Estimation of Individual Network Size from a Randomly Sampled Subnetwork

• Activity Number: 326
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Apratim Ganguly* and Eric Kolaczyk
• Companies: Boston University and Boston University
• Keywords: Social Network ; Degree Estimation ; Degree Distribution ; Network Sampling ; Quasi Likelihood ; Empirical Bayes

Abstract

The problem of estimating vertex degree in a large network, from a subnetwork of actors, arises in a number of practical applications (e.g., how many friends in a social network, or peers in a peer-to-peer computer network). We study a generalized version of this problem, where in the goal is, given a randomly sampled subnetwork from a large parent network, to estimate the degree of the sampled nodes. Depending on the sampling scheme, sometimes one might use a trivial maximum likelihood estimate. However, the MLE is not expected, in general, to use all relevant network information. In this study, we propose better estimates based on pertinent network information from the sample. Using quasi-likelihood and Bayesian methods, our estimates make use of hidden covariance information and improve upon the MLE. We consider several standard sampling designs and compare the relative performances of our estimates to traditional estimates, both theoretically and empirically.