Open Access
March 2016 Fast parameter estimation in loss tomography for networks of general topology
Ke Deng, Yang Li, Weiping Zhu, Jun S. Liu
Ann. Appl. Stat. 10(1): 144-164 (March 2016). DOI: 10.1214/15-AOAS883


As a technique to investigate link-level loss rates of a computer network with low operational cost, loss tomography has received considerable attentions 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 estimation in loss tomography. By introducing a group of novel statistics and alternative parameter systems, we find that the likelihood function of the observed data from loss tomography keeps exactly the same mathematical formulation for tree and general topologies, revealing that networks with different 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.


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Ke Deng. Yang Li. Weiping Zhu. Jun S. Liu. "Fast parameter estimation in loss tomography for networks of general topology." Ann. Appl. Stat. 10 (1) 144 - 164, March 2016.


Received: 1 September 2014; Revised: 1 July 2015; Published: March 2016
First available in Project Euclid: 25 March 2016

zbMATH: 1362.94073
MathSciNet: MR3480491
Digital Object Identifier: 10.1214/15-AOAS883

Keywords: general topology , likelihood equation , loss tomography , Network tomography , pattern-collapsed EM algorithm

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.10 • No. 1 • March 2016
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