Cross-entropy minimization given fully decomposable subset and aggregate constraints
Cross-entropy minimization given fully decomposable subset and aggregate constraints
复制标题
给定完全可分解子集和聚合约束的交叉熵最小化
DOI：
10.1109/tit.1982.1056572
复制
发表时间：
1982
期刊：
影响因子：
--
通讯作者：
J. Shore
中科院分区：
文献类型：
--
作者：
J. Shore
最近，最大熵原理和最小交叉熵原理（最小定向发散、最小鉴别信息）已被应用于排队论和计算机系统性能建模中的问题。这些信息论原理基于已知期望值形式的信息来估计概率分布。在排队论和计算机系统建模的情况下，已知的期望值来自速率平衡方程。这种对应关系涉及的情况下，系统状态概率分解成不相交的子集，其中已知的期望值是期望条件的特定子集或期望涉及聚合子集概率。最小交叉熵分布的新性质的推导和计算这些分布的一个有效的方法。计算的例子包括在内。在排队论和计算机系统建模的情况下，不相交的子集对应于内部设备状态，并且聚合概率对应于整体设备状态。这里的结果适用于当一个有速率平衡方程的设备平衡，涉及内部设备状态概率，以及速率平衡方程的系统平衡，涉及总设备状态概率。
The principle of maximum entropy and the principle of minimum cross-entropy (minimum directed divergence, minimum discrimination information) have been applied recently to problems in queuing theory and computer-system performance modeling. These information-theoretic principles estimate probability distributions based on information in the form of known expected values. In the case of queuing theory and computer-system modeling, the known expected values arise from rate balance equations. This correspondence concerns situations in which the system state probabilities decompose into disjoint subsets and in which the known expected values are either expectations conditional on a specific subset or expectations involving aggregate subset probabilities. New properties of minimum cross-entropy distributions are derived and an efficient method of computing these distributions is derived. Computational examples are included. In the case of queuing theory and computer-system modeling, the disjoint subsets correspond to internal device states, and the aggregate probabilities correspond to overall device states. The results here apply when one has both rate balance equations for device equilibrium involving internal device state probabilities, as well as rate balance equations for system equilibrium involving aggregate device state probabilities.