Examinando por Autor "Buciulea, Andrei"

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Joint Network Topology Inference in the Presence of Hidden Nodes
(Institute of Electrical and Electronics Engineers, 2024-04-23) Navarro, Madeline; Rey, Samuel; Buciulea, Andrei; Garcia Marques, Antonio; Segarra, Santiago
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more difficult scenario where a subset of nodes are hidden and cannot be measured. Under the assumptions that the partially observed nodal signals are graph stationary and the networks have similar connectivity patterns, we derive structural characteristics of the connectivity between hidden and observed nodes. This allows us to formulate an optimization problem for estimating networks while accounting for the influence of hidden nodes. We identify conditions under which a convex relaxation yields the sparsest solution, and we formalize the performance of our proposed optimization problem with respect to the effect of the hidden nodes. Finally, synthetic and real-world simulations provide evaluations of our method in comparison with other baselines
Learning graphs from smooth and graph-stationary signals with hidden variables
(Institute of Electrical and Electronics Engineers, 2022-03-22) Buciulea, Andrei; Rey, Samuel; Garcia Marques, Antonio
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical environments, only a subset of nodes is accessible. A natural (and sometimes effective) approach is to disregard the role of unobserved nodes, but this ignores latent network effects, deteriorating the quality of the estimated graph. Differently, this paper investigates the problem of inferring the topology of a network from nodal observations while taking into account the presence of hidden (latent) variables . Our schemes assume the number of observed nodes is considerably larger than the number of hidden variables and build on recent graph signal processing models to relate the signals and the underlying graph. Specifically, we go beyond classical correlation and partial correlation approaches and assume that the signals are smooth and/or stationary in the sought graph. The assumptions are codified into different constrained optimization problems, with the presence of hidden variables being explicitly taken into account. Since the resulting problems are ill-conditioned and non-convex, the block matrix structure of the proposed formulations is leveraged and suitable convex-regularized relaxations are presented. Numerical experiments over synthetic and real-world datasets showcase the performance of the developed methods and compare them with existing alternatives