Recovering Unobserved Network Links from Aggregated Relational Data: Discussions on Bayesian Latent Surface Modeling and Penalized Regression

Accurate network data are essential in fields such as economics, finance, sociology, epidemiology, and computer science. However, real-world constraints often prevent researchers from collect- ing a complete adjacency matrix, compelling them to rely on partial or aggregated information. One widespread example is Aggregated Relational Data (ARD), where respondents or institutions merely report the number of links they have to nodes possessing certain traits, rather than enu- merating all neighbors explicitly. This dissertation provides an in-depth examination of two major frameworks for reconstruct- ing networks from ARD: the Bayesian latent surface model and frequentist penalized regression ap- proaches. We supplement the original discussion with additional theoretical considerations on identifiability, consistency, and potential misreporting mechanisms. We also incorporate robust estimation techniques and references to privacy-preserving strategies such as differential privacy. By embedding nodes in a hyperspherical space, the Bayesian method captures geometric distance- based link formation, while the penalized regression approach casts unknown edges in a high- dimensional optimization problem, enabling scalability and the incorporation of covariates. Sim- ulations explore the effects of trait design, measurement error, and sample size. Real-world ap- plications illustrate the potential for partially observed networks in domains like financial risk, social recommendation systems, and epidemic contact tracing, complementing the original text with deeper investigations of large-scale inference challenges. Our aim is to show that even though ARD may be coarser than full adjacency data, it retains sub- stantial information about network structures, allowing reasonably accurate inference at scale. We conclude by discussing how adaptive trait selection, hybrid geometry-penalty methods, and privacy- aware data sharing can further advance this field. This enhanced treatment underscores the prac- tical relevance and theoretical rigor of ARD-based network inference.