Statistics and Probability seminar
Speaker: Arindam Chatterjee (ISI Delhi)
Host: Debraj Das
Title: Statistical inference using network sampling in a sparse Stochastic Block Model (SBM) setup
Time, day and date: 4:00:00 PM, Thursday, May 29
Venue: Ramanujan Hall
Abstract: We consider the problem of predicting subgraph counts and the clustering coefficient of a large population network on $N$ nodes using a network sampling scheme. The population network is assumed to be generated from a SBM with edge probabilities decaying to zero at the rate $N^{-\beta}$, for some $\beta\in [0,2]$. We study Bernoulli node sampling (with a fixed node selection probability $p\in (0,1)$), followed by either induced or ego-centric subgraph formation. Given a fixed target subgraph $H$ with $R$ nodes and $T$ edges, we show that the limiting distribution of the scaled and centered sample based subgraph count is asymptotically normal, if $\beta\in [0, R/T)$, and the limit law is Poisson, if $\beta = R/T$. Using a multivariate version of this result we obtain limit laws for the sample based clustering coefficient. As a follow up, for specific choices of subgraphs, we also investigate the case where $p = p_N$ is allowed to decay to zero at a certain rate. We find surprising differences between the effects of induced and ego-centric sampling in this setting.

(This is an ongoing work with my PhD student, Anirban Mandal)