Mutual information (English Wikipedia)

Kreer, J. G. (1957). "A question of terminology". IRE Transactions on Information Theory. 3 (3): 208. doi:10.1109/TIT.1957.1057418.
Wolpert, D.H.; Wolf, D.R. (1995). "Estimating functions of probability distributions from a finite set of samples". Physical Review E. 52 (6): 6841–6854. Bibcode:1995PhRvE..52.6841W. doi:10.1103/PhysRevE.52.6841. PMID 9964199. S2CID 9795679.
Archer, E.; Park, I.M.; Pillow, J. (2013). "Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data". Entropy. 15 (12): 1738–1755. Bibcode:2013Entrp..15.1738A. doi:10.3390/e15051738.
Wolpert, D.H; DeDeo, S. (2013). "Estimating Functions of Distributions Defined over Spaces of Unknown Size". Entropy. 15 (12): 4668–4699. arXiv:1311.4548. Bibcode:2013Entrp..15.4668W. doi:10.3390/e15114668. S2CID 2737117.
Tomasz Jetka; Karol Nienaltowski; Tomasz Winarski; Slawomir Blonski; Michal Komorowski (2019). "Information-theoretic analysis of multivariate single-cell signaling responses". PLOS Computational Biology. 15 (7) e1007132. arXiv:1808.05581. Bibcode:2019PLSCB..15E7132J. doi:10.1371/journal.pcbi.1007132. PMC 6655862. PMID 31299056.
Rajski, C. (1961). "A metric space of discrete probability distributions". Information and Control. 4 (4): 371–377. doi:10.1016/S0019-9958(61)80055-7.
Rajski, C. (1961). "A metric space of discrete probability distributions". Information and Control. 4 (4): 371–377. doi:10.1016/S0019-9958(61)80055-7.
McGill, W. (1954). "Multivariate information transmission". Psychometrika. 19 (1): 97–116. doi:10.1007/BF02289159. S2CID 126431489.
Hu, K.T. (1962). "On the Amount of Information". Theory Probab. Appl. 7 (4): 439–447. doi:10.1137/1107041.
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 (1): 13637. Bibcode:2018NatSR...813637T. doi:10.1038/s41598-018-31765-z. PMC 6134142. PMID 30206240.
Baudot, P.; Tapia, M.; Bennequin, D.; Goaillard, J.M. (2019). "Topological Information Data Analysis". Entropy. 21 (9). 869. arXiv:1907.04242. Bibcode:2019Entrp..21..869B. doi:10.3390/e21090869. PMC 7515398. S2CID 195848308.
Brenner, N.; Strong, S.; Koberle, R.; Bialek, W. (2000). "Synergy in a Neural Code". Neural Comput. 12 (7): 1531–1552. doi:10.1162/089976600300015259. PMID 10935917. S2CID 600528.
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 (1): 302–313. Bibcode:2009NYASA1158..302W. doi:10.1111/j.1749-6632.2008.03757.x. PMID 19348651. S2CID 8846229.
Haghighat, M. B. A.; Aghagolzadeh, A.; Seyedarabi, H. (2011). "A non-reference image fusion metric based on mutual information of image features". Computers & Electrical Engineering. 37 (5): 744–756. doi:10.1016/j.compeleceng.2011.07.012. S2CID 7738541.
Permuter, Haim Henry; Weissman, Tsachy; Goldsmith, Andrea J. (February 2009). "Finite State Channels With Time-Invariant Deterministic Feedback". IEEE Transactions on Information Theory. 55 (2): 644–662. arXiv:cs/0608070. doi:10.1109/TIT.2008.2009849. S2CID 13178.
Wijaya, Dedy Rahman; Sarno, Riyanarto; Zulaika, Enny (2017). "Information Quality Ratio as a novel metric for mother wavelet selection". Chemometrics and Intelligent Laboratory Systems. 160: 59–71. doi:10.1016/j.chemolab.2016.11.012.
Strehl, Alexander; Ghosh, Joydeep (2003). "Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions" (PDF). The Journal of Machine Learning Research. 3: 583–617. doi:10.1162/153244303321897735.
Jerdee, M., Kirkley, A. & Newman, M. Normalized mutual information is a biased measure for classification and community detection. Nat Commun (2025). https://doi.org/10.1038/s41467-025-66150-8
Kvålseth, T. O. (1991). "The relative useful information measure: some comments". Information Sciences. 56 (1): 35–38. doi:10.1016/0020-0255(91)90022-m.
Everett, Hugh (1957). "Relative State Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454–462. Bibcode:1957RvMP...29..454E. doi:10.1103/revmodphys.29.454. Archived from the original on 2011-10-27. Retrieved 2012-07-16.
Nicoletti, Giorgio; Busiello, Daniel Maria (2021-11-22). "Mutual Information Disentangles Interactions from Changing Environments". Physical Review Letters. 127 (22) 228301. arXiv:2107.08985. Bibcode:2021PhRvL.127v8301N. doi:10.1103/PhysRevLett.127.228301. PMID 34889638. S2CID 236087228.
Nicoletti, Giorgio; Busiello, Daniel Maria (2022-07-29). "Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities". Physical Review E. 106 (1) 014153. arXiv:2204.01644. Bibcode:2022PhRvE.106a4153N. doi:10.1103/PhysRevE.106.014153. PMID 35974654.
Lee, Se Yoon (2021). "Gibbs sampler and coordinate ascent variational inference: A set-theoretical review". Communications in Statistics - Theory and Methods. 51 (6): 1549–1568. arXiv:2008.01006. doi:10.1080/03610926.2021.1921214. S2CID 220935477.
Keys, Dustin; Kholikov, Shukur; Pevtsov, Alexei A. (February 2015). "Application of Mutual Information Methods in Time Distance Helioseismology". Solar Physics. 290 (3): 659–671. arXiv:1501.05597. Bibcode:2015SoPh..290..659K. doi:10.1007/s11207-015-0650-y. S2CID 118472242.
Nicoletti, Giorgio; Busiello, Daniel Maria (2024-04-08). "Information Propagation in Multilayer Systems with Higher-Order Interactions across Timescales". Physical Review X. 14 (2) 021007. arXiv:2312.06246. Bibcode:2024PhRvX..14b1007N. doi:10.1103/PhysRevX.14.021007.

infotopo.readthedocs.io (Global: low place; English: low place)

"InfoTopo: Topological Information Data Analysis. Deep statistical unsupervised and supervised learning - File Exchange - Github". github.com/pierrebaudot/infotopopy/. Retrieved 26 September 2020.

jmlr.org (Global: low place; English: low place)

Strehl, Alexander; Ghosh, Joydeep (2003). "Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions" (PDF). The Journal of Machine Learning Research. 3: 583–617. doi:10.1162/153244303321897735.

man.ac.uk (Global: low place; English: low place)

cs.man.ac.uk

Pocock, A. (2012). Feature Selection Via Joint Likelihood (PDF) (Thesis). Archived from the original (PDF) on 2018-11-05.

mathworks.com (Global: low place; English: 9,012^th place)

"Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central". www.mathworks.com. Retrieved 4 April 2018.

mlr.press (Global: low place; English: low place)

proceedings.mlr.press

Janssen, Joseph; Guan, Vincent; Robeva, Elina (2023). "Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees". International Conference on Artificial Intelligence and Statistics: 10782–10814. arXiv:2204.09938.

nih.gov (Global: 5^th place; English: 5^th place)

pubmed.ncbi.nlm.nih.gov

Wolpert, D.H.; Wolf, D.R. (1995). "Estimating functions of probability distributions from a finite set of samples". Physical Review E. 52 (6): 6841–6854. Bibcode:1995PhRvE..52.6841W. doi:10.1103/PhysRevE.52.6841. PMID 9964199. S2CID 9795679.
Tomasz Jetka; Karol Nienaltowski; Tomasz Winarski; Slawomir Blonski; Michal Komorowski (2019). "Information-theoretic analysis of multivariate single-cell signaling responses". PLOS Computational Biology. 15 (7) e1007132. arXiv:1808.05581. Bibcode:2019PLSCB..15E7132J. doi:10.1371/journal.pcbi.1007132. PMC 6655862. PMID 31299056.
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 (1): 13637. Bibcode:2018NatSR...813637T. doi:10.1038/s41598-018-31765-z. PMC 6134142. PMID 30206240.
Brenner, N.; Strong, S.; Koberle, R.; Bialek, W. (2000). "Synergy in a Neural Code". Neural Comput. 12 (7): 1531–1552. doi:10.1162/089976600300015259. PMID 10935917. S2CID 600528.
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 (1): 302–313. Bibcode:2009NYASA1158..302W. doi:10.1111/j.1749-6632.2008.03757.x. PMID 19348651. S2CID 8846229.
Nicoletti, Giorgio; Busiello, Daniel Maria (2021-11-22). "Mutual Information Disentangles Interactions from Changing Environments". Physical Review Letters. 127 (22) 228301. arXiv:2107.08985. Bibcode:2021PhRvL.127v8301N. doi:10.1103/PhysRevLett.127.228301. PMID 34889638. S2CID 236087228.
Nicoletti, Giorgio; Busiello, Daniel Maria (2022-07-29). "Mutual information in changing environments: Nonlinear interactions, out-of-equilibrium systems, and continuously varying diffusivities". Physical Review E. 106 (1) 014153. arXiv:2204.01644. Bibcode:2022PhRvE.106a4153N. doi:10.1103/PhysRevE.106.014153. PMID 35974654.

ncbi.nlm.nih.gov

Tomasz Jetka; Karol Nienaltowski; Tomasz Winarski; Slawomir Blonski; Michal Komorowski (2019). "Information-theoretic analysis of multivariate single-cell signaling responses". PLOS Computational Biology. 15 (7) e1007132. arXiv:1808.05581. Bibcode:2019PLSCB..15E7132J. doi:10.1371/journal.pcbi.1007132. PMC 6655862. PMID 31299056.
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 (1): 13637. Bibcode:2018NatSR...813637T. doi:10.1038/s41598-018-31765-z. PMC 6134142. PMID 30206240.
Baudot, P.; Tapia, M.; Bennequin, D.; Goaillard, J.M. (2019). "Topological Information Data Analysis". Entropy. 21 (9). 869. arXiv:1907.04242. Bibcode:2019Entrp..21..869B. doi:10.3390/e21090869. PMC 7515398. S2CID 195848308.

nrbook.com (Global: low place; English: low place)

apps.nrbook.com

Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Section 14.7.3. Conditional Entropy and Mutual Information". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN 978-0-521-88068-8. Archived from the original on 2011-08-11. Retrieved 2011-08-13.

omsk.su (Global: low place; English: low place)

univer.omsk.su

Everett, Hugh (1957). "Relative State Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454–462. Bibcode:1957RvMP...29..454E. doi:10.1103/revmodphys.29.454. Archived from the original on 2011-10-27. Retrieved 2012-07-16.

pbs.org (Global: 260^th place; English: 176^th place)

Hugh Everett Theory of the Universal Wavefunction, Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)

psu.edu (Global: 299^th place; English: 159^th place)

citeseerx.ist.psu.edu

Massey, James (1990). "Causality, Feedback And Directed Informatio". Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990. Archived from the original on 2018-04-07. Retrieved 2018-12-16.{{cite conference}}: CS1 maint: miscellaneous url (link)
"Parsing a Natural Language Using Mutual Information Statistics". Archived from the original on 2014-02-25.{{cite web}}: CS1 maint: miscellaneous url (link) by David M. Magerman and Mitchell P. Marcus

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Wolpert, D.H.; Wolf, D.R. (1995). "Estimating functions of probability distributions from a finite set of samples". Physical Review E. 52 (6): 6841–6854. Bibcode:1995PhRvE..52.6841W. doi:10.1103/PhysRevE.52.6841. PMID 9964199. S2CID 9795679.
Wolpert, D.H; DeDeo, S. (2013). "Estimating Functions of Distributions Defined over Spaces of Unknown Size". Entropy. 15 (12): 4668–4699. arXiv:1311.4548. Bibcode:2013Entrp..15.4668W. doi:10.3390/e15114668. S2CID 2737117.
McGill, W. (1954). "Multivariate information transmission". Psychometrika. 19 (1): 97–116. doi:10.1007/BF02289159. S2CID 126431489.
Baudot, P.; Tapia, M.; Bennequin, D.; Goaillard, J.M. (2019). "Topological Information Data Analysis". Entropy. 21 (9). 869. arXiv:1907.04242. Bibcode:2019Entrp..21..869B. doi:10.3390/e21090869. PMC 7515398. S2CID 195848308.
Brenner, N.; Strong, S.; Koberle, R.; Bialek, W. (2000). "Synergy in a Neural Code". Neural Comput. 12 (7): 1531–1552. doi:10.1162/089976600300015259. PMID 10935917. S2CID 600528.
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 (1): 302–313. Bibcode:2009NYASA1158..302W. doi:10.1111/j.1749-6632.2008.03757.x. PMID 19348651. S2CID 8846229.
Haghighat, M. B. A.; Aghagolzadeh, A.; Seyedarabi, H. (2011). "A non-reference image fusion metric based on mutual information of image features". Computers & Electrical Engineering. 37 (5): 744–756. doi:10.1016/j.compeleceng.2011.07.012. S2CID 7738541.
Permuter, Haim Henry; Weissman, Tsachy; Goldsmith, Andrea J. (February 2009). "Finite State Channels With Time-Invariant Deterministic Feedback". IEEE Transactions on Information Theory. 55 (2): 644–662. arXiv:cs/0608070. doi:10.1109/TIT.2008.2009849. S2CID 13178.
Nicoletti, Giorgio; Busiello, Daniel Maria (2021-11-22). "Mutual Information Disentangles Interactions from Changing Environments". Physical Review Letters. 127 (22) 228301. arXiv:2107.08985. Bibcode:2021PhRvL.127v8301N. doi:10.1103/PhysRevLett.127.228301. PMID 34889638. S2CID 236087228.
Lee, Se Yoon (2021). "Gibbs sampler and coordinate ascent variational inference: A set-theoretical review". Communications in Statistics - Theory and Methods. 51 (6): 1549–1568. arXiv:2008.01006. doi:10.1080/03610926.2021.1921214. S2CID 220935477.
Keys, Dustin; Kholikov, Shukur; Pevtsov, Alexei A. (February 2015). "Application of Mutual Information Methods in Time Distance Helioseismology". Solar Physics. 290 (3): 659–671. arXiv:1501.05597. Bibcode:2015SoPh..290..659K. doi:10.1007/s11207-015-0650-y. S2CID 118472242.

web.archive.org (Global: 1^st place; English: 1^st place)

Massey, James (1990). "Causality, Feedback And Directed Informatio". Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990. Archived from the original on 2018-04-07. Retrieved 2018-12-16.{{cite conference}}: CS1 maint: miscellaneous url (link)
Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Section 14.7.3. Conditional Entropy and Mutual Information". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN 978-0-521-88068-8. Archived from the original on 2011-08-11. Retrieved 2011-08-13.
White, Jim; Steingold, Sam; Fournelle, Connie. Performance Metrics for Group-Detection Algorithms (PDF). Interface 2004. Archived from the original on 2016-07-05. Retrieved 2014-02-19.
Pocock, A. (2012). Feature Selection Via Joint Likelihood (PDF) (Thesis). Archived from the original (PDF) on 2018-11-05.
"Parsing a Natural Language Using Mutual Information Statistics". Archived from the original on 2014-02-25.{{cite web}}: CS1 maint: miscellaneous url (link) by David M. Magerman and Mitchell P. Marcus
Everett, Hugh (1957). "Relative State Formulation of Quantum Mechanics". Reviews of Modern Physics. 29 (3): 454–462. Bibcode:1957RvMP...29..454E. doi:10.1103/revmodphys.29.454. Archived from the original on 2011-10-27. Retrieved 2012-07-16.

Mutual information (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

aps.org (Global: 1,264th place; English: 951st place)

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arxiv.org (Global: 49th place; English: 31st place)

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cs.man.ac.uk

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mlr.press (Global: low place; English: low place)

proceedings.mlr.press

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ncbi.nlm.nih.gov

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univer.omsk.su

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citeseerx.ist.psu.edu

semanticscholar.org (Global: 15th place; English: 8th place)

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aps.org (Global: 1,264^th place; English: 951^st place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

code.google.com (Global: 6,691^st place; English: 6,208^th place)

columbia.edu (Global: 554^th place; English: 368^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

mathworks.com (Global: low place; English: 9,012^th place)

nih.gov (Global: 5^th place; English: 5^th place)

pbs.org (Global: 260^th place; English: 176^th place)

psu.edu (Global: 299^th place; English: 159^th place)

semanticscholar.org (Global: 15^th place; English: 8^th place)

web.archive.org (Global: 1^st place; English: 1^st place)