Estimation of Message Source and Destination From Network Intercepts

Justice, D.H.; Hero, Alfred O.

doi:10.1109/tifs.2006.879291

Cited by 3 publications

(4 citation statements)

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“…Nevertheless, although the source-dependent model more accurately reflects how routing is performed in actual communication systems, there are scenarios where a single transition matrix estimate is preferable. For example, a more holistic characterization of network routing is valuable if one is interested in predicting the route between a source and destination that was not previously observed, or if one is interested in predicting the endpoints of a route given only the activated internal routers [12].…”

Section: Discussion and Ongoing Researchmentioning

confidence: 99%

“…This procedure always produces a feasible reconstruction. The parameter estimates produced by the EM algorithm may be useful for other tasks such as guiding an expert to alternative reconstructions by assigning likelihoods to different permutations, or predicting unobserved paths through the network as in [12]. One could also analyze properties of an ensemble of solutions obtained by running the EM algorithm from different initializations, and then posit a new set of experiments to be conducted based on this analysis.…”

Section: Discussion and Ongoing Researchmentioning

confidence: 99%

“…The E-step [see (12) and (13)] consists of computing the conditional expectations and . A naive Monte Carlo approximation would be based on random permutations, sampled from the uniform distribution over .…”

Section: F Incorporating Prior Informationmentioning

confidence: 99%

“…Also, these heuristics do not readily lend themselves to incorporating side information. A different approach, introduced by Justice and Hero in [12], involves averaging over an ensemble of feasible topologies sampled uniformly from the feasible set. In general there is an enormous number of feasible topologies (exponential in the problem dimensions) exhibiting a wide variety of characteristics, and it is not clear that an average of feasible topologies will be optimal in any sense.…”

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Network Inference From Co-Occurrences

Rabbat

Figueiredo

Nowak

2008

IEEE Trans. Inform. Theory

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Abstract-The discovery of networks is a fundamental problem arising in numerous fields of science and technology, including communication systems, biology, sociology, and neuroscience. Unfortunately, it is often difficult, or impossible, to obtain data that directly reveal network structure, and so one must infer a network from incomplete data. This paper considers inferring network structure from "co-occurrence" data: observations that identify which network components (e.g., switches, routers, genes) carry each transmission but do not indicate the order in which they handle the transmission. Without order information, the number of networks that are consistent with the data grows exponentially with the size of the network (i.e., the number of nodes). Yet, the basic engineering/evolutionary principles underlying most networks strongly suggest that not all data-consistent networks are equally likely. In particular, nodes that co-occur in many observations are probably closely connected. With this in mind, we model the co-occurrence observations as independent realizations of a random walk on the network, subjected to a random permutation to account for the lack of order information. Treating permutations as missing data, we derive an expectation-maximization (EM) algorithm for estimating the random walk parameters. The model and EM algorithm significantly simplify the problem, but the computational complexity of the reconstruction process does grow exponentially in the length of each transmission path. For networks with long paths, the exact E-step may be computationally intractable. We propose a polynomial-time Monte Carlo EM algorithm based on importance sampling and derive conditions that ensure convergence of the algorithm with high probability. Simulations and experiments with Internet measurements demonstrate the promise of this approach.

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Section: Discussion and Ongoing Researchmentioning

confidence: 99%

Section: Discussion and Ongoing Researchmentioning

confidence: 99%

Section: F Incorporating Prior Informationmentioning

confidence: 99%

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