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Learning about the social structure of hidden and hard-to-reach populations--- such as drug users and sex workers --- is a major goal of epidemiologicaland public health research on risk behaviors and disease prevention.Respondent-driven sampling (RDS) is a peer-referral process widely used by manyhealth organizations, where research subjects recruit other subjects from theirsocial network. In such surveys, researchers observe who recruited whom, alongwith the time of recruitment and the total number of acquaintances (networkdegree) of respondents. However, due to privacy concerns, the identities ofacquaintances are not disclosed. In this work, we show how to reconstruct theunderlying network structure through which the subjects are recruited. Weformulate the dynamics of RDS as a continuous-time diffusion process over theunderlying graph and derive the likelihood for the recruitment time seriesunder an arbitrary recruitment time distribution. We develop an efficientstochastic optimization algorithm called RENDER (REspoNdent-Driven nEtworkReconstruction) that finds the network that best explains the collected data.We support our analytical results through an exhaustive set of experiments onboth synthetic and real data.

Seeing the Unseen Network: Inferring Hidden Social Ties from Respondent-Driven Sampling