Two Measures of Dependence

Abstract

Two families of dependence measures between random variables are introduced. They are based on the Rényi 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.

40 pages; 1 figure; published in Entropy

References in corpus (1)

• Guessing under source uncertainty

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