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Exact Expressions for Kullback-Leibler Divergence for Univariate Distributions
Victor Nawa1, Saralees Nadarajah2
1Department of Mathematics and Statistics, University of Zambia, Lusaka 10101, Zambia.
Entropy (Basel, Switzerland)
|November 27, 2024
Summary
Researchers derived exact formulas for Kullback-Leibler (KL) divergence, a key measure of information loss between probability distributions. This work provides precise mathematical expressions for many distributions, aiding statistical analysis and machine learning applications.
Area of Science:
- Statistics
- Information Theory
- Machine Learning
Background:
- Kullback-Leibler (KL) divergence quantifies information lost when approximating one probability distribution with another.
- It is fundamental in information theory, statistics, and machine learning for model evaluation.
Purpose of the Study:
- To derive a comprehensive collection of exact expressions for KL divergence.
- To extend existing knowledge by providing precise formulations for numerous univariate distributions.
Main Methods:
- Derivation of exact mathematical expressions for KL divergence.
- Inclusion of various special functions in the derived formulas.
- Numerical checks to validate the accuracy of the expressions.
Main Results:
- A comprehensive set of exact expressions for KL divergence was developed for multivariate and matrix-variate distributions.
- Precise formulations were provided for over sixty univariate distributions.
- The accuracy of the derived expressions was confirmed through numerical validation.
Conclusions:
- The study significantly advances the understanding of KL divergence by providing validated, exact mathematical formulations.
- The findings offer valuable tools for statistical analysis and the development of more accurate models in machine learning.
- This research enriches the mathematical toolkit for quantifying differences between probability distributions.
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