Non-isomorphic distribution supports for calculating entropic vectors
Non-isomorphic distribution supports for calculating entropic vectors
复制标题
非同构分布支持计算熵向量
DOI：
10.1109/allerton.2015.7447064
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Walsh
中科院分区：
文献类型：
--
作者：
Yunshu Liu;J. Walsh
如果一个2N - 1维的向量的每一项都可以看作是N个离散随机变量的特定子集的联合熵，那么这个向量就是熵的。对于N≥4，熵向量Γ *N区域闭包的显式表征是未知的。为了计算和优化熵向量，提出了一种系统的方法来生成非同构分布支持列表。结果表明，基于这些支撑构造内界可以更好地理解熵域的结构。在全维和变换后的Csirmaz和Matúš三维空间中，比较了基于不同支撑构造的内边界。
A 2N - 1 dimensional vector is said to be entropic if each of its entries can be regarded as the joint entropy of a particular subset of N discrete random variables. The explicit characterization of the closure of the region of entropic vectors Γ̅*N is unknown for N ≥ 4. A systematic approach is proposed to generate the list of non-isomorphic distribution supports for the purpose of calculating and optimizing entropic vectors. It is shown that a better understanding of the structure of the entropy region can be obtained by constructing inner bounds based on these supports. The constructed inner bounds based on different supports are compared both in full dimension and in a transformed three dimensional space of Csirmaz and Matúš.