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The proposal of Reshef et al. (2011) is an interesting new approach fordiscovering non-linear dependencies among pairs of measurements in exploratorydata mining. However, it has a potentially serious drawback. The authors laudthe fact that MIC has no preference for some alternatives over others, but asthe authors know, there is no free lunch in Statistics: tests which strive tohave high power against all alternatives can have low power in many importantsituations. To investigate this, we ran simulations to compare the power of MICto that of standard Pearson correlation and distance correlation (dcor). Wesimulated pairs of variables with different relationships (most of which wereconsidered by the Reshef et. al.), but with varying levels of noise added. Todetermine proper cutoffs for testing the independence hypothesis, we simulatedindependent data with the appropriate marginals. As one can see from theFigure, MIC has lower power than dcor, in every case except the somewhatpathological high-frequency sine wave. MIC is sometimes less powerful thanPearson correlation as well, the linear case being particularly worrisome.

Comment on "Detecting Novel Associations In Large Data Sets" by Reshef Et Al, Science Dec 16, 2011