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Cross-Modal Multivariate Pattern Analysis
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Exact Expressions for Kullback-Leibler Divergence for Multivariate and Matrix-Variate Distributions
Victor Nawa1, Saralees Nadarajah2
1Department of Mathematics and Statistics, University of Zambia, Lusaka 10101, Zambia.
Entropy (Basel, Switzerland)
|August 29, 2024
Summary
This study derives exact Kullback-Leibler divergence expressions for numerous multivariate and matrix-variate distributions. These findings advance statistical and information theory applications by providing previously unknown formulas.
Area of Science:
- Statistics
- Information Theory
- Probability Theory
Background:
- Kullback-Leibler divergence measures differences between probability distributions.
- Exact expressions are often unknown for complex multivariate and matrix-variate distributions.
Purpose of the Study:
- To derive exact expressions for Kullback-Leibler divergence.
- To cover over twenty multivariate and matrix-variate distributions.
- To expand the applicability of Kullback-Leibler divergence in statistical analysis.
Main Methods:
- Derivation of exact mathematical formulas.
- Application of advanced statistical and information theory principles.
- Utilizing special functions in the derived expressions.
Main Results:
- Exact expressions for Kullback-Leibler divergence were successfully derived.
- Formulas were obtained for more than twenty multivariate and matrix-variate distributions.
- The derived expressions incorporate various special functions.
Conclusions:
- The paper provides novel, exact Kullback-Leibler divergence formulas for a wide range of distributions.
- These results fill a critical gap in statistical and information theory.
- The findings facilitate more accurate analysis and applications involving complex probability distributions.
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