Consistency of the Maximal Information Coefficient Estimator

TL;DR

This paper proves that the Maximal Information Coefficient (MIC) is a consistent estimator of the true dependence measure, correcting a previous error in the literature.

Contribution

It establishes the theoretical consistency of MIC as an estimator, addressing and correcting a prior mistake in the original proof.

Findings

MIC is a consistent estimator of the population statistic

Corrects an earlier error in the proof of MIC's consistency

Provides theoretical validation for MIC's use in dependence measurement

Abstract

The Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding population statistic MIC$_*$. This corrects an error in an argument of Reshef et al. (JMLR, 2016), which we describe.