Bootstrap of Count Features in Stochastic Networks

• Activity Number: 465
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Sharmodeep Bhattacharyya*+ and Peter Bickel
• Companies: University of California at Berkeley and University of California at Berkeley
• Keywords: networks ; bootstrap ; resampling ; moments

Abstract

Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences. But a proper statistical analysis of features of different stochastic models of networks is still underway. Theoretically determining the expectations and variances of the count features, such as 'moments' (Bickel, Chen & Levina, AoS, 2011) and smooth functions of these can become highly difficult. We propose bootstrap methods for finding empirical distribution of such count features of the networks. The proposed resampling estimates depend on the size of the count features as well as the degree distribution of the network. Using these methods, we can not only estimate variance of count features but also get good estimates of such feature counts, which are usually expensive to compute numerically in large networks. In our paper, we prove theoretical properties of the bootstrap variance estimates of the count features as well as show their efficacy through simulation. We also use the method on publicly available Facebook network data for estimate of variance and expectation of some count features. (Joint work with Peter J. Bickel).