Conditional Entropy and Data Processing: An Axiomatic Approach Based on Core-Concavity

被引：10

作者：

Americo, Arthur ^{[1
]}

Khouzani, MHR. ^{[1
]}

Malacaria, Pasquale ^{[1
]}

机构：

[1] Queen Mary Univ London, Sch Elect Engn & Comp Sci, London E1 4NS, England

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 09期

关键词：

Entropy; Uncertainty; Random variables; Decision making; Probability distribution; Information theory; Head; Information entropy; INFORMATION;

D O I：

10.1109/TIT.2020.2987713

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work presents an axiomatization for entropy based on an extension of concavity called core-concavity. We show that core-concavity characterizes the largest class of functions for which the data-processing inequality holds, under the assumption that conditional entropy is defined as a generalized average. Also, under the same assumption, we show that data-processing and "conditioning reduces entropy" properties are equivalent. We prove several properties of core-concave functions, including generalization of perfect secrecy and of Fano's inequality. We also show that definitions of conditional entropy based on worst-case can be retrieved as limit cases of generalized averages. A connection between statistical decision making and this axiomatic approach is also presented.

引用

页码：5537 / 5547

页数：11