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Summary
This summary is machine-generated.

This study introduces a novel method for estimating Shannon differential entropy in multidimensional random variables. The approach accurately and efficiently calculates entropy, especially for high-dimensional data, by decomposing distributions and utilizing copulas.

Keywords:
copulasentropy estimationmultivariate continuous distributions

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Area of Science:

  • Information Theory
  • Statistical Modeling
  • Machine Learning

Background:

  • Estimating Shannon differential entropy for multidimensional variables is challenging.
  • Existing methods struggle with high-dimensional data and unknown or mixed support types.

Purpose of the Study:

  • To develop an accurate and efficient method for estimating Shannon differential entropy of multidimensional random variables.
  • To address limitations of current methods in handling complex data distributions and high dimensions.

Main Methods:

  • Decomposition of probability distributions into marginals and copulas.
  • One-dimensional estimation for marginal entropies.
  • Recursive estimation of copula entropy by splitting data along dependent dimensions.

Main Results:

  • The method accurately estimates entropy for both compact and non-compact supports.
  • Demonstrated superior accuracy and efficiency compared to existing methods for dimensions > 20.
  • Effective for unknown or mixed support types across dimensions.

Conclusions:

  • The proposed method offers a robust solution for multidimensional entropy estimation.
  • It significantly advances the state-of-the-art for high-dimensional statistical analysis.
  • Applicable across diverse data types and dimensionalities.