Information theory | Covariance and correlation

Maximal information coefficient

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. In a simulation study, MIC outperformed some selected low power tests, 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). Comparisons with these methods, in which MIC was outperformed, were made in Simon and Tibshirani and in Gorfine, Heller, and Heller. It is claimed that MIC approximately satisfies a property called equitability which is illustrated by selected simulation studies. It was later proved that no non-trivial coefficient can exactly satisfy the equitability property as defined by Reshef et al., although this result has been challenged. Some criticisms of MIC are addressed by Reshef et al. in further studies published on arXiv. (Wikipedia).

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