Local Tomography of Large Networks Under the Low-Observability Regime

Santos, Augusto; Matta, Vincenzo; Sayed, Ali H.

doi:10.1109/tit.2019.2945033

Cited by 21 publications

(21 citation statements)

References 54 publications

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“…5 for an illustration. In order to avoid confusion, we remark that the method proposed in this work does not allow retrieving the topology of the network (for that purpose, we refer the reader instead to [34], [35]), but the influence (quantified by the aggregate weights x sk ) that each sending sub-network exerts on each receiving agent. While this information has the real topology of the network embedded in it, some other information is missing.…”

Section: Topology Learningmentioning

confidence: 99%

Interplay Between Topology and Social Learning Over Weak Graphs

Matta

Bordignon

Santos

et al. 2020

IEEE Open J. Signal Process.

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This work examines a distributed learning problem where the agents of a network form their beliefs about certain hypotheses of interest. Each agent collects streaming (private) data and updates continually its belief by means of a diffusion strategy, which blends the agent's data with the beliefs of its neighbors. We focus on weakly-connected graphs, where the network is partitioned into sending and receiving sub-networks, and we allow for heterogeneous models across the agents. First, we examine what agents learn (social learning) and provide an analytical characterization for the long-term beliefs at the agents. Among other effects, the analysis predicts when a leader-follower behavior is possible, where some sending agents control the beliefs of the receiving agents by forcing them to choose a particular and possibly fake hypothesis. Second, we consider the dual or reverse learning problem that reveals how agents learn: given the beliefs collected at a receiving agent, we would like to discover the influence that any sending sub-network might have exerted on this receiving agent (topology learning). An unexpected interplay between social and topology learning emerges: given H hypotheses and S sending sub-networks, topology learning can be feasible when H ≥ S. The latter being only a necessary condition, we then examine the feasibility of topology learning for two useful classes of problems. The analysis reveals that a critical element to enable topology learning is a sufficient degree of diversity in the statistical models of the sending sub-networks.

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Section: Topology Learningmentioning

confidence: 99%

Interplay Between Topology and Social Learning Over Weak Graphs

Matta

Bordignon

Santos

et al. 2020

IEEE Open J. Signal Process.

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“…However, all the aforementioned works do not consider the time dynamics of the signals emitted by the nodes, and, hence, they are not applicable to dynamical systems like the VAR model considered here. For dynamical graph models, relevant results under full observability were presented in [13][14][15][16][17][18][19], whereas partial observability was recently addressed in [20][21][22][23][24][25]. Particularly relevant to our work is the setting considered in [23][24][25], where the VAR model (1) runs on top of an Erdős-Rényi random graph [26,27].…”

Section: Related Workmentioning

confidence: 99%

Learning Bollobás-Riordan Graphs Under Partial Observability

Cirillo

Matta

Sayed

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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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 heterogeneity 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.

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“…In the literature, a large body of researches has been developed to tackle the problem due to their massive employments [10]. For example, [11]- [13] utilize Granger estimator to capture the casual relationships between agents. Spectral decomposition based method is also a popular tool to estimate the topology [14]- [16], which rely on the diagonalization of the sample matrices and then find the most suitable eigenvalues and eigenvectors to reconstruct the topology matrix.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, the results are hard to be generalized to account for the directed dependency between nodes, like [20], [21]. Second, most well-established techniques focus on the asymptotic performance with a large number of observation rounds or horizons (like [13], [14]), yet making it unclear how the inference error involves with the observation scale grows. Since small observation scale will give rise to poor inference results, it is also meaningful to investigate feasible techniques to improve the inference accuracy.…”

Section: Introductionmentioning

confidence: 99%

On Topology Inference for Networked Dynamical Systems: Principles and Performances

Li¹,

He²,

Chen³

et al. 2021

Preprint

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Topology inference for networked dynamical systems (NDSs) plays a crucial role in many areas. Knowledge of the system topology can aid in detecting anomalies, spotting trends, predicting future behavior and so on. Different from the majority of pioneering works, this paper investigates the principles and performances of topology inference from the perspective of node causality and correlation. Specifically, we advocate a comprehensive analysis framework to unveil the mutual relationship, convergence and accuracy of the proposed methods and other benchmark methods, i.e., the Granger and ordinary least square (OLS) estimators. Our method allows for unknown observation noises, both asymptotic and marginal stabilities for NDSs, while encompasses a correlation-based modification design to alleviate performance degradation in small observation scale. To explicitly demonstrate the inference performance of the estimators, we leverage the concentration measure in Gaussian space, and derive the non-asymptotic rates of the inference errors for linear timeinvariant (LTI) cases. Considering when the observations are not sufficient to support the estimators, we provide an excitationbased method to infer the one-hop and multi-hop neighbors with probability guarantees. Furthermore, we point out the theoretical results can be extended to switching topologies and nonlinear dynamics cases. Extensive simulations highlight the outperformance of the proposed method.

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Local Tomography of Large Networks Under the Low-Observability Regime

Cited by 21 publications

References 54 publications

Interplay Between Topology and Social Learning Over Weak Graphs

Interplay Between Topology and Social Learning Over Weak Graphs

Learning Bollobás-Riordan Graphs Under Partial Observability

On Topology Inference for Networked Dynamical Systems: Principles and Performances

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