Yakir Reshef writes:

Our technical comment on Kinney and Atwal’s paper on MIC and equitability has come out in PNAS along with their response. Similarly to Ben Murrell, who also wrote you a note when he published a technical comment on the same work, we feel that they “somewhat missed the point.” Specifically: one statistic can be more or less equitable than another, and our claim has been that MIC is more equitable than other existing methods in a wide variety of settings. Contrary to what Kinney and Atwal write in their response (“Falsifiability or bust”), this claim is indeed falsifiable — it’s just that they have not falsified it.

2. We’ve just posted a new theoretical paper that defines both equitability and MIC in the language of estimation theory and analyzes them in that paradigm. In brief, the paper contains a proof of a formal relationship between power against independence and equitability that shows that the latter can be seen as a generalization of the former; a closed-form expression for the population value of MIC and an analysis of its properties that lends insight into aspects of the definition of MIC that distinguish it from mutual information; and new estimators for this population MIC that perform better than the original statistic we introduced.

3. In addition to our paper, we’ve also written a short FAQ for those who are interested in a brief summary of where the conversation and the literature on MIC and equitability are at this point, and what is currently known about the properties of these two objects.

PS – at your suggestion, the theory paper now has some pictures!

We’ve posted on this several times before:

16 December 2011: Mr. Pearson, meet Mr. Mandelbrot: Detecting Novel Associations in Large Data Sets

26 Mar 2012: Further thoughts on nonparametric correlation measures

4 Feb 2013: Too many MC’s not enough MIC’s, or What principles should govern attempts to summarize bivariate associations in large multivariate datasets?

14 Mar 2014: The maximal information coefficient

1 May 2014: Heller, Heller, and Gorfine on univariate and multivariate information measures

7 May 2014: Once more on nonparametric measures of mutual information

I still haven’t formed a firm opinion on these things. Summarizing pairwise dependence in large datasets is a big elephant, and I guess it makes sense that different researchers who work in different application areas will have different perspectives on the problem.