Fast Parameter Estimation in Loss Tomography for Networks of General Topology
Fast Parameter Estimation in Loss Tomography for Networks of General Topology
复制标题
一般拓扑网络损耗层析成像中的快速参数估计
DOI：
10.1214/15-aoas883
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Jun S. Liu
中科院分区：
文献类型：
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作者：
Ke Deng;Yang Li;Weiping Zhu;Jun S. Liu
损失层析成像作为一种低成本的链路级损失率测量技术，近年来受到了广泛的关注。对于具有树结构和一般拓扑结构的网络的损失层析成像，已经提出了许多参数估计方法。然而，这些方法要么计算成本高，要么数据中的信息利用不足。本文给出了损耗层析成像中参数估计的理论结果和实用算法。通过引入一组新的统计量和替代参数系统，我们发现，对于树拓扑和一般拓扑，损失层析观测数据的似然函数保持完全相同的数学表达式，揭示了不同拓扑的网络具有相同的损失层析数学性质。更重要的是，我们发现，重新参数化的似然函数属于标准指数族，这是凸的，并有一个唯一的模式下的正则性条件。基于这些理论结果，新的算法来找到最大似然估计的开发。与文献中的现有方法相比，所提出的方法具有很大的计算优势。
As a technique to investigate link-level loss rates of a computer network with low operational cost, loss tomography has received considerable atten- tions in recent years. A number of parameter estimation methods have been proposed for loss tomography of networks with a tree structure as well as a general topological structure. However, these methods suffer from either high computational cost or insufficient use of information in the data. In this paper, we provide both theoretical results and practical algorithms for parameter es- timation in loss tomography. By introducing a group of novel statistics and alternative parameter systems, we find that the likelihood function of the ob- served data from loss tomography keeps exactly the same mathematical for- mulation for tree and general topologies, revealing that networks with differ- ent topologies share the same mathematical nature for loss tomography. More importantly, we discover that a reparametrization of the likelihood function belongs to the standard exponential family, which is convex and has a unique mode under regularity conditions. Based on these theoretical results, novel algorithms to find the MLE are developed. Compared to existing methods in the literature, the proposed methods enjoy great computational advantages..