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

TL;DR

This paper critically evaluates the Maximal Information Coefficient (MIC) proposed by Reshef et al., revealing that MIC generally has lower statistical power compared to distance correlation and Pearson correlation in detecting dependencies, especially in noisy data.

Contribution

The authors provide a comparative analysis showing MIC's limitations in power against other correlation measures through simulation studies.

Findings

MIC has lower power than distance correlation in most cases.

MIC is less effective than Pearson correlation for linear relationships.

MIC performs poorly with noisy data and certain non-linear relationships.

Abstract

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