34 research outputs found
Network tomography based on 1-D projections
Network tomography has been regarded as one of the most promising
methodologies for performance evaluation and diagnosis of the massive and
decentralized Internet. This paper proposes a new estimation approach for
solving a class of inverse problems in network tomography, based on marginal
distributions of a sequence of one-dimensional linear projections of the
observed data. We give a general identifiability result for the proposed method
and study the design issue of these one dimensional projections in terms of
statistical efficiency. We show that for a simple Gaussian tomography model,
there is an optimal set of one-dimensional projections such that the estimator
obtained from these projections is asymptotically as efficient as the maximum
likelihood estimator based on the joint distribution of the observed data. For
practical applications, we carry out simulation studies of the proposed method
for two instances of network tomography. The first is for traffic demand
tomography using a Gaussian Origin-Destination traffic model with a power
relation between its mean and variance, and the second is for network delay
tomography where the link delays are to be estimated from the end-to-end path
delays. We compare estimators obtained from our method and that obtained from
using the joint distribution and other lower dimensional projections, and show
that in both cases, the proposed method yields satisfactory results.Comment: Published at http://dx.doi.org/10.1214/074921707000000238 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Network Tomography: Identifiability and Fourier Domain Estimation
The statistical problem for network tomography is to infer the distribution
of , with mutually independent components, from a measurement model
, where is a given binary matrix representing the
routing topology of a network under consideration. The challenge is that the
dimension of is much larger than that of and thus the
problem is often called ill-posed. This paper studies some statistical aspects
of network tomography. We first address the identifiability issue and prove
that the distribution is identifiable up to a shift parameter
under mild conditions. We then use a mixture model of characteristic functions
to derive a fast algorithm for estimating the distribution of
based on the General method of Moments. Through extensive model simulation and
real Internet trace driven simulation, the proposed approach is shown to be
favorable comparing to previous methods using simple discretization for
inferring link delays in a heterogeneous network.Comment: 21 page
Statistical and Computational Tradeoffs in Stochastic Composite Likelihood
Maximum likelihood estimators are often of limited practical use due to the
intensive computation they require. We propose a family of alternative
estimators that maximize a stochastic variation of the composite likelihood
function. Each of the estimators resolve the computation-accuracy tradeoff
differently, and taken together they span a continuous spectrum of
computation-accuracy tradeoff resolutions. We prove the consistency of the
estimators, provide formulas for their asymptotic variance, statistical
robustness, and computational complexity. We discuss experimental results in
the context of Boltzmann machines and conditional random fields. The
theoretical and experimental studies demonstrate the effectiveness of the
estimators when the computational resources are insufficient. They also
demonstrate that in some cases reduced computational complexity is associated
with robustness thereby increasing statistical accuracy.Comment: 30 pages, 97 figures, 2 author