Authors

Title

Asymptotically Uniformly Minimax Detection and Isolation in Network Monitoring

In

IEEE Transactions on Signal Processing

Volume

60

Issue

7

Pages

3357–3371

Publisher

IEEE

Year

2012

Indexed by

Abstract

This paper addresses the problem of multiple hypothesis
testing (detection and isolation of mean vectors) in the
case of Gaussian linear model with nuisance parameters. An
invariant constrained asymptotically uniformly minimax test is
proposed to solve this problem. The invariance of the test with
respect to the nuisance parameters is obtained by projecting the
measurement vector onto a subspace of invariant statistics. The
proposed test minimizes the maximum probability of false isolation
uniformly with respect to the lower bounded projections of
the vectors defining the alternative hypotheses. This minimization
is achieved provided that the signal-to-noise ratio (SNR) becomes
arbitrary large. The asymptotic probabilities of false alarm and
false isolations and their nonasymptotic bounds are analytically
established. To illustrate the practical relevance of the proposed
test, it is applied to the problem of network monitoring. It is aimed
to detect and isolate volume anomalies in network origin-destination
(OD) traffic demands from simple link load measurements.
The ambient traffic, i.e. the OD traffic matrix corresponding to
the nonanomalous network state, is unknown and considered as a
nuisance parameter. An original linear parsimonious model of the
ambient traffic which is indispensable for the proposed asymptotically
optimal test is designed. The statistical performances of
this approach to detect and isolate the anomalies are evaluated by
using real data from the Abilene network.

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