Fast Parameter Estimation in Loss Tomography for Networks of General Topology

TL;DR

This paper introduces a unified theoretical framework and efficient algorithms for parameter estimation in loss tomography across various network topologies, leveraging novel statistics and re-parametrization to improve computational efficiency.

Contribution

It reveals that the likelihood function's mathematical form is consistent across network topologies and belongs to the exponential family, enabling more efficient estimation algorithms.

Findings

Likelihood function is topology-independent

Re-parametrization belongs to exponential family

Proposed algorithms are computationally efficient

Abstract

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 re-parametrization 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.