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Estimating Information Theoretic Measures via Multidimensional Gaussianization.

Valero Laparra, Juan Emmanuel Johnson, Gustau Camps-Valls

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    This summary is machine-generated.

    This study introduces a novel Gaussianization method for estimating information in complex, high-dimensional data. The approach simplifies multivariate calculations, improving accuracy and overcoming the curse of dimensionality for broader applications.

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    Area of Science:

    • Information theory
    • Statistical modeling
    • Machine learning

    Background:

    • Information theory provides robust measures for uncertainty and dependence in data.
    • The curse of dimensionality hinders the application of information theory to high-dimensional datasets.
    • Existing methods struggle with multivariate and heterogeneous data.

    Purpose of the Study:

    • To develop a novel method for estimating information measures in high-dimensional data.
    • To overcome the limitations imposed by the curse of dimensionality.
    • To provide accurate and interpretable information estimates for complex systems.

    Main Methods:

    • A multivariate iterative Gaussianization transform is proposed.
    • The method reduces multivariate estimation to sequential univariate operations.
    • Estimates for Total Correlation, Entropy, Mutual Information, and Kullback-Leibler Divergence are derived.

    Main Results:

    • The Gaussianization-based method demonstrates superior performance over existing estimators.
    • Effectiveness is particularly pronounced in high-dimensional scenarios.
    • The approach successfully handles multivariate and heterogeneous data.

    Conclusions:

    • The proposed Gaussianization technique offers an effective solution for information estimation in complex data.
    • This method facilitates wider adoption of information theory in practical applications.
    • Publicly available tools and datasets will foster further research and development.