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Wedevelop a privacy-preserving distributed projection least mean squares (LMS) strategy over linear multitask networks, where agents’ local parameters of interest or tasks are linearly related. Each agent is interested in not only improving its local inference performance via in-network cooperation with neighboring agents, but also protecting its own individual task against privacy leakage. In our proposed strategy, at each time instant, each agent sends a noisy estimate, which is its local intermediate estimate corrupted by a zero-mean additive noise, to its neighboring agents. We derive a sufficient condition to determine the amount of noise to add to each agent’s intermediate estimate to achieve an optimal trade-off between the network mean-square-deviation and an inference privacy constraint. We propose a distributed and adaptive strategy to compute the additive noise powers, and study the mean and mean-square behaviors and privacy-preserving performance of the proposed strategy. Simulation results demonstrate that our strategy is able to balance the trade-off between estimation accuracy and privacy preservation. [ABSTRACT FROM AUTHOR]

Each agent in a network makes a local observation that is linearly related to a set of public and private parameters. The agents send their observations to a fusion center to allow it to estimate the public parameters. To prevent leakage of the private parameters, each agent first sanitizes its local observation using a local privacy mechanism before transmitting it to the fusion center. We investigate the utility-privacy tradeoff in terms of the Cramér-Rao lower bounds for estimating the public and private parameters. We study the class of privacy mechanisms given by linear compression and noise perturbation, and derive necessary and sufficient conditions for achieving arbitrarily strong utility-privacy tradeoff in a multi-agent system for both the cases where prior information is available and unavailable, respectively. We also provide a method to find the maximum estimation privacy achievable without compromising the utility and propose an alternating algorithm to optimize the utility-privacy tradeoff in the case where arbitrarily strong utility-privacy tradeoff is not achievable. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Finding the infection sources in a network when we only know the network topology and infected nodes, but not the rates of infection, is a challenging combinatorial problem, and it is even more difficult in practice where the underlying infection spreading model is usually unknown a priori. In this paper, we are interested in finding a source estimator that is applicable to various spreading models, including the susceptible–infected (SI), susceptible–infected–recovered (SIR), susceptible–infected–recovered–infected (SIRI), and susceptible–infected–susceptible (SIS) models. We show that under the SI, SIR, and SIRI spreading models and with mild technical assumptions, the Jordan center is the infection source associated with the most likely infection path in a tree network with a single infection source. This conclusion applies for a wide range of spreading parameters, while it holds for regular trees under the SIS model with homogeneous infection and recovery rates. Since the Jordan center does not depend on the infection, recovery, and reinfection rates, it can be regarded as a universal source estimator. We also consider the case where there are $k>1$ infection sources, generalize the Jordan center definition to a $k$ -Jordan center set, and show that this is an optimal infection source set estimator in a tree network for the SI model. Simulation results on various general synthetic networks and real-world networks suggest that Jordan center-based estimators consistently outperform the betweenness, closeness, distance, degree, eigenvector, and pagerank centrality-based heuristics, even if the network is not a tree. [ABSTRACT FROM PUBLISHER]

We consider a multitask estimation problem where nodes in a network are divided into several connected clusters, with each cluster performing a least-mean-squares estimation of a different random parameter vector. Inspired by the adapt-then-combine diffusion strategy, we propose a multitask diffusion strategy whose mean stability can be ensured whenever individual nodes are stable in the mean, regardless of the inter-cluster cooperation weights. In addition, the proposed strategy is able to achieve an asymptotically unbiased estimation when the parameters have same mean. We also develop an inter-cluster cooperation weights selection scheme that allows each node in the network to locally optimize its inter-cluster cooperation weights. Numerical results demonstrate that our approach leads to a lower average steady-state network mean-square deviation, compared with using weights selected by various other commonly adopted methods in the literature. [ABSTRACT FROM PUBLISHER]

We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, gSPAWN allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that gSPAWN converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of gSPAWN to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs per sensor, with comparable root-mean-square errors. [ABSTRACT FROM PUBLISHER]

In a cognitive radio network, a primary user (PU) shares its spectrum with secondary users (SUs) temporally and spatially, while allowing for some interference. We consider the problem of estimating the no-talk region of the PU, i.e., the region outside which SUs may utilize the PU's spectrum regardless of whether the PU is transmitting or not. We propose a distributed boundary estimation algorithm that allows SUs to estimate the boundary of the no-talk region collaboratively through message passing between SUs, and analyze the trade-offs between estimation error, communication cost, setup complexity, throughput and robustness. Simulations suggest that our proposed scheme has better estimation performance and communication cost trade-off compared to several other alternative benchmark methods, and is more robust to SU sensing errors, except when compared to the least squares support vector machine approach, which however incurs a much higher communication cost. [ABSTRACT FROM AUTHOR]

A rumor spreading in a social network or a disease propagating in a community can be modeled as an infection spreading in a network. Finding the infection source is a challenging problem, which is made more difficult in many applications where we have access only to a limited set of observations. We consider the problem of estimating an infection source for a Susceptible-Infected model, in which not all infected nodes can be observed. When the network is a tree, we show that an estimator for the source node associated with the most likely infection path that yields the limited observations is given by a Jordan center, i.e., a node with minimum distance to the set of observed infected nodes. We also propose approximate source estimators for general networks. Simulation results on various synthetic networks and real world networks suggest that our estimators perform better than distance, closeness, and betweenness centrality based heuristics . [ABSTRACT FROM PUBLISHER]

We consider the problem of localizing two devices using signals of opportunity from beacons with known positions. Beacons and devices have asynchronous local clocks or oscillators with unknown clock skews and offsets. We model clock skews as random, and analyze the biases introduced by clock asynchronism in the received signals. By deriving the equivalent Fisher information matrix for the modified Bayesian Cramér-Rao lower bound (CRLB) of device position and velocity estimation, we quantify the errors caused by clock asynchronism. We propose an algorithm based on differential time-difference-of-arrival (DTDOA) and frequency-difference-of-arrival (FDOA) that mitigates the effects of clock asynchronism to estimate the device positions and velocities. Simulation results suggest that our proposed algorithm is robust and approaches the CRLB when clock skews have small standard deviations. [ABSTRACT FROM PUBLISHER]