Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

A Sparsity-Aware Adaptive Algorithm for Distributed Learning

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed convex set, known as property set, is constructed based on the received measurements; this defines the region in which the solution is searched for. In this paper, the property sets take the form of hyperslabs. The goal is to find a point that belongs to the intersection of these hyperslabs. To this end, sparsity encouraging variable metric projections onto the hyperslabs have been adopted. Moreover, sparsity is also imposed by employing variable metric projections onto weighted $\ell_1$ balls. A combine adapt cooperation strategy is adopted. Under some mild assumptions, the scheme enjoys monotonicity, asymptotic optimality and strong convergence to a point that lies in the consensus subspace. Finally, numerical examples verify the validity of the proposed scheme, compared to other algorithms, which have been developed in the context of sparse adaptive learning

A Multitask Diffusion Strategy with Optimized Inter-Cluster Cooperation

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.Comment: 30 pages, 8 figures, submitted to IEEE Journal of Selected Topics in Signal Processin

On the genericity properties in networked estimation: Topology design and sensor placement

In this paper, we consider networked estimation of linear, discrete-time dynamical systems monitored by a network of agents. In order to minimize the power requirement at the (possibly, battery-operated) agents, we require that the agents can exchange information with their neighbors only \emph{once per dynamical system time-step}; in contrast to consensus-based estimation where the agents exchange information until they reach a consensus. It can be verified that with this restriction on information exchange, measurement fusion alone results in an unbounded estimation error at every such agent that does not have an observable set of measurements in its neighborhood. To over come this challenge, state-estimate fusion has been proposed to recover the system observability. However, we show that adding state-estimate fusion may not recover observability when the system matrix is structured-rank ($S$-rank) deficient. In this context, we characterize the state-estimate fusion and measurement fusion under both full $S$-rank and $S$-rank deficient system matrices.Comment: submitted for IEEE journal publicatio

Perception of categories: from coding efficiency to reaction times

Reaction-times in perceptual tasks are the subject of many experimental and theoretical studies. With the neural decision making process as main focus, most of these works concern discrete (typically binary) choice tasks, implying the identification of the stimulus as an exemplar of a category. Here we address issues specific to the perception of categories (e.g. vowels, familiar faces, ...), making a clear distinction between identifying a category (an element of a discrete set) and estimating a continuous parameter (such as a direction). We exhibit a link between optimal Bayesian decoding and coding efficiency, the latter being measured by the mutual information between the discrete category set and the neural activity. We characterize the properties of the best estimator of the likelihood of the category, when this estimator takes its inputs from a large population of stimulus-specific coding cells. Adopting the diffusion-to-bound approach to model the decisional process, this allows to relate analytically the bias and variance of the diffusion process underlying decision making to macroscopic quantities that are behaviorally measurable. A major consequence is the existence of a quantitative link between reaction times and discrimination accuracy. The resulting analytical expression of mean reaction times during an identification task accounts for empirical facts, both qualitatively (e.g. more time is needed to identify a category from a stimulus at the boundary compared to a stimulus lying within a category), and quantitatively (working on published experimental data on phoneme identification tasks)