The Annals of Applied Statistics

Fast parameter estimation in loss tomography for networks of general topology

Ke Deng, Yang Li, Weiping Zhu, and Jun S. Liu

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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.

Article information

Ann. Appl. Stat., Volume 10, Number 1 (2016), 144-164.

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

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Zentralblatt MATH identifier

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


Deng, Ke; Li, Yang; Zhu, Weiping; Liu, Jun S. Fast parameter estimation in loss tomography for networks of general topology. Ann. Appl. Stat. 10 (2016), no. 1, 144--164. doi:10.1214/15-AOAS883.

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