This paper studies the problem of interconnected agents collaborating to track a dynamic state from partially informative observations, where the dynamic state evolves according to a slowly varying finite-state Markov chain. Although the centralized version of this problem has been extensively studied in the literature, the decentralized setting, particularly in the context of social learning, remains largely underexplored. The main result of this work is to establish that adaptive social learning (ASL), a recent social learning strategy suited for non-stationary environments, achieves the same error probability scaling law as the centralized solution in the rare transitions regime. Theoretical findings are supported by simulations, offering valuable insights into social learning under Markovian state transitions.

In social learning, a network of agents assigns probability scores (beliefs) to some hypotheses of interest, based on the observation of streaming data. First, each agent updates locally its belief with the information extracted from the current data through a suitable likelihood model. Then, these beliefs are diffused across the network, and the agents aggregate the beliefs received from their neighbors by means of a pooling rule. This work studies social learning in the context of fully online problems, where the true hypothesis and the likelihood models can drift over time. Traditional social learning fails to address both cases. To overcome this limitation, we propose the doubly adaptive social learning (A2SL) strategy, which infuses traditional social learning with the necessary adaptation capabilities to face drifts in the hypotheses and/or models. The A2SL strategy achieves this goal by employing two adaptation stages, and we show that all agents learn well (i.e., they end up placing full belief mass on the correct hypothesis) in the regime of small adaptation parameters.

We examine the learning performance achievable by a network of agents that solve a distributed regression problem using the recently proposed ACTC (Adapt-Compress-Then-Combine) diffusion strategy. The agents operate under communication constraints: they are allowed to communicate only with their immediate neighbors, and the exchanged signals are encoded by using randomized differential compression operators. We show that the mean-square estimation error of each agent comprises the error that the agents would achieve without communication constraints plus a compression loss. Our results reveal the fundamental quantitative relationship existing between the compression loss and the peculiar attributes of the distributed regression problem. We show how these quantitative relationships can be used to optimize the allocation of communication resources across the agents and improve their learning performance as compared to a uniform allocation.

In social learning, a group of agents linked by a graph topology collect data and exchange opinions on some topic of interest, represented by a finite set of hypotheses. Traditional social learning algorithms allow all agents in the network to gain full confidence on the true underlying hypothesis as the number of observations increases. Under partial information sharing, agents can exchange opinions only on a single hypothesis. This introduces significant challenges as compared to the standard case of full opinion sharing. We propose a novel strategy where each agent forms a valid belief by completing the partial beliefs received from its neighbors. The completion process exploits the knowledge accumulated in the past beliefs, thanks to a principled memory-aware rule inspired by a Bayesian criterion. We provide a detailed characterization of the memory-aware strategy, which reveals novel learning dynamics and highlights its advantages over previously considered schemes.

This work examines the problem of learning a network graph from signals emitted by the network nodes, according to a diffusion model ruled by a Laplacian combination policy. The challenging regime of partial observability is considered, where signals are collected from a limited subset of nodes, and we wish to estimate the subgraph of connections between these probed nodes. For the static setting where the network graph is fixed during the estimation process, we examine the sample complexity (number of time samples necessary to achieve consistent learning as the network size grows) of Erdős-Rényi and Bollobás-Riordan graphs. This complexity is almost quadratic for the former and almost linear for the latter class of graphs. We then examine the dynamic graph setting where the graph of latent nodes grows over time, while the probed subset remains fixed. We show that in this case the sample complexity can be reduced, implying the unexpected conclusion that dynamic graphs might help topology inference under partial observability.

This work addresses the problem of sharing partial information within social learning strategies. In social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate information from private observations to form their beliefs over a set of hypotheses; second, agents combine the entirety of their beliefs locally among neighbors. Within a sufficiently informative environment and as long as the connectivity of the network allows information to diffuse across agents, these algorithms enable agents to learn the true hypothesis. Instead of sharing the entirety of their beliefs, this work considers the case in which agents will only share their beliefs regarding one hypothesis of interest, with the purpose of evaluating its validity, and draws conditions under which this policy does not affect truth learning. We propose two approaches for sharing partial information, depending on whether agents behave in a self-aware manner or not. The results show how different learning regimes arise, depending on the approach employed and on the inherent characteristics of the inference problem. Furthermore, the analysis interestingly points to the possibility of deceiving the network, as long as the evaluated hypothesis of interest is close enough to the truth.

This work proposes a decentralized architecture, where individual agents aim at solving a classification problem while observing streaming features of different dimensions and arising from possibly different distributions. In the context of social learning, several useful strategies have been developed, which solve decision making problems through local cooperation across distributed agents and allow them to learn from streaming data. However, traditional social learning strategies rely on the fundamental assumption that each agent has significant prior knowledge of the underlying distribution of the observations. In this work we overcome this issue by introducing a machine learning framework that exploits social interactions over a graph, leading to a fully data-driven solution to the distributed classification problem. In the proposed social machine learning (SML) strategy, two phases are present: in the training phase, classifiers are independently trained to generate a belief over a set of hypotheses using a finite number of training samples; in the prediction phase, classifiers evaluate streaming unlabeled observations and share their instantaneous beliefs with neighboring classifiers. We show that the SML strategy enables the agents to learn consistently under this highly-heterogeneous setting and allows the network to continue learning even during the prediction phase when it is deciding on unlabeled samples. The prediction decisions are used to continually improve performance thereafter in a manner that is markedly different from most existing static classification schemes where, following training, the decisions on unlabeled data are not re-used to improve future performance.

This work addresses the problem of learning the topology of a network from the signals emitted by the network nodes. These signals are generated over time through a linear diffusion process, where neighboring nodes exchange messages according to the underlying network topology, and aggregate them according to a certain combination matrix. We consider the demanding setting of graph learning under partial observability, where signals are available only from a limited fraction of nodes, and we want to establish whether the topology of these nodes can be estimated faithfully, despite the presence of possibly many latent nodes. Recent results examined this problem when the network topology is generated according to an Erdős-Rényi random model. However, Erdős-Rényi graphs feature homogeneity across nodes and independence across edges, while, over several real-world networks, significant heterogeneity is observed between very connected “hubs” and scarcely connected peripheral nodes, and the edge construction process entails significant dependencies across edges. Preferential attachment random graphs were conceived primarily to fill these gaps. We tackle the problem of graph learning over preferential attachment graphs by focusing on the following setting: first-order vector autoregressive models equipped with a stable Laplacian combination matrix, and a network topology drawn according to the popular Bollobás-Riordan preferential attachment model. The main result established in this work is that a combination-matrix estimator known as Granger estimator achieves graph learning under partial observability.

We consider multi-agent networks that aim at solving, cooperatively and online, distributed optimization problems under communication constraints. We propose the ACTC (Adapt-Compress-Then-Combine) diffusion strategy, which leverages differential randomized compression to infuse the classical ATC strategy with the ability to handle compressed data. We consider the flexible setting of directed graphs and left-stochastic policies, and require strong convexity only at a network level (i.e., some agents might even have non-convex risks). We prove that each agent is able to learn the optimal solution up to a small error on the order of the step-size, achieving remarkable savings in terms of bits exchanged between neighboring agents.

This work deals with cyber-threat propagation across a communication network designed according to the network-slicing paradigm. Exploiting the multi-dimensional Birth-Death-Immigration model, we examine threat percolation from a vulnerable slice to a virtually secured slice. The analysis quantifies the role played by slice-coupling on threat propagation, revealing how cross-slice attacks can be particularly dangerous in applications where the attacker opens a door in some slice relative, e.g., to ordinary services, breaking through into a slice that delivers critical services such as healthcare or financial services.

This work proposes a new way of combining independently trained classifiers over space and time. Combination over space means that the outputs of spatially distributed classifiers are aggregated. Combination over time means that the classifiers respond to streaming data during testing and continue to improve their performance even during this phase. By doing so, the proposed architecture is able to improve prediction performance over time with unlabeled data. Inspired by social learning algorithms, which require prior knowledge of the observations distribution, we propose a Social Machine Learning (SML) paradigm that is able to exploit the imperfect models generated during the learning phase. We show that this strategy results in consistent learning with high probability, and it yields a robust structure against poorly trained classifiers. Simulations with an ensemble of feedforward neural networks are provided to illustrate the theoretical results.

We consider the problem of identifying the members of a botnet under an application-layer (L7) DDoS attack, where a target site is flooded with a large number of requests that emulate legitimate users’ patterns. This challenging problem has been recently addressed with reference to two simplified scenarios, where either all bots pick requests from the same emulation dictionary (total overlap), or they are divided in separate clusters corresponding to distinct emulation dictionaries (no overlap at all). However, over real networks these two extreme conditions are difficult to realize, and the intermediate situation is observed where the emulation patterns of distinct bots belong to partially overlapped dictionaries. This intermediate situation introduces significant sophistication in the bot identification problem. In order to address this issue, we provide an analytical characterization of the pairwise cluster interaction, which is exploited to devise an identification rule to discriminate legitimate users from bots and to identify the individual bot clusters.

This work examines the problem of learning the topology of a network (graph learning) from the signals produced at a subset of the network nodes (partial observability). This challenging problem was recently tackled assuming that the topology is drawn according to an Erdős-Rényi model, for which it was shown that graph learning under partial observability is achievable, exploiting in particular homogeneity across nodes and independence across edges. However, several real-world networks do not match the optimistic assumptions of homogeneity/independence, for example, high het-erogeneity is often observed between very connected nodes (hubs) and scarcely connected peripheral nodes. Random graphs with preferential attachment were conceived to overcome these issues. In this work, we discover that, over first-order vector autoregressive systems with a stable Laplacian combination matrix, graph learning is achievable under partial observability, when the network topology is drawn according to a popular preferential attachment model known as the Bollobás-Riordan model.

This work examines propagation of cyber-threats over networks under an adversarial formulation. Exploiting Kendall's birth-death-immigration model, we propose an analytical framework to describe the stochastic dynamics of cyber-threat propagation in a collection of heterogeneous sub-networks characterized by different attributes. We propose two formalisations of the problem as zero-sum games involving two adversaries: an attacker, who launches cyber-threats across the distinct sub-networks; and a defender, who tries to mitigate the threats by delivering suitable countermeasures. According to the first formalisation, the interplay between the defender and the attacker is modelled as a Stackelberg leader-follower game, while the second formalisation considers a strategic game wherein the two contenders play simultaneously without knowing the choice of the other player. We derive the equilibrium strategies for both versions of the game, and discuss a number of insightful interplays and ramifications of the different equilibrium points for the problem at hand. The equilibrium strategies depend on three fundamental attributes: i) the available resource budget of the attacker and the defender; ii) the capacity of the legitimate nodes to (unintentionally) forward the threat across the network, after they have been compromised during the propagation of the threat; iii) the intrinsic characteristics of the sub-networks, namely, their immunity to the attacks, their inertia in responding to the countermeasures, and the importance of the individual sub-networks. The relevance of the proposed solution is illustrated through a series of examples and numerical simulations.

In a Distributed Denial of Service (DDoS) attack, a network (botnet) of dispersed agents (bots) sends requests to a website to saturate its resources. Since the requests are sent by automata, the typical way to detect them is to look for some repetition pattern or commonalities between requests of the same user or from different users. For this reason, recent DDoS variants exploit communication layers that offer broader possibility in terms of admissible request patterns, such as, e.g., the application layer. In this case, the malicious agents can pick legitimate messages from an emulation dictionary, and each individual agent sends a relatively low number of admissible requests, so as to make its activity non suspicious. This problem has been recently addressed under the assumption that all the members of the botnet use the same emulation dictionary. This situation is an idealization of what occurs in practice, since different clusters of agents are typically sharing only part of a global emulation dictionary. The diversity among the emulation dictionaries across different clusters introduces significant complexity in the botnet identification challenge. This work tackles this issue and provides the following main contributions. We obtain an analytical characterization of the message innovation rate of the DDoS attack with multiple emulation dictionaries. Exploiting this result, we design a botnet identification algorithm equipped with a cluster expurgation rule, which, under appropriate technical conditions, is shown to provide exact classification of bots and normal users as the observation window size increases. Then, an experimental campaign over real network traces is conducted to assess the validity of the theoretical analysis, as well as to examine the effect of a number of non-ideal effects that are unavoidably observed in practical scenarios.

This work proposes a novel strategy for social learning by introducing the critical feature of adaptation. In social learning, several distributed agents update continually their belief about a phenomenon of interest through: i) direct observation of streaming data that they gather locally; and ii) diffusion of their beliefs through local cooperation with their neighbors. Traditional social learning implementations are known to learn well the underlying hypothesis (which means that the belief of every individual agent peaks at the true hypothesis), achieving steady improvement in the learning accuracy under stationary conditions. However, these algorithms do not perform well under nonstationary conditions commonly encountered in online learning, exhibiting a significant inertia to track drifts in the streaming data. In order to address this gap, we propose an Adaptive Social Learning (ASL) strategy, which relies on a small step-size parameter to tune the adaptation degree. First, we provide a detailed characterization of the learning performance by means of a steady-state analysis. Focusing on the small step-size regime, we establish that the ASL strategy achieves consistent learning under standard global identifiability assumptions. We derive reliable Gaussian approximations for the probability of error (i.e., of choosing a wrong hypothesis) at each individual agent. We carry out a large deviations analysis revealing the universal behavior of adaptive social learning: the error probabilities decrease exponentially fast with the inverse of the step-size, and we characterize the resulting exponential learning rate. Second, we characterize the adaptation performance by means of a detailed transient analysis, which allows us to obtain useful analytical formulas relating the adaptation time to the step-size. The revealed dependence of the adaptation time and the error probabilities on the step-size highlights the fundamental trade-off between adaptation and learning emerging in adaptive social learning.

This work studies the learning abilities of agents sharing partial beliefs over social networks. The agents observe data that could have risen from one of several hypotheses and interact locally to decide whether the observations they are receiving have risen from a particular hypothesis of interest. To do so, we establish the conditions under which it is sufficient to share partial information about the agents' belief in relation to the hypothesis of interest. Some interesting convergence regimes arise.

In social learning, agents form their opinions or beliefs about certain hypotheses by exchanging local information. This work considers the recent paradigm of weak graphs, where the network is partitioned into sending and receiving components, with the former having the possibility of exerting a domineering effect on the latter. Such graph structures are prevalent over social platforms. We will not be focusing on the direct social learning problem (which examines what agents learn), but rather on the dual or reverse learning problem (which examines how agents learned). Specifically, from observations of the stream of beliefs at certain agents, we would like to examine whether it is possible to learn the strength of the connections (influences) from sending components in the network to these receiving agents.

Many optimization, inference, and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among neighboring nodes. There is a large body of literature examining the effect of the graph structure on the performance of decentralized processing strategies. In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes of a graph convey about the underlying topology? For large-scale networks, the difficulty in addressing such inverse problems is compounded by the fact that usually only a limited fraction of the nodes can be probed, giving rise to a second important question: Despite the presence of unobserved nodes, can partial observations still be sufficient to discover the graph linking the probed nodes? The article surveys recent advances on this challenging learning problem and related questions.

A network attacker wants to transmit Voice-over-IP (VoIP) traffic streams covertly. He tries to evade the detection system by manipulating the VoIP streams through padding, shifting, and splitting operations, so as to conceal them amidst the Internet traffic. A defender wants to detect the manipulated VoIP streams. Tackling this problem from an adversarial perspective, we provide two contributions: 1) we obtain a highly stylized representation of VoIP streams in terms of transmission frequency F and packet length L, and characterize the (F, L) region achievable by the attacker's transformation and 2) We formulate the VoIP detection game, and find both theoretical conditions and a practical algorithm to find the Nash equilibrium of the game. As a result, we are able to design an optimal (from the adversarial perspective) algorithm for VoIP detection, which is nicknamed as ADVoIP. Simulations over real network traces, and comparison with existing approaches, show the effectiveness of the proposed approach.

This article studies the problem of reconstructing the topology of a network of interacting agents via observations of the state-evolution of the agents. We focus on the large-scale network setting with the additional constraint of partial observations, where only a small fraction of the agents can be feasibly observed. The goal is to infer the underlying subnetwork of interactions and we refer to this problem as local tomography. In order to study the large-scale setting, we adopt a proper stochastic formulation where the unobserved part of the network is modeled as an Erdös-Rényi random graph, while the observable subnetwork is left arbitrary. The main result of this work is to establish that, under this setting, local tomography is actually possible with high probability, provided that certain conditions on the network model are met (such as stability and symmetry of the network combination matrix). Remarkably, such conclusion is established under the low-observability regime, where the cardinality of the observable subnetwork is fixed, while the size of the overall network scales to infinity.

We consider a distributed social learning problem where a network of agents is interested in selecting one among a finite number of hypotheses. The data collected by the agents might be heterogeneous, meaning that different sub-networks might observe data generated by different hypotheses. For example, some sub-networks might be receiving (or even intentionally generating) data from a fake hypothesis and will bias the rest of the network via social influence. This work focuses on a two-step diffusion algorithm where each agent: i) first updates individually its belieffunction using its private data; ii) then computes a new belief function by exponentiating a linear combination of the log-beliefs of its neighbors. We obtain analytical formulas that reveal how the agents' detection capability and the network topology interplay to influence the asymptotic beliefs of the agents. Some interesting behaviors arise, such as the “mind-control” effect or the “truth-is-somewhere-in-between” effect.

In this work we consider the problem of learning an Erdös-Rényi graph over a diffusion network when: i) data from only a limited subset of nodes are available (partial observation); ii) and the inferential goal is to discover the graph of interconnections linking the accessible nodes (local structure learning). We propose three matrix estimators, namely, the Granger, the one-lag correlation, and the residual estimators, which, when followed by a universal clustering algorithm, are shown to retrieve the true subgraph in the limit of large network sizes. Remarkably, it is seen that a fundamental role is played by the uniform concentration of node degrees, rather than by sparsity.

This paper studies the problem of inferring whether an agent is directly influenced by another agent over a network. Agent i influences agent j if they are connected (according to the network topology), and if agent j uses the data from agent i to update its online learning algorithm. The solution of this inference task is challenging for two main reasons. First, only the output of the learning algorithm is available to the external observer that must perform the inference based on these indirect measurements. Second, only output measurements from a fraction of the network agents is available, with the total number of agents itself being also unknown. The main focus of this paper is ascertaining under these demanding conditions whether consistent tomography is possible, namely, whether it is possible to reconstruct the interaction profile of the observable portion of the network, with negligible error as the network size increases. We establish a critical achievability result, namely, that for symmetric combination policies and for any given fraction of observable agents, the interacting and non-interacting agent pairs split into two separate clusters as the network size increases. This remarkable property then enables the application of clustering algorithms to identify the interacting agents influencing the observations. We provide a set of numerical experiments that verify the results for finite network sizes and time horizons. The numerical experiments show that the results hold for asymmetric combination policies as well, which is particularly relevant in the context of causation.

This work studies the problem of inferring from streaming data whether an agent is directly influenced by another agent over an adaptive network of interacting agents. Agent i influences agent j if they are connected, and if agent j uses the information from agent i to update its inference. The solution of this inference task is challenging for at least two reasons. First, only the output of the learning algorithm is available to the external observer and not the raw data. Second, only observations from a fraction of the network agents is available, with the total number of agents itself being also unknown. This work establishes, under reasonable conditions, that consistent tomography is possible, namely, that it is possible to reconstruct the interaction profile of the observable portion of the network, with negligible error as the network size increases. We characterize the decaying behavior of the error with the network size, and provide a set of numerical experiments to illustrate the results.

This work considers a diffusion network responding to streaming data, and studies the problem of identifying the topology of a subnetwork of observable agents by tracking their output measurements. Topology inference from indirect and/or incomplete datasets (network tomography) is in general an ill-posed problem. Under an appropriate Erdos-Renyi random graph model for the unobserved part, the problem of network tomography is well-posed in the thermodynamic limit: when the number of network agents grows to infinity, any arbitrary subnetwork topology associated with the observed agents can be recovered with high probability.

We consider the problem of mitigating the effect of malicious cyber-threats spreading across multiple subnets of a data network. Three fundamental issues arise: 1) providing a manageable model of threat propagation; 2) quantifying the danger associated to different subnets; and 3) optimizing the allocation of the countermeasures. We address these issues by providing the following novel contributions. First, a convenient mathematical abstraction of threat propagation is proposed, which employs the birth-and-death process with immigration pioneered by Kendall in his seminal work of 1948. Then, exploiting the notable properties of such a model, we show how to retrieve analytical solutions for optimal resource allocation across subnets, for the case where the parameters of the attack are perfectly known. Finally, the assumption of perfect knowledge is removed, and the unknown attack parameters are estimated using maximum-likelihood estimators.

In modern heterogeneous sensor networks huge volumes of information rapidly flow across the system, and it is often too difficult or costly to associate data to the sensors that produced them. Then, the set of observations appears to be unlabeled: What comes from whom? We study the classical problem of detecting a known signal embedded in Gaussian noise, but under the peculiar assumption that the signal samples have been scrambled (e.g., in time or space) in an unknown way. Our study sheds light on questions like: How much detection performance is contained in the samples' values and how much in their ordering? Are there nicely-performing detectors with affordable computational complexity?

Distributed Denial-of-Service (DDoS) attacks are usually launched through the botnet, an “army” of compromised nodes hidden in the network. Inferential tools for DDoS mitigation should accordingly enable an early and reliable discrimination of the normal users from the compromised ones. Unfortunately, the recent emergence of attacks performed at the application layer has multiplied the number of possibilities that a botnet can exploit to conceal its malicious activities. New challenges arise, which cannot be addressed by simply borrowing the tools that have been successfully applied so far to earlier DDoS paradigms. In this paper, we offer basically three contributions: 1) we introduce an abstract model for the aforementioned class of attacks, where the botnet emulates normal traffic by continually learning admissible patterns from the environment; 2) we devise an inference algorithm that is shown to provide a consistent (i.e., converging to the true solution as time elapses) estimate of the botnet possibly hidden in the network; and 3) we verify the validity of the proposed inferential strategy on a test-bed environment. Our tests show that, for several scenarios of implementation, the proposed botnet identification algorithm needs an observation time in the order of (or even less than) 1 min to identify correctly almost all bots, without affecting the normal users' activity.

Parametric estimation for the generative social sensing model proposed in [19,20] is addressed. First, we provide a detailed analysis of the estimation performance bounds, in terms of the Fisher information matrix, with emphasis on the fundamental scaling laws as the number of network agents and/or the number of monitored agents' activities is large. Then, we examine two viable estimation procedures that can be useful even in such large dataset applications: the Expectation-Maximization and the Fisher scoring algorithms, which both achieve the aforementioned performance bounds.

We examine the interplay between learning and privacy over multiagent consensus networks. The learning objective of each individual agent consists of computing some global network statistic, and is accomplished by means of a consensus protocol. The privacy objective consists of preventing inference of the individual agents' data from the information exchanged during the consensus stages, and is accomplished by adding some artificial noise to the observations (obfuscation). An analytical characterization of the learning and privacy performance is provided, with reference to a consensus perturbing and to a consensus-preserving obfuscation strategy.

This paper examines the close interplay between cooperation and adaptation for distributed detection schemes over fully decentralized networks. The combined attributes of cooperation and adaptation are necessary to enable networks of detectors to continually learn from streaming data and to continually track drifts in the state of nature when deciding in favor of one hypothesis or another. The results in this paper establish a fundamental scaling law for the steady-state probabilities of miss detection and false alarm in the slow adaptation regime, when the agents interact with each other according to distributed strategies that employ small constant step-sizes. The latter are critical to enable continuous adaptation and learning. This paper establishes three key results. First, it is shown that the output of the collaborative process at each agent has a steady-state distribution. Second, it is shown that this distribution is asymptotically Gaussian in the slow adaptation regime of small step-sizes. Third, by carrying out a detailed large deviations analysis, closed-form expressions are derived for the decaying rates of the false-alarm and miss-detection probabilities. Interesting insights are gained from these expressions. In particular, it is verified that as the step-size μ decreases, the error probabilities are driven to zero exponentially fast as functions of 1μ, and that the exponents governing the decay increase linearly in the number of agents. It is also verified that the scaling laws governing the errors of detection and the errors of estimation over the network behave very differently, with the former having exponential decay proportional to 1μ, while the latter scales linearly with decay proportional to μ. Moreover, and interestingly, it is shown that the cooperative strategy allows each agent to reach the same detection performance, in terms of detection error exponents, of a centralized stochastic-gradient solution. The results of this paper are illustrated by applying them to canonical distributed detection problems.

In [1], an important step toward the characterization of distributed detection over adaptive networks has been made by establishing the fundamental scaling law of the error probabilities. However, empirical evidence reported in [1] revealed that a refined asymptotic analysis is necessary in order to capture the exact impact of network connectivity on the detection performance of each individual agent. Here we address this open issue by exploiting the framework of exact asymptotics.

In practical target tracking problems, the target detection performance of the sensors may be unknown and may change rapidly with time. In this work we develop a target tracking procedure able to adapt and react to time-varying changes of the detection capability for a network of sensors. The proposed tracking strategy is based on a Bayesian framework, in which the dynamic target state is augmented to include the sensor detection probabilities. The method is validated using computer simulations and real-world experiments conducted by the NATO Science and Technology Organization (STO) - Centre for Maritime Research and Experimentation (CMRE).

In distributed inference, local cooperation among network nodes can be exploited to enhance the performance of each individual agent, but a challenging requirement for networks operating in dynamic real-world environments is that of adaptation. The interplay between these two fundamental aspects of cooperation and adaptation has been investigated in recent years in the context of estimation problems. Less explored in the literature is the case of detection, which is our focus. Capitalizing on the powerful tool of large deviations analysis, we show how to design and characterize the performance of diffusion strategies that reconcile both needs of adaptation and detection in decentralized systems.

This paper presents a Bayesian multi-sensor tracking strategy for a network of autonomous underwater vehicles (AUVs) for the purpose of anti-submarine warfare (ASW). A bistatic configuration and the corresponding acoustic model for the bistatic signal-to-noise ratio (SNR) is used. The Bayesian posterior distribution of the target state based on all available information from sensors and on the acoustic model is reconstructed via particle filtering methods, taking into account the port-starboard ambiguity typical of horizontal line arrays. The posterior distribution is the optimal estimation procedure, the only approximation derives from the particle representation. The effectiveness of the proposed algorithm is demonstrated on a real data set collected by the NATO Centre for Maritime Research and Experimentation (CMRE) during the NATO Proud Manta 2012 exercise (ExPOMA12).

In one of his landmark papers, Cover established the fundamental scaling laws of learning with nearest-neighbor rules (T.M. Cover, 1968). With the recent advances on distributed nearest-neighbor learning in sensor networks novel trade-offs arise, involving the faithfulness of message representation (quantization bits) and the number of delivered messages (transmitting sensors). This is the main theme of this paper.

Nowadays, the most investigated concepts of physical layer security encompass asymptotic criteria of secrecy. Taking a different perspective, in this work we come back to Shannon's original formulation of perfect secrecy, amounting to impose exactly zero mutual information between the source message and the data gathered by the eavesdropper. By jamming the intruder with a special class of noise-that we call pdf-bandlimited-and adopting a novel “out of the (pdf) band” information encoding technique, it is shown that a perfectly secure communication can be in fact sustained over the main channel, leaving no chances to the eavesdropper.

Recently it has been shown that the Multi-Sensor Probability Hypothesis Density (MS-PHD) has some optimality properties in the regime of large number of sensors [1, 2], achieving the same performance of the Bayes multi-sensor/multi-target posterior in the Random Finite Set (RFS) framework [3]. However, when the number of sensors N is relatively large, the traditional PHD filter loses its computational efficiency, the complexity being exponential in N. On the other hand, the complexity of the full Bayes posterior is only linear in N, and this paper suggests an idea for its computation using Sequential Monte Carlo (SMC) methods. The MS-PHD is then evaluated, and numerical examples show that it is possible to deal with a scenario where the number of sensors is very large while targets, appearing and disappearing, evolve in time.

A wireless sensor network is engaged in a statistical learning task, to be accomplished in a decentralized fashion. The focus here is in distributed Nearest-Neighbor (NN) regression, in the presence of communication constraints. We first introduce a general channel access policy which allows the fusion center to recover training-set labels ordered according to the NN criterion, in the absence of any data exchange among sensors. Then, two different paradigms are considered, where the communication cost is measured as: i) the channel accesses; ii) the quantization bits. In the former scenario, we propose a distributed NN strategy reaching an asymptotic performance of twice the minimum achievable mean-square error, with only one sensor transmitting information. In the latter case, we achieve universally consistent distributed NN regression even with one-bit quantized labels.

Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching rule is that of a maximum causal delay, and the problem is related to embedding a flow of packets in cover traffic such that no timing analysis can detect it. We study the best undetectable embedding policy and the corresponding maximum flow rate-that we call the embedding capacity-under the assumption that the cover traffic can be modeled as an arbitrary renewal process. We find that computing the embedding capacity requires the inversion of a very structured linear system that, for a broad range of renewal models encountered in practice, admits a fully analytical expression in terms of the renewal function of the processes. This result enables us to explore the properties of the embedding capacity, obtaining closed-form solutions for selected distribution families and a suite of sufficient conditions on the capacity ordering. We test our solution on real network traces, which shows a remarkable match for tight delay constraints. A gap between the predicted and the actual embedding capacities appears for looser constraints, and further investigation reveals that it is caused by inaccuracy of the renewal traffic model rather than of the solution itself.

The secure networking problem of embedding information flows into cover traffic is addressed. When relayed packets must obey a causal delay constraint, this naturally remaps to a matching problem between point processes (here taken as arbitrary renewal processes). The best hiding policy is thus characterized in terms of the maximum fraction of matched points, which is accordingly referred to as embedding capacity. For a broad range of renewal models encountered in practice, we provide a simple analytical formula for the capacity, which depends only on the renewal function of the underlying processes, and further find conditions for capacity-ordering of different types of cover traffic. The results are also tested on real network traces, and a very good match is observed, especially for tight delay constraints.

A random parameter is estimated by a distributed network of sensors that communicate over a common MAC. The channel implies an enforced additive fusion rule, and the goal here is to design a power-constrained forwarding strategy and the post-processing by the fusion center. To get an explicit solution we appeal to asymptotics, meaning that we design the locally optimal scheme for the limiting case that the received power goes to zero.

Stochastic resonance (SR) is a phenomenon long investigated by physicists that has recently attracted some interest in the signal processing literature. In this paper, we explore the potential benefits of the SR effect for shift-in-mean detection problems, specifically focusing on sequential decision rules. Amenable formulas for the optimal distribution of the SR noise, as well as an asymptotic comparison with the traditional Neyman-Pearson approach are obtained.

We consider the problem of DOA (direction of arrival) estimation of an acoustic wavefront by a wireless sensor network (WSN) within the SENMA architecture (a mobile agent (MA) repeatedly polls the sensors lying inside its field of view). The sensors, which are random in number and location, are DOA-blind and simply emit a pulse train synchronized to the acoustic event's passage; taken in aggregate, however, the MA can exploit its non-isotropic field of view (FOV) to infer an accurate DOA. In this paper we (i) use a more realistic "soft" FOV; (ii) account for multiple sources; and (iii) suggest a strategy for the MA. We find that the presence of more than one source can improve DOA estimation, and also that an optimal strategy for the MA squints near the expected DOA, as opposed to directly at it.

We introduce a likelihood based multiple access (LBMA) communication/estimation scheme for nonrandom parameter estimation in wireless sensor networks with additive multiple access channels. Constraining the system in terms of energy and allowing the available number of degrees of freedom to scale as nα, 0.5 <; α <; 1, we prove that LBMA is asymptotically efficient. Thus, the new scheme is appropriate for large networks. LBMA is, in addition, simple to implement and relies upon an intuitive approach.

Quantization for estimation is explored for the case that it must be performed jointly with data association; that is, the case in which measurements are of uncertain origin. Data association requires some sort of gating of distributed observations, and a censoring strategy is proposed. Several quantization philosophies are explored, specifically uniform quantization, uniform quantization with measurement exchangeability incorporated (the "type" method), and uniform quantization of sorted measurements. It is shown, perhaps surprisingly, that the third scheme preserves more information that may be useful for estimation; and a simple procedure for optimal fused estimation based on this third scheme is given. Interestingly, when compared in terms of rate-distortion curves, the schemes two and three perform similarly; their censored versions offer further improvement in performances due to the uncertain-origin property of the measurements.

Following the SENMA concept, we consider a wireless network of very dumb and cheap sensors, polled by a travelling "rover". Sensors are randomly placed and isotropic: individually they have no ability to resolve the direction of arrival (DOA) of an acoustic wave. We assume that the communication load must be as limited as possible, so that these times cannot be communicated to the rover. Notwithstanding the lack of transmission of arrival times and the lack of DOA resolution ability of the individual sensors, DOA estimation is possible, and asymptotic efficiency becomes closely approximated after a reasonable number of rover snapshots. Key features are the directionality of the rover antenna, the area it surveys, and the average number of sensors inside that area, as accorded a Poisson distribution.

Following the SENMA concept, we consider a wireless network of very dumb and cheap sensors, polled by a travelling "rover". Sensors are randomly placed and isotropic: Individually, they have no ability to resolve the direction of arrival (DOA) of an acoustic wave. However, they do observe the wavefront at different times. We assume that the communication load must be as limited as possible, so that these times cannot be communicated to the rover. Notwithstanding the lack of transmission of arrival times and the lack of DOA resolution ability of the individual sensors, DOA estimation is possible and simple, and asymptotic efficiency becomes closely approximated after a reasonable number of rover snapshots. Key features are the directionality of the rover antenna, the area it surveys, and the average number of sensors inside that area, as accorded a Poisson distribution.