References

[1]

Adam B Barrett. Exploration of synergistic and redundant information sharing in static and dynamical gaussian systems. Physical Review E, 91(5):052802, 2015.

[2]

Federico Battiston, Enrico Amico, Alain Barrat, Ginestra Bianconi, Guilherme Ferraz de Arruda, Benedetta Franceschiello, Iacopo Iacopini, Sonia Kéfi, Vito Latora, Yamir Moreno, and others. The physics of higher-order interactions in complex systems. Nature Physics, 17(10):1093–1098, 2021.

[3]

Federico Battiston, Giulia Cencetti, Iacopo Iacopini, Vito Latora, Maxime Lucas, Alice Patania, Jean-Gabriel Young, and Giovanni Petri. Networks beyond pairwise interactions: structure and dynamics. Physics Reports, 874:1–92, 2020.

[4]

Pierre Baudot, Monica Tapia, Daniel Bennequin, and Jean-Marc Goaillard. Topological information data analysis. Entropy. An International and Interdisciplinary Journal of Entropy and Information Studies, 2019. Number: 869. URL: https://www.mdpi.com/1099-4300/21/9/869, doi:10.3390/e21090869.

[5]

Gal Chechik, Amir Globerson, M Anderson, E Young, Israel Nelken, and Naftali Tishby. Group redundancy measures reveal redundancy reduction in the auditory pathway. Advances in neural information processing systems, 2001.

[6]

Georges A Darbellay and Igor Vajda. Estimation of the information by an adaptive partitioning of the observation space. IEEE Transactions on Information Theory, 45(4):1315–1321, 1999.

[7]

Dominik Endres and Peter Foldiak. Bayesian bin distribution inference and mutual information. IEEE Transactions on Information Theory, 51(11):3766–3779, 2005.

[8]

Andrew M Fraser and Harry L Swinney. Independent coordinates for strange attractors from mutual information. Physical review A, 33(2):1134, 1986.

[9]

Amir Globerson, Eran Stark, Eilon Vaadia, and Naftali Tishby. The minimum information principle and its application to neural code analysis. Proceedings of the National Academy of Sciences, 106(9):3490–3495, 2009.

[10]

Nathaniel R Goodman. Statistical analysis based on a certain multivariate complex gaussian distribution (an introduction). The Annals of mathematical statistics, 34(1):152–177, 1963.

[11]

Virgil Griffith and Christof Koch. Quantifying synergistic mutual information. In Guided self-organization: inception, pages 159–190. Springer, 2014.

[12]

Robin AA Ince, Bruno L Giordano, Christoph Kayser, Guillaume A Rousselet, Joachim Gross, and Philippe G Schyns. A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula. Human brain mapping, 38(3):1541–1573, 2017.

[13]

Ryan G James, Christopher J Ellison, and James P Crutchfield. Anatomy of a bit: information in a time series observation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011.

[14]

Alexander Kraskov, Harald Stögbauer, and Peter Grassberger. Estimating mutual information. Physical review E, 69(6):066138, 2004.

[15]

Young-Il Moon, Balaji Rajagopalan, and Upmanu Lall. Estimation of mutual information using kernel density estimators. Physical Review E, 52(3):2318, 1995.

[16]

Fernando E. Rosas, Pedro A. M. Mediano, Michael Gastpar, and Henrik J. Jensen. Quantifying high-order interdependencies via multivariate extensions of the mutual information. Physical Review E, 100(3):032305, September 2019. Publisher: American Physical Society. URL: https://link.aps.org/doi/10.1103/PhysRevE.100.032305 (visited on 2022-12-17), doi:10.1103/PhysRevE.100.032305.

[17]

Tomas Scagliarini, Davide Nuzzi, Yuri Antonacci, Luca Faes, Fernando E Rosas, Daniele Marinazzo, and Sebastiano Stramaglia. Gradients of o-information: low-order descriptors of high-order dependencies. Physical Review Research, 5(1):013025, 2023.

[18]

Elad Schneidman, Susanne Still, Michael J Berry, William Bialek, and others. Network information and connected correlations. Physical review letters, 91(23):238701, 2003.

[19]

Claude Elwood Shannon. A mathematical theory of communication. The Bell system technical journal, 27(3):379–423, 1948.

[20]

Milan Studen\`y and Jirina Vejnarová. The multiinformation function as a tool for measuring stochastic dependence. Learning in graphical models, pages 261–297, 1998.

[21]

TH Sun. Linear dependence structure of the entropy space. Inf Control, 29(4):337–68, 1975.

[22]

Mónica Tapia, Pierre Baudot, Christine Formisano-Tréziny, Martial A Dufour, Simone Temporal, Manon Lasserre, Béatrice Marquèze-Pouey, Jean Gabert, Kazuto Kobayashi, and Jean-Marc Goaillard. Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons. Scientific reports, 8(1):13637, 2018.

[23]

Han Te Sun. Nonnegative entropy measures of multivariate symmetric correlations. Information and Control, 36:133–156, 1978.

[24]

Nicholas Timme, Wesley Alford, Benjamin Flecker, and John M Beggs. Synergy, redundancy, and multivariate information measures: an experimentalist’s perspective. Journal of computational neuroscience, 36:119–140, 2014.

[25]

Thomas F Varley. Information theory for complex systems scientists. arXiv preprint arXiv:2304.12482, 2023.

[26]

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

[27]

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