Inference of multiple sparse networks in the presence of hidden nodes

We 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2023

Author dc:creator

• Navarro, Madeline

Advisor dc:contributor.advisor

• Segarra, Santiago

• Graph learning
• network topology inference
• hidden nodes
• graph signal processing
• graph stationarity
• multi-layer graphs

Statement dc:rights

• Copyright 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.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/115162

OAI identifier oai:identifier

oai:repository.rice.edu:1911/115162