부산대학교 도서관

Summary: ``How should one quantify the strength of association betweentwo random variables without bias for relationships of a specific form?Despite its conceptual simplicity, this notion of statistical`equitability' has yet to receive a definitive mathematicalformalization. Here we argue that equitability is properly formalizedby a self-consistency condition closely related to Data ProcessingInequality. Mutual information, a fundamental quantity in informationtheory, is shown to satisfy this equitability criterion. These findingsare at odds with the recent work of D. N. Reshef et al. [Science {\bf 334}(2011), no. 6062, 1518--1524, \doi{10.1126/science.1205438}], which proposed analternative definition of equitability and introduced a new statistic,the `maximal information coefficient' (MIC), said to satisfyequitability in contradistinction to mutual information. Theseconclusions, however, were supported only with limited simulationevidence, not with mathematical arguments. Upon revisiting theseclaims, we prove that the mathematical definition of equitabilityproposed by Reshef et al. cannot be satisfied by any (nontrivial)dependence measure. We also identify artifacts in the reportedsimulation evidence. When these artifacts are removed, estimates ofmutual information are found to be more equitable than estimates ofMIC. Mutual information is also observed to have consistently higherstatistical power than MIC. We conclude that estimating mutualinformation provides a natural (and often practical) way to equitablyquantify statistical associations in large datasets.''