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Comment
. 2014 Aug 19;111(33):E3362-3.
doi: 10.1073/pnas.1408920111.

Cleaning up the record on the maximal information coefficient and equitability

David N Reshef  1 , Yakir A Reshef  2 , Michael Mitzenmacher  3 , Pardis C Sabeti  4
Affiliations
Comment

Cleaning up the record on the maximal information coefficient and equitability

David N Reshef et al. Proc Natl Acad Sci U S A. .
No abstract available

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Equitability of MIC and mutual information under a range of noise models. The equitability of MIC and mutual information across a subset of noise models analyzed in refs. and . For each noise model, the relationships tested are as in ref. . In each plot in A, each shaded region denotes 90% probability intervals based on 500 trials of a given relationship at each of 40 noise levels. In the noise models in A, Nx and Ny represent Gaussians, and X-values are chosen so that the noiseless data points are spaced uniformly along the graph of f(X). The intervals plotted in red for each noise model in A represent the largest range of R2 values that correspond to a single value of the statistic in question. This provides a quantitative measure of the equitability of each statistic (the shorter the interval, the more equitable the statistic). The values in B correspond to the lengths of these intervals across a larger range of sample sizes and the noise models found in ref. , and table cells are colored proportionally (red = interval of length 0; white = interval of length 1). In A, both the worst and average interval lengths are reported. As in ref. , results for the Kraskov et al. mutual information estimator are presented for both k=1 and k=6. The left plot legend applies to the leftmost noise model, and the right legend to the other two as in refs. and . In almost every noise model tested, MIC is more equitable than mutual information, consistent with results reported in refs. and . To ensure proper comparison, MIC was estimated as in ref. ; however, we expect that as better estimators of MIC become available they will lead to further superior equitability over mutual information estimators and the MIC estimator used here.
See this image and copyright information in PMC

Comment in

  • Reply to Reshef et al.: Falsifiability or bust.
    Kinney JB, Atwal GS. Kinney JB, et al. Proc Natl Acad Sci U S A. 2014 Aug 19;111(33):E3364. doi: 10.1073/pnas.1410317111. Proc Natl Acad Sci U S A. 2014. PMID: 25275168 Free PMC article. No abstract available.

Comment on

References

    1. Reshef DN, et al. Detecting novel associations in large data sets. Science. 2011;334(6062):1518–1524. - PMC - PubMed
    1. Kinney JB, Atwal GS. Equitability, mutual information, and the maximal information coefficient. Proc Natl Acad Sci USA. 2014;111(9):3354–3359. - PMC - PubMed
    1. Murrell B, Murrell D, Murrell H. R2-equitability is satisfiable. Proc Natl Acad Sci USA. 2014;111(21):E2160. - PMC - PubMed
    1. Reshef DN, Reshef YA, Mitzenmacher M, Sabeti PC. 2013. Equitability analysis of the maximal information coefficient with comparisons. arXiv:1301.6314v2 [cs.LG]
    1. Kinney JB, Gurinder SA. Reply to Murrell et al.: Noise matters. Proc Natl Acad Sci USA. 2014;111(21):E2161. - PMC - PubMed

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