Recovering Network Structure from Aggregated Relational Data using Penalized Regression

Document pages: 17 pages

Abstract: Social network data can be expensive to collect. Breza et al. (2017) proposeaggregated relational data (ARD) as a low-cost substitute that can be used torecover the structure of a latent social network when it is generated by aspecific parametric random effects model. Our main observation is that manyeconomic network formation models produce networks that are effectivelylow-rank. As a consequence, network recovery from ARD is generally possiblewithout parametric assumptions using a nuclear-norm penalized regression. Wedemonstrate how to implement this method and provide finite-sample bounds onthe mean squared error of the resulting estimator for the distribution ofnetwork links. Computation takes seconds for samples with hundreds ofobservations. Easy-to-use code in R and Python can be found atthis https URL.