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In statistics, the maximal information coefficient (MIC) is a measure of the strength of the linear or non-linear association between two variables X and Y.
The MIC belongs to the maximal information-based nonparametric exploration (MINE) class of statistics.[1] In a simulation study, MIC outperformed some selected low power tests,[1] however concerns have been raised regarding reduced statistical power in detecting some associations in settings with low sample size when compared to powerful methods such as distance correlation and Heller–Heller–Gorfine (HHG).[2] Comparisons with these methods, in which MIC was outperformed, were made in Simon and Tibshirani[3] and in Gorfine, Heller, and Heller.[4] It is claimed[1] that MIC approximately satisfies a property called equitability which is illustrated by selected simulation studies.[1] It was later proved that no non-trivial coefficient can exactly satisfy the equitability property as defined by Reshef et al.,[1][5] although this result has been challenged.[6] Some criticisms of MIC are addressed by Reshef et al. in further studies published on arXiv.[7]
^ abcdeReshef, D. N.; Reshef, Y. A.; Finucane, H. K.; Grossman, S. R.; McVean, G.; Turnbaugh, P. J.; Lander, E. S.; Mitzenmacher, M.; Sabeti, P. C. (2011). "Detecting novel associations in large data sets". Science. 334 (6062): 1518–1524. Bibcode:2011Sci...334.1518R. doi:10.1126/science.1205438. PMC 3325791. PMID 22174245.
^Heller, R.; Heller, Y.; Gorfine, M. (2012). "A consistent multivariate test of association based on ranks of distances". Biometrika. 100 (2): 503–510. arXiv:1201.3522. doi:10.1093/biomet/ass070.
^Noah Simon and Robert Tibshirani, Comment on “Detecting Novel Associations in Large Data Sets” by Reshef et al., Science Dec. 16, 2011
^"Comment on "Detecting Novel Associations in Large Data Sets"" (PDF). Archived from the original (PDF) on 2017-08-08.
^Equitability, mutual information, and the maximal information coefficient by Justin B. Kinney, Gurinder S. Atwal, arXiv Jan. 31, 2013
^Murrell, Ben; Murrell, Daniel; Murrell, Hugh (2014). "R2-equitability is satisfiable". Proceedings of the National Academy of Sciences. 111 (21): E2160. Bibcode:2014PNAS..111E2160M. doi:10.1073/pnas.1403623111. PMC 4040619. PMID 24782547.
^Equitability Analysis of the Maximal Information Coefficient, with Comparisons by David Reshef, Yakir Reshef, Michael Mitzenmacher, Pardis Sabeti, arXiv Jan. 27, 2013
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