21 research outputs found
Network infection source identification under the SIRI model
We study the problem of identifying a single infection source in a network
under the susceptible-infected-recovered-infected (SIRI) model. We describe the
infection model via a state-space model, and utilizing a state propagation
approach, we derive an algorithm known as the heterogeneous infection spreading
source (HISS) estimator, to infer the infection source. The HISS estimator uses
the observations of node states at a particular time, where the elapsed time
from the start of the infection is unknown. It is able to incorporate side
information (if any) of the observed states of a subset of nodes at different
times, and of the prior probability of each infected or recovered node to be
the infection source. Simulation results suggest that the HISS estimator
outperforms the dynamic message pass- ing and Jordan center estimators over a
wide range of infection and reinfection rates.Comment: 5 pages, 3 figures; to present in ICASSP 201
Contamination source inference in water distribution networks
We study the inference of the origin and the pattern of contamination in
water distribution networks. We assume a simplified model for the dyanmics of
the contamination spread inside a water distribution network, and assume that
at some random location a sensor detects the presence of contaminants. We
transform the source location problem into an optimization problem by
considering discrete times and a binary contaminated/not contaminated state for
the nodes of the network. The resulting problem is solved by Mixed Integer
Linear Programming. We test our results on random networks as well as in the
Modena city network
Observer Placement for Source Localization: The Effect of Budgets and Transmission Variance
When an epidemic spreads in a network, a key question is where was its
source, i.e., the node that started the epidemic. If we know the time at which
various nodes were infected, we can attempt to use this information in order to
identify the source. However, maintaining observer nodes that can provide their
infection time may be costly, and we may have a budget on the number of
observer nodes we can maintain. Moreover, some nodes are more informative than
others due to their location in the network. Hence, a pertinent question
arises: Which nodes should we select as observers in order to maximize the
probability that we can accurately identify the source? Inspired by the simple
setting in which the node-to-node delays in the transmission of the epidemic
are deterministic, we develop a principled approach for addressing the problem
even when transmission delays are random. We show that the optimal
observer-placement differs depending on the variance of the transmission delays
and propose approaches in both low- and high-variance settings. We validate our
methods by comparing them against state-of-the-art observer-placements and show
that, in both settings, our approach identifies the source with higher
accuracy.Comment: Accepted for presentation at the 54th Annual Allerton Conference on
Communication, Control, and Computin
On the Properties of Gromov Matrices and their Applications in Network Inference
The spanning tree heuristic is a commonly adopted procedure in network
inference and estimation. It allows one to generalize an inference method
developed for trees, which is usually based on a statistically rigorous
approach, to a heuristic procedure for general graphs by (usually randomly)
choosing a spanning tree in the graph to apply the approach developed for
trees. However, there are an intractable number of spanning trees in a dense
graph. In this paper, we represent a weighted tree with a matrix, which we call
a Gromov matrix. We propose a method that constructs a family of Gromov
matrices using convex combinations, which can be used for inference and
estimation instead of a randomly selected spanning tree. This procedure
increases the size of the candidate set and hence enhances the performance of
the classical spanning tree heuristic. On the other hand, our new scheme is
based on simple algebraic constructions using matrices, and hence is still
computationally tractable. We discuss some applications on network inference
and estimation to demonstrate the usefulness of the proposed method
Estimating Infection Sources in Networks Using Partial Timestamps
We study the problem of identifying infection sources in a network based on
the network topology, and a subset of infection timestamps. In the case of a
single infection source in a tree network, we derive the maximum likelihood
estimator of the source and the unknown diffusion parameters. We then introduce
a new heuristic involving an optimization over a parametrized family of Gromov
matrices to develop a single source estimation algorithm for general graphs.
Compared with the breadth-first search tree heuristic commonly adopted in the
literature, simulations demonstrate that our approach achieves better
estimation accuracy than several other benchmark algorithms, even though these
require more information like the diffusion parameters. We next develop a
multiple sources estimation algorithm for general graphs, which first
partitions the graph into source candidate clusters, and then applies our
single source estimation algorithm to each cluster. We show that if the graph
is a tree, then each source candidate cluster contains at least one source.
Simulations using synthetic and real networks, and experiments using real-world
data suggest that our proposed algorithms are able to estimate the true
infection source(s) to within a small number of hops with a small portion of
the infection timestamps being observed.Comment: 15 pages, 15 figures, accepted by IEEE Transactions on Information
Forensics and Securit
Infection Spreading and Source Identification: A Hide and Seek Game
The goal of an infection source node (e.g., a rumor or computer virus source)
in a network is to spread its infection to as many nodes as possible, while
remaining hidden from the network administrator. On the other hand, the network
administrator aims to identify the source node based on knowledge of which
nodes have been infected. We model the infection spreading and source
identification problem as a strategic game, where the infection source and the
network administrator are the two players. As the Jordan center estimator is a
minimax source estimator that has been shown to be robust in recent works, we
assume that the network administrator utilizes a source estimation strategy
that can probe any nodes within a given radius of the Jordan center. Given any
estimation strategy, we design a best-response infection strategy for the
source. Given any infection strategy, we design a best-response estimation
strategy for the network administrator. We derive conditions under which a Nash
equilibrium of the strategic game exists. Simulations in both synthetic and
real-world networks demonstrate that our proposed infection strategy infects
more nodes while maintaining the same safety margin between the true source
node and the Jordan center source estimator