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Information estimation using nonparametric copulas.

Houman Safaai1,2, Arno Onken3, Christopher D Harvey1

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Summary
This summary is machine-generated.

A new non-parametric copula-based estimator (NPC) accurately estimates mutual information for diverse data. This flexible method works for continuous and discrete variables, even with limited samples, offering robust and generally applicable information estimation.

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Area of Science:

  • Statistics
  • Information Theory
  • Data Science

Background:

  • Accurate estimation of mutual information is vital across scientific disciplines.
  • Existing methods often require assumptions about data distributions or struggle with limited sample sizes.
  • Flexible, assumption-free methods are needed for analyzing complex statistical dependencies.

Purpose of the Study:

  • To introduce a novel, generally applicable information estimator based on non-parametric copulas.
  • To develop a method robust to marginal distribution details and variable interactions.
  • To provide accurate mutual information estimates, especially for small sample sizes.

Main Methods:

  • Developed the non-parametric copula-based estimator (NPC).
  • Utilized copulas to model statistical dependencies independently of marginal distributions.
  • Validated the NPC estimator on artificial samples from various statistical distributions.

Main Results:

  • The NPC estimator demonstrated strong performance compared to existing alternatives.
  • It accurately estimates mutual information for both continuous and discrete variables.
  • The method proved robust to changes in marginal distributions and effective with low sample numbers.

Conclusions:

  • The NPC estimator offers a powerful, flexible, and robust approach to mutual information estimation.
  • It provides a unified framework for continuous and discrete data, excelling in low-sample scenarios.
  • This estimator is anticipated to be a valuable tool for analyzing complex data dependencies across various fields.