Equitability and the Maximal Information Coefficient

• Activity Number: 215
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: WNAR
• Author(s): David Reshef*+ and Yakir Reshef and Pardis Sabeti and Michael Mitzenmacher
• Companies: MIT/Harvard and Harvard/MIT and Harvard and Harvard
• Keywords: Maximal Information Coefficient ; MIC ; Equitability ; Measures of Dependence

Abstract

The maximal information coefficient (MIC) is a statistic for finding the strongest pairwise relationships in a data set with many variables. MIC is useful not just for identifying deviations from statistical independence but also for the more delicate task of ranking relationships by strength, as it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important when the goal is to identify a relatively small set of strongest associations as opposed to as many non-trivial associations as possible, which are often too many to sift through. We will further explore equitability, MIC, and the evaluation of measures of dependence. We formally define equitability and show that it is equivalent to power against a range of null hypotheses corresponding to different noise levels. We then redefine MIC in a parameter estimation framework and introduce new algorithms for estimating it that are more accurate and efficient than existing methods. Finally, we present an extensive comparison of state-of-the-art measures of dependence and a discussion of tradeoffs to consider in choosing an appropriate measure of dependence in various settings