Estimations of f- and Renyi Divergences by Using a Cyclic Refinement of the Jensen's Inequality
Estimations of f- and Renyi Divergences by Using a Cyclic Refinement of the Jensen's Inequality
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DOI：
10.1007/s40840-017-0526-4
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发表时间：
2019-05-01
影响因子：
1.2
通讯作者：
Pecaric, Josip
中科院分区：
文献类型：
--
作者：
Horvath, Laszlo;Pecaric, Dilda;Pecaric, Josip
詹森不等式在获得概率分布之间的分歧的不等式中起着至关重要的作用。本文在f-散度泛函的基础上引入了一个新的泛函，然后利用詹森不等式的循环加细，得到了新泛函、f-散度和Renyi散度的一些估计.得到了Renyi熵和Shannon熵的一些不等式。Zipf-Mandelbrot定律被用来说明结果。
The Jensen's inequality plays a crucial role to obtain inequalities for divergences between probability distributions. In this paper, we introduce a new functional, based on the f-divergence functional, and then, we obtain some estimates for the new functional, the f-divergence and the Renyi divergence by applying a cyclic refinement of the Jensen's inequality. Some inequalities for Renyi and Shannon entropies are obtained too. Zipf-Mandelbrot law is used to illustrate the results.