APPLICATION OF MULTIVARIATE CENTRAL LIMIT THEOREM IN FINGERPRINT DISTRIBUTION AND CENTRED SUBGRAPH COUNT

Abstract

We employ the multivariate central limit theorem to improve the proof of a specific property testing problem in Valiant and Valiant (2010). We hope such improvement will serve as a template for solving more sophisticated distinguishing problems.

Dense graph limit theory was developed by Lovász and Szegedy (2006) to understand the behaviour of very large networks. Kaur and Röllin (2021) proposed to use centred subgraph counts since the sources of randomness are well captured. We use this idea in actual statistical applications for stochastic block models. First, we refine the centred subgraph count statistics to prove multivariate central limit theorems. Second, these statistics are used as diagnostic tests. Third, our statistics can be used to improve the estimation of labels and model selection. As a real example, our statistics indicate that C. elegans network data does not fit the stochastic block model since local structures are not adequately captured.