Multivariate Mutual Information

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HandWiki. Multivariate Mutual Information. Encyclopedia. Available online: https://encyclopedia.pub/entry/29927 (accessed on 22 September 2026).

HandWiki. Multivariate Mutual Information. Encyclopedia. Available at: https://encyclopedia.pub/entry/29927. Accessed September 22, 2026.

HandWiki. "Multivariate Mutual Information" Encyclopedia, https://encyclopedia.pub/entry/29927 (accessed September 22, 2026).

HandWiki. (2022, October 18). Multivariate Mutual Information. In Encyclopedia. https://encyclopedia.pub/entry/29927

HandWiki. "Multivariate Mutual Information." Encyclopedia. Web. 18 October, 2022.

Multivariate Mutual Information

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The content is sourced from: https://handwiki.org/wiki/Multivariate_mutual_information

In information theory there have been various attempts over the years to extend the definition of mutual information to more than two random variables. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams .

mutual information mutual-information information theory

References

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Baudot, P.; Tapia, M.; Bennequin, D.; Goaillard, JM. (2019). "Topological Information Data Analysis". Entropy 21 (9): 869. doi:10.3390/e21090869. https://dx.doi.org/10.3390%2Fe21090869
Tapia, M.; Baudot, P.; Formizano-Treziny, C.; Dufour, M.; Goaillard, J.M. (2018). "Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons". Sci. Rep. 8: 13637. doi:10.1038/s41598-018-31765-z. https://dx.doi.org/10.1038%2Fs41598-018-31765-z
Timme, Nicholas; Alford, Wesley; Flecker, Benjamin; Beggs, John M. (2012). "Multivariate information measures: an experimentalist's perspective". arXiv:1111.6857. Bibcode: 2011arXiv1111.6857T http://adsabs.harvard.edu/abs/2011arXiv1111.6857T
Brenner, N.; Strong, S.; Koberle, R.; Bialek, W. (2000). "Synergy in a Neural Code". Neural Comput 12: 1531–1552. doi:10.1162/089976600300015259. https://dx.doi.org/10.1162%2F089976600300015259
Watkinson, J.; Liang, K.; Wang, X.; Zheng, T.; Anastassiou, D. (2009). "Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information". Chall. Syst. Biol. Ann. N. Y. Acad. Sci. 1158: 302–313. doi:10.1111/j.1749-6632.2008.03757.x. https://dx.doi.org/10.1111%2Fj.1749-6632.2008.03757.x

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