Reeves Galen
Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA.
Department of Statistical Science, Duke University, Durham, NC 27708, USA.
Entropy (Basel). 2020 Nov 1;22(11):1244. doi: 10.3390/e22111244.
This paper explores some applications of a two-moment inequality for the integral of the th power of a function, where 0<r<1. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different moments. When one of the moments is the zeroth moment, these bounds recover previous results based on maximum entropy distributions under a single moment constraint. More generally, evaluation of the bound with two carefully chosen nonzero moments can lead to significant improvements with a modest increase in complexity. The second contribution is a method for upper bounding mutual information in terms of certain integrals with respect to the variance of the conditional density. The bounds have a number of useful properties arising from the connection with variance decompositions.
本文探讨了函数(r)次幂积分的双矩不等式（其中(0\lt r\lt1)）的一些应用。第一个贡献是根据两种不同的矩给出了随机向量的Rényi熵的上界。当其中一个矩为零阶矩时，这些界恢复了基于单矩约束下最大熵分布的先前结果。更一般地，用两个精心选择的非零矩来评估该界，在复杂度适度增加的情况下可以带来显著改进。第二个贡献是一种根据关于条件密度方差的某些积分来给出互信息上界的方法。这些界由于与方差分解的联系而具有许多有用的性质。
