<P> 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 . </P> <P> 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 HHG . Comparisons with these methods, in which MIC was outperformed, were made in and . 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 . </P> <P> The maximal information coefficient uses binning as a means to apply mutual information on continuous random variables . Binning has been used for some time as a way of applying mutual information to continuous distributions; what MIC contributes in addition is a methodology for selecting the number of bins and picking a maximum over many possible grids . </P> <P> The rationale is that the bins for both variables should be chosen in such a way that the mutual information between the variables be maximal . That is achieved whenever H (X b) = H (Y b) = H (X b, Y b) (\ displaystyle \ mathrm (H) \ left (X_ (b) \ right) = \ mathrm (H) \ left (Y_ (b) \ right) = \ mathrm (H) \ left (X_ (b), Y_ (b) \ right)). Thus, when the mutual information is maximal over a binning of the data, we should expect that the following two properties hold, as much as made possible by the own nature of the data . First, the bins would have roughly the same size, because the entropies H (X b) (\ displaystyle \ mathrm (H) (X_ (b))) and H (Y b) (\ displaystyle \ mathrm (H) (Y_ (b))) are maximized by equal - sized binning . And second, each bin of X will roughly correspond to a bin in Y . </P>

Equitability mutual information and the maximal information coefficient