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On Relations Between the Relative Entropy and χ2-Divergence, Generalizations and Applications
Tomohiro Nishiyama1, Igal Sason2
1Independent Researcher, Tokyo 206-0003, Japan.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study explores integral relations between relative entropy and chi-squared divergence, revealing implications for information theory and diverse applications like data compression and Markov chains.
Area of Science:
- Information Theory
- Statistics
- Applied Mathematics
Background:
- Relative entropy and chi-squared divergence are key measures in information theory and statistics.
- Understanding their relationship is crucial for various analytical and applied contexts.
Purpose of the Study:
- To investigate integral relations between relative entropy and chi-squared divergence.
- To explore the implications and information-theoretic applications of these relations.
- To generalize findings to the broader class of f-divergences.
Main Methods:
- Analysis of integral relations between divergence measures.
- Application of theoretical findings to specific problems.
- Generalization of concepts within the framework of f-divergences.
Main Results:
- Established integral relations between relative entropy and chi-squared divergence.
- Demonstrated implications for data compression, large deviations, and Markov chain convergence.
- Extended analysis to f-divergences, providing a unified perspective.
Conclusions:
- The integral relations offer a powerful tool for analyzing divergence measures.
- These findings have practical implications across multiple fields of information theory and statistics.
- The study provides a generalized framework for understanding divergence properties.
Keywords:
Markov chainschi-squared divergencef-divergencesinformation contractionlarge deviationsmaximal correlationmethod of typesrelative entropystrong data–processing inequalitiesMore Related Videos
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