Maximal Rank Correlation

Based on the notion of maximal correlation, we introduce a new measure of correlation between two different rankings of the same group of items. Our measure captures various types of correlation detected in previous measures of rank correlation like the Spearman correlation and the Kendall tau correlation. We show that the maximal rank correlation satisfies the data processing and tensorization properties (that make ordinary maximal correlation applicable to problems in information theory). Furthermore, MRC is shown to be intimately related to the FKG inequality. Finally, we pose the problem of the complexity of the computation of this new measure. We make partial progress by giving a simple but exponential-time algorithm for it.