Thursday, March 20, 2014

Sharmodeep Bhattacharyya: March 26th

Statistical Inference of Features of Networks

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. We follow the nonparametric model proposed by Bickel and Chen (PNAS, 2009) and investigate the statistical properties of local features of the networks generated from such models. We consider subsampling bootstrap methods for finding empirical distribution of count features or `moments' (Bickel, Chen and Levina, AoS, 2011) (such as number of triangles) and smooth functions of these moments for the networks. 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. We derive theoretical properties of the bootstrap estimates of the count features as well as show their efficacy through simulation. We also investigate the behavior of a histogram estimate of a canonical version of the function characterizing the nonparametric model. Lastly, we use the methods on some real network data to answer qualitative questions on the networks. 

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