Information Inequalities for Joint Distributions, With Interpretations and Applications

@article{Madiman2008InformationIF,
  title={Information Inequalities for Joint Distributions, With Interpretations and Applications},
  author={Mokshay M. Madiman and Prasad Tetali},
  journal={IEEE Transactions on Information Theory},
  year={2008},
  volume={56},
  pages={2699-2713}
}
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as inequalities of Han, Fujishige, and Shearer. A duality between the upper and lower bounds for joint entropy is developed. All of these results are shown to be special cases of general, new results for submodular functions-thus, the inequalities presented constitute a… CONTINUE READING

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