multivariate entropy triangle and applications. In Hybrid Artificial Intelligent Systems, pages 647–658. Springer, 2016.
Marten van Dijk. On a special class of broadcast channels with confidential messages. IEEE Transactions on Information Theory, 43(2):712–714, 1997. doi:10.1109/18.556128.
Cristiano Varin, Nancy Reid, and David Firth. An overview of composite likelihood methods. Statistica Sinica, 21(1):5–42, 2011.
Thomas F. Varley. The many faces of multivariate information. arXiv preprint arXiv:2601.08030, 2026.
Praveen Venkatesh, Keerthana Gurushankar, and Gabriel Schamberg. Capturing and interpreting unique information. arXiv preprint arXiv:2302.11873, 2023.
Sergio Verdu and Tsachy Weissman. The information lost in erasures. Information Theory, IEEE Transactions on, 54(11):5030–5058, 2008.
S. Verdú and T. Weissman. Erasure entropy. In Information Theory, 2006 IEEE International Symposium on, 98–102. IEEE, 2006.
K. B. Viswanatha, E. Akyol, and K. Rose. The lossy common information of correlated sources. IEEE Transactions on Information Theory, 60(6):3238–3253, 2014. doi:10.1109/TIT.2014.2315805.
Xiang Wan, Can Yang, Qiang Yang, Hong Xue, Xiaodan Fan, Nelson L. S. Tang, and Weichuan Yu. BOOST: a fast approach to detecting gene-gene interactions in genome-wide case-control studies. The American Journal of Human Genetics, 87(3):325–340, 2010. doi:10.1016/j.ajhg.2010.07.021.
S. Watanabe. Information theoretical analysis of multivariate correlation. IBM Journal of research and development, 4(1):66–82, 1960.
P. Whittle. Some distribution and moment formulae for the Markov chain. Journal of the Royal Statistical Society: Series B (Methodological), 17(2):235–242, 1955. doi:10.1111/j.2517-6161.1955.tb00197.x.
Paul L Williams and Randall D Beer. Nonnegative decomposition of multivariate information. arXiv preprint arXiv:1004.2515, 2010.
Paul L Williams and Randall D Beer. Generalized measures of information transfer. arXiv preprint arXiv:1102.1507, 2011.
Andreas Winter. Secret, public and quantum correlation cost of triples of random variables. In IEEE International Symposium on Information Theory, 2270–2274. 2005. doi:10.1109/ISIT.2005.1523752.
A. D. Wyner. The common information of two dependent random variables. Information Theory, IEEE Transactions on, 21(2):163–179, 1975.
Raymond W Yeung. Information theory and network coding. Springer, 2008.
Hubert P. Yockey. Information Theory, Evolution, and the Origin of Life. Cambridge University Press, Cambridge, 2005.
Lei Yu, Houqiang Li, and Chang Wen Chen. Generalized common informations: measuring commonness by the conditional maximal correlation. arXiv preprint arXiv:1610.09289, 2017. arXiv:1610.09289.
Zhen Zhang. On a new non-Shannon type information inequality. Communications in Information and Systems, 3(1):47–60, 2003. doi:10.4310/CIS.2003.v3.n1.a4.
M. Zwick. An overview of reconstructability analysis. Kybernetes, 33(5/6):877–905, 2004.