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Estimating the Mutual Information between Two Discrete, Asymmetric Variables with Limited Samples.

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We developed a new method to estimate mutual information, a key measure of statistical dependence. This approach accurately quantizes nonlinear relationships even with limited data, outperforming existing techniques.

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Area of Science:

  • Statistics
  • Information Theory
  • Data Science

Background:

  • Quantifying nonlinear, statistical dependencies between variables is vital across research.
  • Mutual information is the standard measure, but estimation from limited samples is challenging and often biased.
  • Existing Bayesian entropy estimators can be used but remain biased in under-sampled scenarios.

Purpose of the Study:

  • Propose a novel, consistent, and low-bias estimator for mutual information.
  • Address the challenge of estimating mutual information in severely under-sampled regimes.
  • Provide an alternative to existing biased methods.

Main Methods:

  • Developed an alternative mutual information estimator.
  • Leveraged a well-sampled marginal distribution of the variable with minimal entropy.
  • The other variable and joint/conditional distributions can be severely under-sampled.

Main Results:

  • The proposed estimator is consistent and exhibits very low bias.
  • Outperforms previous methods, especially with limited data and few coincidences.
  • Focuses on the strength of interaction, not the specific relationship model.

Conclusions:

  • The new estimator is effective for quantifying statistical dependencies with limited data.
  • Offers a significant improvement over existing methods in under-sampled conditions.
  • Highlights the importance of conditional distribution inhomogeneity for mutual information estimation.