Two Measures of Dependence

Amos Lapidoth; Christoph Pfister

doi:10.3390/e21080778

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arXiv · 1607.02330

Two Measures of Dependence

Amos Lapidoth·Christoph Pfister

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Abstract

Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual information when their order $\alpha$ 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.

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Amos Lapidoth, Christoph Pfister. 2016-07-08. Two Measures of Dependence. https://doi.org/10.3390/e21080778

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