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In this paper, we study a class of distributed computing problems where a group of nodes (destinations) is interested in a function of data which are stored by another group of nodes (sources). We assume that the function of interest is separable, i.e., it can be decomposed as a sum of functions of local variables, a case that subsumes several inte...
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Optics is an exciting route for the next generation of computing hardware for machine learning, promising several orders of magnitude enhancement in both computational speed and energy efficiency. However, to reach the full capacity of an optical neural network it is necessary that the computing not only for the inference, but also for the training...
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... The purpose of this work is to fill in this gap, by providing evidence of the potential of NN in this context. While our NN model and our training philosophy can be applied to a wide set of multi-agent algorithms and attack 1 The convergence properties of average consensus gossiping with stubborn agents were studied in [31] scenarios, we focus on testing the approach on a case that has been thoroughly studied in [22], [27], to facilitate the comparison. The learning mechanism in this work is supervised such that NNs are trained in an offline manner with labeled data collecting from the normal nodes. ...
To support the big-data processing needs of large-scale deployments of smart devices, there is significant interest in moving from cloud-computing to multi-agent (fog-computing) models, given these algorithms scalability and self-healing properties with respect to nodes and link failures. However, these algorithms are often based on the average consensus primitive, which is, unfortunately, vulnerable to data injection attacks. Recognizing this challenge, this work proposes three novel methods for detecting and localizing adversarial nodes using neural network (NN) models. The methods proposed are based on fully distributed algorithms, wherein each node locally updates its local states by exchanging information with its neighbors without supervision. Compared to the state-of-the-art, the proposed approach leverages the automatic learning characteristics of NN to reduce the dependence on pre-designed models and human expertise in complex internal attack scenarios. Simulation results show that the NN-based methods can significantly improve the attacker detection and localization performance.
... Let us focus on the steady-state opinions, i.e., the opinions when τ → ∞. Under mild assumptions, it holds [22], [43] y := lim ...
This paper considers a novel framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process -- represented as a graph filter -- that is excited by a set of low-rank inputs. Rather than learning the precise parameters of the graph itself, the proposed method retrieves the community structure directly; Furthermore, as in blind system identification methods, it does not require knowledge of the system excitation. The paper shows that communities can be detected by applying spectral clustering to the low-rank output covariance matrix obtained from the graph signals. The performance analysis indicates that the community detection accuracy depends on the spectral properties of the graph filter considered. Furthermore, we show that the accuracy can be improved via a low-rank matrix decomposition method when the excitation signals are known. Numerical experiments demonstrate that our approach is effective for analyzing network data from diffusion, consumers, and social dynamics.
... An interesting extension in the study of opinion dynamics is to consider the effects of stubborn agents (or zealots), whose opinions remain unchanged throughout the network dynamics. Theoretical studies have focused on characterizing the steadystate of the opinion dynamics when stubborn agents are present [16], [24]- [28], developing techniques to effectively control the network and attain fastest convergence [28]- [31]. More recently, experimental studies have been conducted that confirm the existence of stubborn agents, for instance, [15], [32] suggested that stubborn agents can be used to justify several opinion dynamic models for data collected from controlled experiments; [33] illustrated that the existence of stubborn agents is a plausible cause for the emergence of extreme opinions in social networks; [34] studied the controllability of opinions in real networks using stubborn agents. ...
... An interesting extension in the study of opinion dynamics is to consider the effects of stubborn agents (or zealots), whose opinions remain unchanged throughout the network dynamics. Theoretical studies have focused on characterizing the steadystate of the opinion dynamics when stubborn agents are present [16], [24]- [28], developing techniques to effectively control the network and attain fastest convergence [28]- [31]. More recently, experimental studies have been conducted that confirm the existence of stubborn agents, for instance, [15], [32] suggested that stubborn agents can be used to justify several opinion dynamic models for data collected from controlled experiments; [33] illustrated that the existence of stubborn agents is a plausible cause for the emergence of extreme opinions in social networks; [34] studied the controllability of opinions in real networks using stubborn agents. ...
... Observation 1 [28] Let x(t; k) (z(t; k), y(t; k)) T ∈ R n where z(t; k) ∈ R ns and y(t; k) ∈ R n−ns are the opinions of stubborn agents and ordinary agents, respectively. Consider (1) by setting t → ∞, we have: ...
This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors’ information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model under the influence of stubborn agents; i.e., agents whose opinions are not influenced by their neighbors. This method can be viewed as a social RADAR, where the stubborn agents excite the system and the latter can be estimated through the reverberation observed from the analysis of the agents’ opinions. We show that the social network sensing problem can be viewed as a blind compressed sensing problem with a sparse measurement matrix. We prove that the network structure will be revealed when a sufficient number of stubborn agents independently influence a number of ordinary (non-stubborn) agents. We investigate the scenario with a deterministic or randomized DeGroot model and propose a consistent estimator for the steady states. Simulation results on synthetic and real world networks support our findings.
... The derived method does not depend on any time stamp information. Our idea is to introduce a set of stubborn agents, i.e., agents who never change their opinions [11], [12], [29], [30], into the social network. The stubborn agents change the terminal behavior of the opinion dynamics and reveal the social system in the form of an underdetermined linear system. ...
... To begin with, we assume that the opinion exchange is static, i.e., W (t) = W for all t; this assumption will be relaxed later in Section IV. Observe the following: Observation 3.3: [11] Under the assumption that W (t) = W and (I − D) is non-singular. Consider (2) by setting t → ∞, we get: ...
... However, to identify the system we need, therefore, to prevent trivial consensus. Our idea is to introduce a set of stubborn agents, i.e., agents who are not swayed by other opinions [11], [12], [29], [30], into the social network. The stubborn agents serve as 'probes' inserted on the social network that injects input to a social system. ...
... Observation 3.2: [11] Under the assumption that W (t) = W . Consider (2) by setting t → ∞, we get: ...
The focus of this paper is modeling what we call a Social Radar, i.e. a
method to estimate the relative influence between social agents, by sampling
their opinions and as they evolve, after injecting in the network stubborn
agents. The stubborn agents opinion is not influenced by the peers they seek to
sway, and their opinion bias is the known input to the social network system.
The novelty is in the model presented to probe a social network and the
solution of the associated regression problem. The model allows to map the
observed opinion onto system equations that can be used to infer the social
graph and the amount of trust that characterizes the links.
... More complex solutions are most suited for other contexts, including widespread communication networks, like Internet [11], or decentralized reputation systems [12]. It has been recently shown that gossip algorithms can also be effectively applied when, in a sensor network, there is a group of nodes that must acquire a function of data stored by another group of nodes [13]. A further interesting application field is gossip-based peer-to-peer video streaming [14]. ...
Though capillary sensor networks have the advantage of reporting punctual estimations of their sensed quantity, it is often useful for the nodes to know the overall average value of the same quantity. This is required, for example, when the network can make autonomous decisions. Several algorithms exist for solving the averaging problem in a distributed manner. Their efficiency can be measured by the number of iterations needed to converge to the average sensed value. In this paper, we consider two point-to-point and one point-to-multipoint distributed averaging algorithms that can be seen as variants of the same averaging solution. We define a set of analytical tools to evaluate the performance of these algorithms and to optimize their parameters in such a way to accelerate convergence. We also provide a performance assessment, based on numerical simulations, aimed at verifying the results of the analytical treatment and at comparing the considered schemes.
... We have studied this asymmetric information diffusion problem in [5] for static networks where nodes utilize synchronous gossiping algorithm. In this work,we will summarize some of the previous results and extend our analysis to the case of dynamic networks. ...
... The proof of the theorem can be found in [5]. We note that the partition A governs the communication among source nodes, B governs the flow from source nodes and to the rest of the network, D governs the communication among nonsource nodes. ...
... Interestingly, the formulation given above does not simplify our design problem, since constructing transition probability matrices for complex chains with given stationary distributions is a notoriously open problem in the literature. However , the relationship between our formulation and absorbing Markov chain theory is important and extremely valuable for further mathematical analysis [5] ...
In this paper we consider the problem of gossiping in a network to diffuse the average of a sub-set of nodes, called sources, and directing it to another sub-set of nodes in the network called destinations. This case generalizes the typical average consensus gossiping policy, where all nodes are both sources and destinations. We first describe prior results we obtained on a static network topology and gossip policy, high-lighting what conditions lead to the desired information flow. We show that, through semi-directed flows, this formulation allows to solve the problem with lower complexity than using plain gossiping policies. Inspired by these results, we move on to design algorithms to solve the problem in the dynamic case. For the dynamic network scenario we derive conditions under which the network converges to the desired result in the limit. We also provide policies that trade-off accuracy with increased mixing speed for the dynamic asymmetric diffusion problem.
This paper considers a new framework to detect communities in a graph from the observation of signals at its nodes. We model the observed signals as noisy outputs of an unknown network process, represented as a graph filter that is excited by a set of unknown low-rank inputs/excitations. Application scenarios of this model include diffusion dynamics, pricing experiments, and opinion dynamics. Rather than learning the precise parameters of the graph itself, we aim at retrieving the community structure directly. The paper shows that communities can be detected by applying a spectral method to the covariance matrix of graph signals. Our analysis indicates that the community detection performance depends on an intrinsic ‘low-pass’ property of the graph filter. We also show that the performance can be improved via a low-rank matrix plus sparse decomposition method when the latent parameter vectors are known. Numerical results demonstrate that our approach is effective.
This paper aims at modeling and inferring the influence among individuals from voting data (or more generally from actions that are selected by choosing one of m different options). The voting data are modeled as outcomes of a discrete random process, that we refer to as the discuss-then-vote model, whose evolution is governed by the DeGroot opinion dynamics with stubborn nodes. Based on the proposed model, we formulate the maximum-a-posterior estimator for the opinions and influence matrix (or the transition matrix) and derive a tractable approximation that results in a convex optimization problem. In the paper, the identifiability of the network dynamics' parameters and the vote prediction procedure based on the influence matrix, are discussed in depth. Our methodology is tested through numerical simulations as well as through its application to a set of the United States Senate roll call data. Interestingly, in spite of the relatively small data record available, the influence matrix inferred from the real data is consistent with the common intuition about the influence structure in the US Senate.
