Inference of multiple sparse networks in the presence of hidden nodes

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dc.contributor.advisorSegarra, Santiago
dc.creatorNavarro, Madeline
dc.date.accessioned2023-08-09T18:58:43Z
dc.date.created2023-05
dc.date.issued2023-04-19
dc.date.submittedMay 2023
dc.date.updated2023-08-09T18:58:43Z
dc.descriptionEMBARGO NOTE: This item is embargoed until 2024-05-01
dc.description.abstractWe investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. Joint network inference has been investigated extensively to expose the benefits of inferring multiple networks while accounting for their structural similarities. However, the primary assumption is that observations are available at all nodes, which is often violated in practice. In this thesis, we consider the realistic and more challenging scenario where a subset of nodes are hidden and cannot be measured. To address this ill-posed problem, we assume that there exist sets of graph signals that are stationary on the networks, which provides a global relationship between the observations and the network topologies such that we may characterize the effect of the hidden nodes. Under the assumptions that signals are 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 multiple sparse networks while accounting for the influence of hidden nodes. We prove that convex relaxations maintain the sparsest solution under mild conditions, 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 validate the theoretical results and provide evaluations of our method in comparison with other state-of-the-art baselines.
dc.embargo.lift2024-05-01
dc.embargo.terms2024-05-01
dc.format.mimetypeapplication/pdf
dc.identifier.citationNavarro, Madeline. "Inference of multiple sparse networks in the presence of hidden nodes." (2023) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/115162">https://hdl.handle.net/1911/115162</a>.
dc.identifier.urihttps://hdl.handle.net/1911/115162
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectGraph learning
dc.subjectnetwork topology inference
dc.subjecthidden nodes
dc.subjectgraph signal processing
dc.subjectgraph stationarity
dc.subjectmulti-layer graphs
dc.titleInference of multiple sparse networks in the presence of hidden nodes
dc.typeThesis
dc.type.materialText
thesis.degree.departmentElectrical and Computer Engineering
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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