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Equitability, mutual information, and the maximal information coefficient.

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Summary
This summary is machine-generated.

Statistical equitability, measuring association strength without bias, is best defined by self-consistency. Mutual information satisfies this, contrary to claims about the maximal information coefficient (MIC). Mutual information offers a practical approach for quantifying associations in large datasets.

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Area of Science:

  • Information Theory
  • Statistical Association

Background:

  • Quantifying statistical association strength equitably, without bias for specific relationship forms, lacks a definitive mathematical formalization.
  • The concept of statistical 'equitability' is crucial for unbiased association measurement.
  • Previous work proposed the maximal information coefficient (MIC) as an equitable measure, challenging mutual information.

Purpose of the Study:

  • To mathematically formalize statistical equitability.
  • To evaluate whether mutual information or MIC better satisfies equitability.
  • To compare the statistical power of mutual information and MIC.

Main Methods:

  • Formalizing equitability using a self-consistency condition related to the Data Processing Inequality.
  • Mathematically analyzing the equitability criterion for dependence measures.
  • Revisiting and correcting simulation evidence from prior studies.

Main Results:

  • Mutual information satisfies the proposed equitability criterion.
  • The mathematical definition of equitability proposed by Reshef et al. cannot be satisfied by any nontrivial dependence measure.
  • After correcting simulation artifacts, mutual information estimates demonstrated greater equitability and higher statistical power than MIC estimates.

Conclusions:

  • Mutual information provides a mathematically sound and practically effective method for equitably quantifying statistical associations.
  • The claims that MIC is more equitable than mutual information are unsubstantiated.
  • Estimating mutual information is a natural and often practical approach for analyzing large datasets.