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In distributed processing, agents generally collect data generated by the same underlying unknown model (represented by a vector of parameters) and then solve an estimation or inference task cooperatively. In this paper, we consider the situation in which the data observed by the agents may have risen from two different models. Agents do not know beforehand which model accounts for their data and the data of their neighbors. The objective for the network is for all agents to reach agreement on which model to track and to estimate this model cooperatively. In these situations, where agents are subject to data from unknown different sources, conventional distributed estimation strategies would lead to biased estimates relative to any of the underlying models. We first show how to modify existing strategies to guarantee unbiasedness. We then develop a classification scheme for the agents to identify the models that generated the data, and propose a procedure by which the entire network can be made to converge towards the same model through a collaborative decision-making process. The resulting algorithm is applied to model fish foraging behavior in the presence of two food sources., Comment: 42 pages, 11 figures, to appear in IEEE Transactions on Signal Processing, 2014

This erratum corrects the article arXiv:0806.2044 published in Ann. Probab. 36 (2008) 931--970, Comment: Published in at http://dx.doi.org/10.1214/11-AOP684 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Adaptive networks consist of a collection of nodes with adaptation and learning abilities. The nodes interact with each other on a local level and diffuse information across the network to solve estimation and inference tasks in a distributed manner. In this work, we compare the mean-square performance of two main strategies for distributed estimation over networks: consensus strategies and diffusion strategies. The analysis in the paper confirms that under constant step-sizes, diffusion strategies allow information to diffuse more thoroughly through the network and this property has a favorable effect on the evolution of the network: diffusion networks are shown to converge faster and reach lower mean-square deviation than consensus networks, and their mean-square stability is insensitive to the choice of the combination weights. In contrast, and surprisingly, it is shown that consensus networks can become unstable even if all the individual nodes are stable and able to solve the estimation task on their own. When this occurs, cooperation over the network leads to a catastrophic failure of the estimation task. This phenomenon does not occur for diffusion networks: we show that stability of the individual nodes always ensures stability of the diffusion network irrespective of the combination topology. Simulation results support the theoretical findings., Comment: 37 pages, 7 figures, To appear in IEEE Transactions on Signal Processing, 2012

Adaptive networks consist of a collection of agents with adaptation and learning abilities. The agents interact with each other on a local level and diffuse information across the network through their collaborations. In this work, we consider two types of agents: informed agents and uninformed agents. The former receive new data regularly and perform consultation and in-network tasks, while the latter do not collect data and only participate in the consultation tasks. We examine the performance of adaptive networks as a function of the proportion of informed agents and their distribution in space. The results reveal some interesting and surprising trade-offs between convergence rate and mean-square performance. In particular, among other results, it is shown that the performance of adaptive networks does not necessarily improve with a larger proportion of informed agents. Instead, it is established that the larger the proportion of informed agents is, the faster the convergence rate of the network becomes albeit at the expense of some deterioration in mean-square performance. The results further establish that uninformed agents play an important role in determining the steady-state performance of the network, and that it is preferable to keep some of the highly connected agents uninformed. The arguments reveal an important interplay among three factors: the number and distribution of informed agents in the network, the convergence rate of the learning process, and the estimation accuracy in steady-state. Expressions that quantify these relations are derived, and simulations are included to support the theoretical findings. We further apply the results to two models that are widely used to represent behavior over complex networks, namely, the Erdos-Renyi and scale-free models., Comment: 35 pages, 8 figures

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory., Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal Processing, June 2012

The successful operation of cognitive radio (CR) between CR transmitter and CR receiver (CR link) relies on reliable spectrum sensing. To network CRs requires spectrum sensing at CR transmitter and further information regarding the spectrum availability at CR receiver. Redefining the spectrum sensing along with statistical inference suitable for cognitive radio networks (CRN), we mathematically derive conditions to allow CR transmitter forwarding packets to CR receiver under guaranteed outage probability, and prove that the correlation of localized spectrum availability between a cooperative node and CR receiver determines effectiveness of the cooperative scheme. Applying our novel mathematical model to potential hidden terminals in CRN, we illustrate that the allowable transmission region of a CR, defined as neighborhood, is no longer circular shape even in a pure path loss channel model. This results in asymmetric CR links to make bidirectional links generally inappropriate in CRN, though this challenge can be alleviated by cooperative sensing. Therefore, spectrum sensing capability determines CRN topology. For multiple cooperative nodes, to fully utilize spectrum availability, the selection methodology of cooperative nodes is developed due to limited overhead of information exchange. Defining reliability as information of spectrum availability at CR receiver provided by a cooperative node and by applying neighborhood area, we can compare sensing capability of cooperative nodes from both link and network perspectives. In addition, due to lack of centralized coordination in dynamic CRN, CRs can only acquire local and partial information within limited sensing duration, robust spectrum sensing is therefore proposed. Limits of cooperative schemes and their impacts on network operation are also derived., Comment: 26 pages, 7 figures, 47 references, submitted to IEEE Trans. on Information Theory