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Edgeworth approximation of multivariate differential entropy.

Marc M Van Hulle1

  • 1K. U. Leuven, Laboratorium voor Neuro- en Psychofysiologie, B-3000 Leuven, Belgium. marc@neuro.kuleuven.ac.be

Neural Computation
|August 19, 2005
PubMed
Summary

We present a new multivariate Edgeworth approximation for differential entropy, outperforming nearest-neighbor methods in accuracy and scalability. This method also enhances mutual information estimation for complex datasets.

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Area of Science:

  • Information Theory
  • Statistical Inference
  • Machine Learning

Background:

  • Estimating differential entropy is crucial for understanding complex data distributions.
  • Existing methods like nearest-neighbor approaches face challenges in high-dimensional spaces and with large datasets.
  • Accurate entropy estimation is fundamental for various machine learning tasks.

Purpose of the Study:

  • To generalize the Edgeworth approximation for differential entropy to the multivariate case.
  • To evaluate the performance of the proposed method against established techniques.
  • To demonstrate the utility of the Edgeworth approximation in mutual information estimation.

Main Methods:

  • Developed a general, multivariate Edgeworth approximation for differential entropy.

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  • Compared its accuracy and computational scaling with the nearest-neighbor method using simulated and real-world data.
  • Applied the approximation to estimate mutual information between variables.

    • Main Results:

    • The multivariate Edgeworth approximation shows improved accuracy compared to the nearest-neighbor method.
    • The proposed method exhibits better scalability with increasing sample size.
    • Successful application in mutual information estimation, demonstrating practical utility.

    Conclusions:

    • The generalized Edgeworth approximation offers a more accurate and scalable approach for multivariate differential entropy estimation.
    • This advancement has significant implications for information-theoretic analyses in high-dimensional data.
    • The method provides a robust tool for mutual information estimation in machine learning and statistics.