Two Measures of Dependence
- 2019-8-8
Published in:
- Entropy. - MDPI AG. - 2019, vol. 21, no. 8, p. 778
English
Two families of dependence measures between random variables are introduced. They are based on the Rényi divergence of order
α
and the relative
α
-entropy, respectively, and both dependence measures reduce to Shannon’s mutual information when their order
α
is one. The first measure shares many properties with the mutual information, including the data-processing inequality, and can be related to the optimal error exponents in composite hypothesis testing. The second measure does not satisfy the data-processing inequality, but appears naturally in the context of distributed task encoding.
α
and the relative
α
-entropy, respectively, and both dependence measures reduce to Shannon’s mutual information when their order
α
is one. The first measure shares many properties with the mutual information, including the data-processing inequality, and can be related to the optimal error exponents in composite hypothesis testing. The second measure does not satisfy the data-processing inequality, but appears naturally in the context of distributed task encoding.
- Language
-
- English
- Open access status
- gold
- Identifiers
-
- DOI 10.3390/e21080778
- ISSN 1099-4300
- Persistent URL
- https://sonar.ch/global/documents/249632
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